MOLECULAR ORBITAL STUDIES OF THE BENZILIC ACID AND OTHER REARRANGEMENTS

A thesis presented by

INDIRA HARJIVAN RAJYAGURU

in partial fulfilment for the degree of

DOCTOR OF PHILOSOPHY OF THE UNIVERSITY OF LONDON

Theoretical Chemistry Laboratory Department of Chemistiy Imperial College London SW7 2AY July 1987 ACKNOWLEDGEMENTS

I would like to thank the following people :

* Dr. H. S. Rzepa for his professional guidance, patience and confidence throughout;

* Dr. Rzepa for providing me with ample Computing facilities, without which this thesis would be threadbare.

* The Science and Engineering Research Council for finance;

* Dr. S. V. Ley for the use of his Laser Printer;

* My parents and family for their unceasing support and active encouragement.

* Mayank, for all his faith, patience and encouragement and also for providing me with a 'chauffeured' service whenever required.

* I would like to give special thanks to my mum, who has played a vital and unenviable role throughout the creation of this thesis.

* Finally, I would like to remember my father, to whose spirit I would like to dedicate this thesis.

2 ABSTRACT

Reported in this thesis are the mechanisms of several rearrangement and transfer reactions studied at the semi-empirical and ab initio molecular orbital levels of theory. This includes the analysis of thermodynamic properties such as enthalpy, entropy, isotope effects and molecular orbitals.

Two of the simplest hydride transfer reactions, namely that of glyoxal in the benzilic acid rearrangement and that of formaldehyde in the Cannizzaro reaction were studied at the MNDO, AMI and ab initio levels of theory. The linearity of the intermolecular hydride transfer of formaldehyde was found to be highly basis set dependent, with MNDO and AMI predicting essentially linear transition states whilst the 3-21G and 6-31+G ab initio basis sets predicting more bent geometries. Kinetic isotope effects and tunnelling were also calculated and all methods predicted the kinetic isotope effect to be larger for glyoxal than for formaldehyde, though the values were substantial for both systems.

Mechanisms for the benzilic acid and related rearrangements were studied at the MNDO SCF-MO level of theory. The barriers to concerted closed shell [1,2] migration of formally nucleophilic R" migration were found to display a much smaller range of values than is commonly found in rearrangements involving cations or radicals. Both the attack by base (pre-equilibrium) and the rearrangement were predicted to be enhanced if either the migrating or non-migrating groups bore electron withdrawing substituents. Alternative open shell pathways involving intramolecular single electron transfer were found to be relatively high in energy if the non-migrating substituent was not capable of stabilising an adjacent radical centre like for eg. hydrogen but were much more favourable for eg. the case of aromatic substituents. The intervention of a counter-ion was modelled with Li(H20)2+ coordinating to two oxygen atoms during migration. The migratory barriers were actually increased as a result and so it is suggested that the role of the counter-ion in non-polar solvents is to alter the pre-equilibrium favourably.

The transition state properties for hydride, proton and radical hydrogen transfer reactions were studied for inter- and intramolecular systems by the MNDO SCF-MO method of theory. On decreasing the angle of transfer for eg. on going from inter- to intramolecular systems, the enthalpy of activation of was found to increase much more dramatically for proton rather than for the hydride transfer systems. The entropy of activation for both these systems changed favourably on going from the inter- to intramolecular system, but the unfavourable increase in enthalpy of activation for proton transfer was more than enough to compensate for this and so overall, proton transfers were much less favourable for the 3 intramolecular system. Hydride transfers were also predicted to tolerate bending much more than proton transfers. The behaviour of radical transfers was found to be intermediate between the proton and hydride systems. These results were interpreted in terms of molecular orbital differences in the transition states.

The barriers to inversion of configuration and ring opening in a series of isoelectronic three-membered ring systems were investigated at the single determintal MNDO and ab initio SCF-MO levels of theory. The MNDO-method-predicted barriers to inversion at carbanionic centres were too low compared with experiment and with the ab initio calculations. In the specific case of cyclopropyl carbanion, the MNDO method incorrectly predicted the C- centre to be planar. The two theoretical methods gave more comparable results for inversion at nitrogen and oxygen centres. At the highest level of theory employed (RHF-MP4//6-31+G), the loss of configuration in oxirane, aziridine and thirane carbanion systems was predicted to occur via ring opening to give an enolate anion, rather than via direct inversion at C". The reverse was predicted for the cyclopropyl anion, where direct transfer at the carbon centre had the lower barrier. These results lead to the prediction that oxirane and aziridine anions should be configurationally stable species, whereas thirane carbanions are predicted to ring-open rapidly to give a thioenol.

The biosynthetic pathway for ethene formation was modelled by studying the mechanism of ring opening of 1-aminocyclopropanecarboxylic acid. The potential surface for this reaction was investigated by MNDO and AMI levels of theory and the mechanism was found to be stepwise.

4 CONTENTS PAGE

CHAPTER 1: Review of Quantum Mechanical Molecular Models 10 for the Investigation of Reaction Mechanisms

1.1 INTRODUCTION 11

1.2 Outline of the Theory Underlying Ab initio and Semi-Empirical Methods 12 1.2.1 The Bom-Oppenheimer Approximation 14 1.2.2 The Orbital Approximation 14 1.2.3 RHF and UHF Procedures for Closed-Shell and Open-Shell 15 Systems 1.2.4 Basis Sets 18 1.2.5 Neglect of Correlation Energy in HF Methods 20

1.3 Semi-Empirical Methods 22 1.3.1 MINDO/3, MNDO and AMI Semi-Empirical Methods 23

1.4 Ab initio Methods 27 1.4.1 Choice of Basis Sets 27

1.5 Comparison of the Accuracy of Ab initio and Semi-Empirical Methods 29 1.5.1 Choice of Methods for Investigation of Reaction Mechanisms 31

1.6 Potential Energy Surfaces and the Location Transition States 32

1.7 Some Examples of Calculations on Pericyclic Reactions 35

CHAPTER 2: The Mechanism of the Benzilic Acid Rearrangement 41

2.1 INTRODUCTION 42 2.1.1 Mechanism 42 2.1.2 Migratory Aptitudes 45 5 PAGE 2.1.3 Single Electron Transfer 50

2.2 RESULTS AND DISCUSSION 52 2.2.1 Rearrangement of Glyoxal to Glycolic Acid (R = X = H) 52 2.2.1.1 Mechanism 52 2.2.1.1.1 Conclusion 58 2.2.1.2 Kinetic Isotope Effects for the Hydride Transfer in 59 Glyoxal (2.1, R = X = H) relative to the Cannizzaro Reaction of Formaldehyde 2.2.1.2.1 Conclusions 66 2.2.2 Migration of Group R via Transition State 2.7 with X = H 68 2.2.2.1 Conclusions 74 2.2.3 The Effect of Substituent X on the Migration of R 75 2.2.3.1 The Rearrangement of Phenylglyoxal via Transition 77 State 2.7 (R/X = H/Ph) 2.2.3.1.1 Conclusions 77 2.2.3.2 The Rearrangement of Phenylglyoxal involving Epoxide 77 Formation 2.2.3.2.1 Conclusions 78 2.2.3.3 The Rearrangement of Phenylglyoxal involving Single 79 Electron Transfer 2.2.3.3.1 Conclusions 81 2.2.3.4 The Rearrangement of R/ X = Cyclopropyl / CO 2 H 82 2.2.2.4.1 Conclusion 83 2.2.3.5 The Benzilic Acid Rearrangement Proper (R = X = Ph) 83 2.2.3.5.1 Conclusions 86 2.2.4 The Role of the Positive Counter-Ion on the Mechanism of 87 Rearrangement 2.2.4.1 Conclusions 88 2.2.5 The Benzilic Acid-like Rearrangement of Thioglyoxal Systems 88 2.2.5.1 Rearrangements of Mono-and Di-Thioglyoxals 88

6 PAGE (R = X = H) 2.2.5.1.1 Conclusions 92 2.2.5.2 The Rearrangement of Monosubstituted 93 Mono-Thioglyoxal, (R, X = H) 2.2.5.2.1 Conclusions 96

CHAPTER 3 : A MNDO SCF-MO Study of Proton, Hydride and 97 Radical Hydrogen Transfer Reactions

3.1 INTRODUCTION 98 3.1.1 The Nature Of the Transition State and Isotope Effects for 98 Hydride Transfer Reactions 3.1.2 Effective Concentrations and Entropy in Hydride Transfer 102 Reactions

3.2 RESULTS AND DISCUSSION 105 3.2.1 Effective Concentrations and Entropy Effects on the Nature 105 of the Transition State for Proton and Hydride Transfers 3.2.1.1 Conclusions 109 3.2.2 The Angle Dependency of the Enthalpy of Activation for 109 Proton and Hydride Transfer Reactions 3.2.2.1 Conclusions 111 3.2.3 The Anomalous Behaviour of Systems where R = (CH 2 )3 112 3.2.3.1 Conclusions 113 3.2.4 The Effect of Bending on the Transition States for Proton, 122 Hydride and Radical Hydrogen Transfer Reactions 3.2.4.1 Conclusions 122 3.2.5 Molecular Orbital Effects on Proton, Hydride and Radical 126 Hydrogen Transfer Reactions 3.2.5.1 Conclusions 127 3.2.6 Kinetic Isotope Effects for Proton and Hydride Transfer 133

7 PAGE Reactions (at 323K) 3.2.6.1 Conclusions 134

CHAPTER 4: An SCF-MO Study of the Relative Barriers 136 to Inversion and Ring Opening in Three- Membered Ring Carbanions

4.1 INTRODUCTION 137

4.2 RESULTS AND DISCUSSION 142 4.2.1 Barriers to Inversion at the Centre X in Compounds 142 (4.1) - (4.3) 4.2.1.1 Conclusions 143 4.2.2 The Relative Barriers for Inversion and Ring Opening 143 for the Carbanion Systems (4.1a) - (4.3a), 4.4 4.2.2.1 Conclusions 152 4.2.3 Transition State Properties for the Carbanions, 153 4.1abc and 4.4 4.2.3.1 Conclusions 159

CHAPTER 5: The Mechanism of Ethene Biosynthesis: A 160 MNDO and AMI SCF-MO Theoretical Study

5.1 INTRODUCTION 161 5.1.1 Theoretical Studies on the Mechanism of ACC to 165 Ethene Conversion

5.2 RESULTS AND DISCUSSION 167 5.2.1 The Energetics of Pirrung and Baldwin’s Hypotheses 167 5.2.2 Conclusions 180

5.3 The Effect of Alkyl Substituents on the Mechanism : Future 181

8 PAGE Theoretical Studies

CHAPTER 6: Computational Procedure 184

6.1 The Benzilic Acid Rearrangement 185 6.1.1 Geometry Optimisation and Location of Transition States 185 at the MNDO or AMI Levels 6.1.2 Geometry Optimisation and Location of Transition States 187 at the Ab initio Level 6.1.3 Calculation of Thermodynamic Properties from Molecular 188 Vibrational Frequencies 6.1.4 Calculation of Kinetic and Equilibrium Isotope Effects 188 6.1.5 Calculation of Entropies 190

6.2 A MNDO SCF-MO Study of Proton, Hydride and Radical 191 Hydrogen Transfer Reactions

6.3 An SCF-MO Study of the Relative Barriers to Inversion and 192 Ring Opening in Three-Membered Ring Carbanions

6.4 A MNDO and AMI SCF-MO Study of the Mechanism of the 194 Biosynthesis of Ethene

6.5 Computers Employed in the Calculations 194

6.6 Plotting of Contour Maps and Molecular Orbitals 195

6.7 Some Examples of Reaction Path Calculations 195 REFERENCES TO CHAPTERS 1-6 199 LIST OF ABBREVIATIONS 210 PUBLICATIONS 211

9 CHAPTER 1

REVIEW OF QUANTUM MECHANICAL MOLECULAR MODELS FOR

THE INVESTIGATION OF REACTION MECHANISMS WITH

EXAMPLES.

10 1.1 INTRODUCTION

The aim of this research was to obtain quantitative and chemically significant results in the study of several chemical rearrangement reactions of interest, by the application of suitable quantum chemical models. The reactions targeted for study were : i) The benzilic acid rearrangement with a view to assessing any involvement by a single electron transfer process in the mechanism, and also to establish migratory preferences for a wide range of groups. ii) Proton and hydride transfer reactions to establish the differences between these two processes in terms of transition state properties and molecular orbital studies. Then comparison of both these reactions with analogous radical hydrogen transfer reactions. iii) The inversion of configuration in iso-electronic three-membered ring systems containing carbon, nitrogen, oxygen and sulphur to establish the ease of simple inversion versus inversion via reversible rearrangement. iv) The mechanism of biosynthesis of ethene in plants with a view to establishing the mechanism of ring opening of the intermediate 1-aminocyclopropanecarboxylic acid (ACC) in the absence of enzyme.

A theoretical approach was chosen for these mechanistic studies, since theoretical techniques are at their most powerful in this area, yielding information about reaction mechanisms that cannot readily be obtained by experiment. It is the only approach, in fact, that directly yields information about transition states. In order to carry out these mechanistic studies, the theoretical method or methods of choice would have to fulfill certain criteria and these deciding conditions were : i) The reproduction of accurate molecular energies, geometries including bond lengths and bond angles to within ± 0 .0 1 A and ±T respectively, and thermodynamic properties over a wide range of molecules. In fact, as far as the energy is concerned, the accurate reproduction of molecular energy differences, such as the enthalpy and entropy of activation is sufficient for the study of reaction mechanisms since it is these energies that govern the course of a chemical reaction because of their relationship to free energy. ii) Calculation of potential energy surfaces for reactions. iii) Location of stationary points, ie. ground states and transition states.

11 iv) Characterisation of stationary points located as ground states and transition states by force constant calculation, where the force constants are calculated to within a few percent to allow the calculation of thermodynamic properties. v) Computational economy.

The first condition is the most fundamental one and its fulfillment would result in using a theoretical method that has been 'calibrated' ie. one where errors in molecular energies or in the energy differences and the other properties mentioned have been established by comparing calculated values with experiment or another independent reliable source for a wide range of reactions. This point will be discussed further in relation to the actual methods considered.

1.2 Outline of the theory underlying ab initio and semi-empirical methods

At this point, it seems appropriate to discuss the theory underlying theoretical methods, in order gauge their capabilities and limitations. Figure 1.2.1 shows the development of theory from its beginnings, leading to ab initio and semi-empirical approaches emphasising the common origins of these two methods. The starting point for all theoretical methods is the Schrodinger equation, solution of which should provide answers to questions concerning chemical reactivity : H'Fk = Ek^k ...1.1 In the time independent Schrodinger equation 1 for an arbitrary stationary state of a many- electron system, eg. a molecule, H is the Hamiltonian ie.the total energy operator for the system. The solutions to this equation, are wavefunctions (molecular wavefunctions in the case of molecules) of states with eigenenergies E^. Exact solutions of this equation (1 .1 ) are impractical for all but the simplest of systems so approximations have to be introduced.

12 Figure 1.2.1

13 1.2.1 The Bom-Oppenheimer Approximation

The first simplification to be applied is the Born-Oppenheimer approximation^, which enables the separation of nuclear and electronic motions due to the great difference in mass between nuclei and electrons. This supposition leads to the important concept of the potential energy surface, that is, the idea that the motions of the nuclei are governed by a potential energy function, depending only on the nuclear co-ordinates. Hence, the value of the potential function at any nuclear configuration is equal to the total electronic energy calculated assuming the nuclei to be fixed at this given configuration, plus the nucleai repulsion energy. The notion that the spatial rearrangement of nuclei which occurs during a chemical reaction can be considered as being governed by a static potential surface is central to almost all the theoretical models used in organic chemistry. Indeed, the goal of quantum chemistry and this thesis is often the calculation of such surfaces.

Solving the molecular Schrodinger equation is thus reduced to the problem of solving an 'electronic' Schrodinger equation in which the nuclear coordinates play the role of parameters in the electronic wavefunction. This approximation (Born-Oppenheimer) is usually valid except for instance, when the energies of two electronic states are close together or identical, the approximation then breaks down. A non-trivial coupling of electronic and nuclear motion then arises leading to such phenomena as the Jahn-Teller^ or the Rennet^ effect.

1.2.2 The Orbital Approximation

Despite the introduction of the Born-Oppenheimer approximation, the electronic Schrodinger equation resulting can only be solved exactly for the hydrogen molecule ion, H2 +. Hence, further approximations are required to extend solution to a wider range of molecular systems. A convenient approximation is the concept of a one-electron function in a many-electron system. By this approximation, a many-electron Schrodinger equation can be separated into a set of independent one-particle equations called orbitals (or spinorbitals).! For the system as a whole, the wavefunction is the product of these 'orbitals'. However, due to the Fermion character of electrons, the wavefunction for the

14 system is actually the anti-symmetrised product of the orbitals. The physical basis underlying the idea of orbitals is that a given electron in a molecule may be considered as moving in an average field set up by the other electrons, not depending on their instantaneous positions and momenta.^

Rather than attempt to formulate the form of this average potential, the approach taken by Fock^ was to use the variation principle to determine the best wavefunction in independent particle form. This procedure leads to the Hartree-Fock (HF) equations^, solutions of which are the best molecular orbitals ie. those giving the most accurate wavefunction, in a variational sense. The HF equations are a set of coupled one-electron equations and hence each equation depends on the solution to all the others. Accordingly, an iterative procedure is required. A self-consistent field (SCF) procedure ensures that the wavefunctions calculated are compatible with corresponding HF equations.

A word of warning concerning the orbital approximation is appropriate here. The concept of one-electron functions, orbitals, neglects the so-called dynamical correlation of electron motions since the probability of finding an electron in any given volume of space is independent of the instantaneous positions of all the remaining electrons, in a many- electron system. Hence, even for the best available orbitals ie. Hartree-Fock orbitals, the orbital approximation introduces some error in the calculated total energy, of the amount of neglected electron correlation energy. The correlation energy is usually small compared to the total energy of a many-electron system. On the other hand, this quantity is comparable to energy changes that take place during typical chemical processes. This point about correlation energy will expanded later on when discussing the accuracy of various theoretical methods.

1.2.3 RHF and UHF Procedures for Closed-Shell and Open-Shell Systems.

Despite the simplification of the electronic Schrodinger equation to the HF equations, exact solutions are still not feasible. Roothaan^ and Hall's^ contribution was the introduction of the linear combination of basis set orbitals {%r(r)}to represent molecular orbitals {cj>i(r)}. The coefficients Cj-j are different for each basis set orbital, and so it is to these to which the

15 variation procedure is applied to get the lowest energy (ie. best) molecular orbitals. The basis set is chosen in advance and so is not normally subject to variation.

^i ~ r^ criXr ... 1.2

When the basis set orbitals are atomic orbitals, this becomes the linear combination of atomic orbitals (LCAO) leading to the Roothaan Hartree Fock equations. In practice, in order to carry out LCAO, a finite basis set has to be used, the larger the size of this basis set, the better the molecular orbitals calculated (the limit of an 'infinite* set being 'Hartree- Fock limit' orbitals).

The introduction of equation 1.2 into the HF equations allows them to change from integro-differential equations to algebraic ones involving matrix eigenvalue equations, which can be efficiently manipulated by digital computers. For closed-shell systems, further restrictions on the molecular orbitals lead to the Restricted Hartree Fock? (RHF) procedure. The assumption for closed-shell systems is that orbitals are 'doubly occupied' ie. each orbital is occupied by two electrons with distinct spin functions (spin, ms = 1 /2 or -1/2). For the restricted Hartree-Fock method, assuming that the basis functions are orthonormal, the Roothaan Hartree Fock equations can be concisely stated as :

Fci = eiCi ...1.3 where C{ is a column vector containing the elements Cj-j (see equation 1.2). F is known as the Fock matrix and has elements defined by :

Fjj = hy + r£s2 Prs ( < ri I sj > - (1/2) < ri I js >) ...1.4

In equation 1.4, the matrix of elements Prs is called the 'density matrix' and is given by

Prs = 2 k ^ crkcsk —1*5 where k labels the molecular orbitals (see equation 1 .2 ), and the summation is taken over all doubly occupied orbitals. The summations over r and s in equation 1.4 are taken over all 16 functions in the basis set. (The basis functions have been assumed to be real).

The quantities hy and < ri I sj > represent integrals, hjj is related to the one-electron operator corresponding to the energy of an electron moving in a field of fixed nuclei without the electron repulsion terms. < ri Isj > deals with these repulsion terms, ic.the potential energy of interaction of an electron with all other electrons.

The quantities q in equation 1.3 are the eigenvalues of the Fock matrix. Each molecular orbital has an associated eigenvalue which is sometimes referred to as the 'orbital energy'. The solution of the matrix eigenvalue equation (1.3) thus specifies the molecular orbitals in terms of the basis set by providing the co-efficients of equation 1.2. However, because of equation 1.5 involving the bond order-charge density function, it is necessary to know these coefficients before hand. Hence, this coupled nature of the equations necessitates an iterative procedure. Some suitable initial set of co-efficients is chosen and used to construct a Fock matrix from equation 1.4 (the integrals having been calculated previously). The eigenfunctions of this Fock matrix are then found by solution of equation 1.4, and used to build another Fock matrix. This process is then repeated until 'self-consistence' is reached ie. until a set of co-efficients is found which satisfy both equations 1.3 and 1.4 simultaneously.

The Hartree Fock Roothaan^® procedure can also be applied to open-shell systems by partitioning orbitals into closed- and open-shell orbitals respectively. The closed-shell system is regarded as 'doubly occupied' as before, but this time for the open-shell system, each spinorbital is assigned its individual spatial part so that electrons of different spin (spinorbital) are no longer assigned the same spatial orbital. Roothaan's procedure^ for open-shell systems suffers from the disadvantage that partitioning of electrons between closed- and open-shells is not completely general^. Also, the method can suffer from problems in achieving self-consistence in the iterative procedure (due to the shifting of all the non-Lagrangian multipliers into the definition of the HF operator by Roothaan^).

A better and more general alternative for open-shell systems is the spin unrestricted Hartree Fock procedure (UHF) developed by Pople and Nesbet,^ it is used in this thesis for

17 calculating the energies of all open-shell systems. In this case, each spinorbital has an independent spatial part (DODS, different orbitals for different spin functions) and so leads to an unrestricted wavefunction which can be variationally optimised. This method, however, has the disadvantage that the resulting wavefunctions are not eigenfunctions of the square of the total spin operator, and therefore, do not represent real states of molecules. This difficulty can be circumvented by projecting out the required spin state, or by annihilating contributions from other spin states. This then results in wave functions that are not variationally optimised. 13

A third option for open shell systems is the 'half-electron' (HE) formalism and is usually used only by some semi-empirical methods. This was first introduced by Longuet-Higgins and Pople^ and later developed independently by Dewar et. In this procedure, the electrons occupying singly occupied orbitals are replaced by pairs of 'half-electrons' of opposite spin. A small correction, the half-electron correction, is then applied to compensate for the pairing energy of two half-electrons and in this way, a weighted average energy of the various spin states of the molecule is obtained with the corresponding number of unpaired electrons. The energies of the individual spin states are then obtained by adding and/or subtracting appropriate multiples of exchange integrals between singly occupied molecular orbitals. Hence, the HE method can be regarded as a simple approximation to the Roothaan^ RHF procedure and in fact it is on the same energy scale as the latter so that the relative energies of species calculated by both methods can be compared directly. The HE method also has the advantage of being variationally optimised. On the other hand, the disadvantages are that the method gives no information about spin densities, and it is not well suited for optimizations using analytically calculated forces. HE optimizations may be very slow.

1.2.4 Basis Sets

The next step in any theoretical procedure is the choice of basis set and it is at this point that the distinction between ab initio and semi-empirical approaches begins to emerge. From the form of the HFR (Hartree Fock Roothaan) equations the calculation of several integrals is required to perform calculations with an assumed set of basis functions. From the computational point of view, the calculation of molecular integrals represents the most 18 cumbersome step in the solution of the HFR equations. The numerical differences depend largely on the choice of basis functions.

In an exact formulation, an infinite basis constituting a so-called complete set of functions, should be used. In practice, a finite basis set of atomic orbitals (in the LCAO approach) is used and the choice of these basis functions is governed by calculational feasibility. The type of basis functions used and their number are both crucial factors in determining the computational time required. For example, the number of one- and two-electron integrals to be evaluated increase rapidly with the dimension of the basis set (N) in an ab initio approach, ie. number of 1-electron integrals, p = NYN+ll 2 number of 2 -electron integrals, q= pfp+l") 2

For atomic orbitals, two types of analytic functions are used in molecular computations, namely, atomic Slater-type orbitals (STO) and atomic Gaussian-type orbitals (GTO). These two functions differ in their accuracy and speed of computing integrals. Slater-type orbitals are superior to Gaussian-type orbitals in their short- and long-range behaviour so a relatively small basis set size can give fairly accurate results. The main disadvantage, however, is that the integral evaluation is slow. With GTOs it is possible to compute the integrals very quickly but only a fairly large basis set size yields accurate results.

Semi-empirical methods utilise STOs whereas ab initio methods tend to use GTOs. The exact size of basis set chosen and the nature of the functions varies greatly for ab initio methods and particular semi-empirical methods, and so these details will be discussed in connection with actual methods. On choosing a basis set, the next stage is the evaluation of the integrals in the Fock matrix proceeding with a SCF calculation. If this procedure is carried out in full, then an ab initio calculation results. However, due to the large amount of computational time required by such a procedure, particularly for medium-sized and large organic molecules, semi-empirical procedures short-circuit this somewhat by the introduction of empirical parameters and approximations governing differential overlap.

19 1.2.5 Neglect of Correlation Energy in IIF Methods

Before discussing the details of specific theoretical methods, it seems appropriate to deal with the problem of correlation energy errors inherent in any HF method as mentioned earlier in Section 1.2.2. Figure 1.2.2 shows how the energies calculated by HF methods compare with the experimental energy. Two corrections need to be applied to match these two energies, one is the correlation energy which arises due to the neglect of correlation of the motions of electrons in the orbital approximation, and the second is the relativistic correction. The latter arises since relativistic effects are neglected by using the non- relativistic Schrodinger equation. Although both these effects are small relative to the total energy, the correlation energy is comparable^ with the heat of atomization (dissociation). Since correlation energy is associated with electron pairing, then, any process that involves unpaired electrons (eg. ionization, electronic excitation), involves significant errors due to the neglect of correlation energy.

Figure 1.2.2

'Beyond Hartree-Fock' methods can be used which deal directly with the correlation of electrons and so go towards reducing the error so incurred in normal HF procedures.

20 (Some semi-empirical procedures like, MINDO/3, MNDO and AMI, include parameters to compensate for the correlation energy.) The traditional way to compensate for correlation energy is to use Configuration Interaction (0)17. In this method, an SCF calculation is performed in the normal way on one electronic configuration (the reference configuration in SCF Cl). The orbitals so generated are used to generate more configurations by excitation of electrons from ground states (occupied orbitals) to virtual orbitals (empty orbitals). The resulting wavefunction is a linear combination of the ground and excited states configurations. Of course, this is not completely accurate since only the reference configuration orbitals are variationally optimised but as more and more electronic configurations are included (in theory all should be included) the less the error resulting from this. In theory, this single SCF Cl (ie. one reference electronic configuration) is successful for most systems because one configuration usually makes up most of the electronic ground state. However, for certain species like biradicals or transition states with biradical character, one reference configuration is not enough since one configuration is no longer dominant. In these cases, a multiconfiguration self consistent field (MCSCF Cl) is more appropriate. In this case, more than one reference electronic configuration is used in a SCF procedure to obtain the orbitals to be used to derive the resulting electronically excited configurations. In this case, the basis orbitals as well as the coefficients of the excited state configurations are variationally optimised. In theory, full Cl (either single SCF or multi­ configuration SCF) where all possible configurations are included gives the best results. However, even for a relatively small molecule the total number of possible configurations is extremely large so that usually a limited number are used. Various methods of determining the optimum, yet practical, number of configurations are available. The details of such procedures can be found elsewhere. 17 Despite these elaborate measures to compensate for correlation energy, none of the best Cl methods recover more than 80-90% of the correlation energy 16, whilst the effort to recover this much involves unreasonable increases in the amount of computing time required.

Therefore, other less time-consuming techniques for calculating the correlation energy are often desirable. There are many methods^ for the calculation of correlation energy based on one reference configuration. Amongst the best known are based on the Rayleigh- Schrodinger many-body perturbation theory (RSMBPT) including the application to molecular systems by Moller and Plesset.19 This method however is only suitable for 21 those systems in which one configuration is dominant since the Moller-Plesset theory essentially involves starting with a Hartree-Fock Hamiltonian. This is treated as a perturbed independent electron Hamiltonian and the energy and wave function is expanded in orders of the perturbation. The Moller-Plesset expansion taken to infinite order is in effect, like performing a full single SCF CL The expansion, however, is usually terminated up to the fourth order (RMP4) where convergence is effectively reached for those systems in which one configuration dominates. Such a calculation in itself could be used as a test for such systems since the failure to reach convergence would indicate that more than one configuration is important. In the cases where MP calculations were carried out in this work, convergence was reached thus justifying their use. The accuracy of Moller-Plesset calculations are dependent on the quality of basis set used since they require a good description of the virtual orbitals used in constructing the electronic configurations. In practice, Moller-Plesset calculations do not recover the correlation energy in full but the Moller-Plesset expansion terminated to second order (MP2) is normally estimated to recover about half of the correlation energy.

1.3 Semi-Empirical Methods

The solution of Hartree Fock Roothaan (HFR) equations involves the calculation of a great many one- and two electron many centre integrals, which increase rapidly with the size of the basis set as was seen in Section 1.2.4. Most semi-empirical methods tend to use minimal basis sets (MBS) ie. the size of the basis functions used is that corresponding to the number of atomic orbitals of all partly or completely filled sub-shells of the individual atoms. Even for minimal basis set calculations, the number of integrals still remains large so that further reductions are necessary. Semi-empirical methods reduce the computational burden in two ways : firstly, by the introduction of approximations that reduce the number of integrals to be calculated and secondly, by the use of empirical parameters to estimate most of the remaining elements.

The first approximation to be introduced is the 'all-valence-electron' approximation which allows the separation of inner shell and valence electrons so that the inner shell electrons can be treated as an inert core. This procedure reduces the number of electrons explicitly

22 considered. Further reductions are then achieved by the introduction of the so-called Zero Differential Overlap (ZDO) approximation in which the overlap and differential overlap between basis set atomic orbitals is formally neglected. Methods based on this approximation are shown in Figure 1.3.1 which traces their development in chronological order and shows some of the popular modifications. This discussion has neglected other less accurate semi-empirical approaches which focus on 7C-electrons only and/or use empirical Hamiltonians (as opposed to HF Hamiltonians). Such methods^ include the Huckel Molecular Orbital (HMO) method, the Extended Huckel Theory and the Pople, Parr and Pariser (PPP) approach which are historically significant but do not satisfy the criteria set out in Section 1.1 for the investigation of reaction mechanisms. Hence, such methods will not be elaborated here. Likewise, those semi-empirical methods that have been parametrised to reproduce minimal basis set ab initio calculation are not mentioned here.

The three main prototype methods based on the ZDO approximation are CNDO^O (Complete Neglect of Differential Overlap), INDO20>21 (Intermediate Neglect of Differential Overlap) and NDDO^^,22 (Neglect of Diatomic Differential Overlap), in order of increasing accuracy. CNDO assumes the atomic orbitals to be spherically symmetrical, whilst INDO includes one-centre repulsion integrals between atomic orbitals on the same atom. NDDO however, does consider the directionality of the atomic orbitals in the calculation of the repulsion integrals. The various methods incorporating different parametrisation schemes based on these approximations are shown in Figure 1.3.1 in chronological order, and are discussed in detail elsewhere 7 The different parametrisation schemes are chosen in such a way, that the results of SCF calculations performed on a small set of molecules are made to fit some kind of experimental data (from thermodynamic properties such as heats of atomization, to experimental geometries, to electronic and spectroscopic properties). These values are then assumed appropriate for a wider range of molecules.

1.3.1 MINDO/3, MNDO and AMI Semi-Empirical Methods

Perhaps the most successful of these semi-empirical methods to be used in calculating reaction mechanisms is MINDO/3 (Modified Intermediate Neglect of Differential

23 Figure 1.3.1 Development of Semi-Empirical Methods from the ZDO Approximation

24 Overlap)^ and MNDO (Modified Neglect of Diatomic Differential Overlap)/^,45 Tjie parametrisation of MINDO/3 and MNDO is based upon experimental heats of formation and so the effect of correlation energy is included via parametrisation. A better procedure in which parametrisation with a direct correlation correction is applied in fitting to experimental data is employed by MNDO/C.46 However, this method does not offer any significant improvement over MNDO for ground-state molecules, although excited states are treated considerably better than by MNDO. Cl (Configuration Interaction) methods are also available in the MINDO/3 and MNDO programs, but in this way correlation is then included twice : once through parametrisation and second, through a direct correction procedure.

A com parison^ ,49 0f MINDO/3 and MNDO shows that the mean absolute errors in MNDO are uniformly smaller than those in MINDO/3 by about a factor of 2, whilst the increase in computational time required to perform MNDO calculations is only about 20%. Since most of the methods discussed including MINDO/3 and MNDO are based on the Hartree-Fock model, inaccuracies arise due to the neglect of electron correlation. Hence, the errors resulting in the total energy are enormous, being comparable to the heat of atomization for molecules^ (see Section 1.2.5). However, since MINDO/3 and MNDO contain a semi-empirical correction for electron correlation, heats of formation are reproduced with reasonable accuracy. A recent comparison of the errors in theoretical methods^ showed that the average error (relative to experimental energies) in calculating the heats of formation for 45 neutral molecules was 6.3 kcal mol'l for MNDO and 9.0 kcal mol'l for MINDO/3. For geometries^, the mean absolute error in bond lengths is 0.014 A for MNDO and 0 .0 2 2 A for MINDO/3, whilst the corresponding mean error in bond angles is 2.8° for MNDO and 5.6° for MINDO/3, for the 80 CHNO compounds tested in the original MNDO paper.

In this way, MNDO is generally superior to MINDO/3, the improvement of the former being mainly due to the greater accuracy of the NDDO approximation^ where directional properties of atomic orbitals are included better than in the corresponding INDO approximation. The exception to the rule is in the area of carbocations, where MINDO/3 performs better than MNDO, and minimal basis set (MBS) ab initio calculations. Another

25 advantage of MNDO is that it needs only parameters specific to each individual element, and not combinations of elements so that many more elements have been able to be parametrised ( ie. C, H, O, N, B, F, Be, Al, Si, P, S, Cl and Br).

Despite the improvements of MNDO over MINDO/3, certain weaknesses remain in both these methods. For example, four-membered ring compounds are predicted to be too stable and sterically crowded molecules are predicted to be too unstable, whilst molecules containing NO bonds have errors in both directions^. The stabilities of non-classical ions are underestimated^ (a failing shared by MBS ab initio methods^) and consequently, the activation energies for hydrogen-transfer reactions are overestimated^ (again, this failing is also shared by MBS ab initio methods^). MNDO also underestimates single bond rotational barriers,45 the corresponding torsional vibration frequencies^ and the puckering in cyclic compounds. The latter fault is also shared by MBS ab initio calculations.^ One of the most disappointing areas of MNDO and MINDO/3, is in its failure to account properly for hydrogen bonding.

In an effort to seek improvements in these areas, particularly for hydrogen bonding, Dewar et. alA^ recently have developed a new method based on the NDDO approximation called AMI (Austin Model 1). A previous attempt to improve MNDO to calculate hydrogen bond energies better had already been tried by Burstein and Isaev57 in the so called MNDO/H method. This method entailed the addition of Gaussian terms for the pairs of atoms taking part in hydrogen bonding. However, the comparison^ 0f calculations for hydrogen- bonded systems by this method with ab initio calculations showed that MNDO/H was unreliable although the results were better than MNDO. In contrast, for AMI, the weaknesses of MNDO with regard to estimating hydrogen bond and non-bonded repulsions in sterically crowded molecules seems to have been overcome with no net increase in computational time required. The AMI method has arisen from modifying the core repulsion function (CRF) of MNDO, since the latter method tended to overestimate repulsions between atoms when at their van der Waals distance apart, (so as to result in the errors referred to above). AMI has, so far, only been optimized for C, H, O and N. The mean error^O (relative to experimental values) in heat of formation for 45 neutral molecules containing C, H, O and N is reduced from 6.3 kcal mol“l for MNDO to 5.8 kcal mol‘l for

26 AMI. The calculation of geometries^ is again quite satisfactory.

1.4 Ab initio Methods 1.4.1 Choice of Basis sets

For ab initio$9 methods, unlike the semi-empirical methods based on the ZDO approximation, the choice of basis set atomic orbitals is quite diverse. Almost all modern ab initio methods employ Gaussian type orbital (GTO) basis sets since these have the advantage of speed in calculating integrals relative to STOs (Slater Type Orbitals, see Section 1.2.4). Several reviews^ have recently been devoted to the different types of basis sets in use. However, only those basis sets available in the GAUSSIAN 82 program of Pople^l will be discussed as these have been calibrated and are popularly used.

Since it has been found that, approximately two to five times as many GTOs as STOs are needed to produce results of a given accuracy,162 this problem is commonly tackled by employing 'contracted Gaussians'. In such a procedure, each basis function is a linear combination of GTOs (termed ’primitives'). The coefficients in the combination may be chosen from atomic or small-molecular calculations. The use of fixed coefficients in the contracted functions necessarily leads to some loss of accuracy in a molecular calculation. Nevertheless, the results can be almost as close to the RHF (Roothaan Hartree Fock) limit as those obtained with an STO basis, containing a similar number of functions.

A basis set in which there is one STO or contracted GTO for each occupied atomic orbital is a minimal basis set (MBS). Such a MBS (or single zeta basis set) employed in the Gaussian series of programs is STO-nG, where each atomic orbital consists of a linear combination of n GTOs. The coefficients are chosen so as to give as good a fit as possible to the corresponding STOs. From early tests, it has been found that basis sets with n > 3, give very similar results, hence, the STO-3G is the most frequent of this series to be used. However, being a minimal basis set, it is very economical but it suffers from drawbacks in that it cannot expand or contract its orbitals, to fit the molecular environment such as may be required for ionic species. Hence, the results from such a basis set cannot always be trusted. In fact, the greatest weakness of this basis set is its tendency to overestimate the stability of small rings, overemphasis of the 7t-acceptor properties of electropositive 27 elements of the first row and complete failure for the second-row elements.

Some of the drawbacks suffered by such a MBS can be overcome by the use of split- valence (or double zeta) basis sets which are minimal for the inner shells but have one or more basis functions per atomic valence orbital. The coefficients of such a basis set can be varied independently during construction of the molecular orbitals and hence, these can be expected to better adjust to the molecular environment. Such a split-valence basis set available in the Gaussian series of programs is n-mlG, where n Gaussians are used per core atomic orbital, whilst inner and outer valence shell orbitals are constructed from m and / Gaussian functions, respectively. The smallest of this type of basis set commonly used is 3-21G63 and it has now replaced STO-3G for all but the largest of molecules, for initial geometry optimisations. An extension to the 3-21G basis set is to include a set of polarisation functions for the second-row elements to make the 3-21G* basis set.^3 Such an extension is particularly important for compounds containing small rings and for compounds containing the second-row elements. This results in an improvement in the mean absolute deviation in bond lengths from 0.071 A for 3-21G to 0.027 A for 3-21G*.

Similarly, increasing the number of primitive Gaussians used to make up the core and inner valence functions, results in 6-31G basis set, which improves upon the energetics of the 3- 21G basis set at the expense of increased computer time. If polarisation is included, then a 6-31G* results. A slightly smaller basis set than this is 6-31+G^, where the (+) indicates the addition of diffuse-augmented basis functions to improve the description of anion geometries. In such a basis set, the six-component cartesian d-orbitals of 6-31G* are replaced by their five-component spherical counterparts. The inclusion of such diffuse functions is particularly important for anion calculations or for problems where an adequate description of lone-pairs is important like that in the calculation of proton affinities.

It is important to note that in the standard basis sets described above (for GAUSSIAN82), the exponents of the s- and p- GTOs within any given shell are equal. This restriction results in some loss of flexibility but saves computer time and the resulting error is not significant for extended basis sets. Also, optimization with incomplete atomic basis sets can result in errors where an electron-rich atom uses the diffuse basis functions of a

28 neighbouring atom to supplement its own. Such an error is termed the Basis Set Superposition Error (BSSE) and the severity of this error increases with the incompleteness of the atomic basis eg. STO-3G. Dissociation energies are particularly sensitive to BSSEs.

Since ab initio methods do not involve parametrisation then the effect of correlation energy is completely neglected unless a direct correction is applied. In principle, the correlation energy may be calculated by full configuration interaction (see Section 1.2.5) in which the wave function is determined as the best linear combination of all possible electron configuration functions. In practice, however, this rapidly becomes impractically time consuming and so other simpler schemes must be used. The Moller-Plesset method1^ for calculating correlation energy (see Section 1.2.5) has been implemented in the Gaussian series of programs. 18 The Moller-Plesset terms can usually be expanded to fourth order (MP4) where convergence is essentially complete. The advantage of the MP method is its speed relative to classical configuration interaction methods, and its ability to reproduce correlation effects in the comparison of molecules. In general, to save computer time, geometries are not normally optimised at the MP level, instead single-point energy calculations are carried out with a large basis set.

1.5 Comparison of the accuracy of ab initio and semi-empirical methods

In a recent paper^ concerning quantum chemical models, Dewar states the importance of realising the shortcomings of both semi:empirical and just as important, ab initio methods. The latter particularly, have tended to be regarded in the past as unfailingly accurate in comparison to the semi-empirical methods. The accuracy of the results of ab initio methods are strongly basis set dependent. However, as has been stated several times already, neither ab initio nor semi-empirical methods are reliable for predicting chemical energetics a priori due to the large errors caused by neglect of electron correlation inherent in the HF model. This results in errors in the total energy amounting to hundreds of kcal mol -1 for even relatively small molecules. In this sense, the results of semi-empirical methods such as MINDO/3, MNDO and AMI are less inaccurate since they at least contain an empirical correction for the correlation energy. However, a cancellation of errors may occur in comparing the heats of formation of molecules. Such cancellations cannot be

29 predicted and only extensive testing can reveal the cases when this occurs, even in the case of ab initio methods. In fact, Dewar and Storch^O have established a systematic procedure by which to evaluate the effective errors in molecular energies calculated by ab initio methods and MINDO/3, MNDO, AMI relative to experimental values (Table 1.5.1).

Table 1.5.1 Average Errors^ Relative to Experimental Values in the Heat of Formation, in kcal mol-1

Type and (Number) of Error in MoleculesSTO-3G 3-21G 6-31G* MINDO/3 MNDOAMI

Neutral 10.7 6.9 6 .1 9.0 6.3 5.8 (Number) (44) (44) (43) (45) (45) (45)

Cations 2 2 . 6 9.2 4.9 (Number) (8) (8) (8)

The results from Table 1.5.1 indicate that MNDO and AMI are comparable in accuracy to the large basis set calculations. In the case of STO-3G, the results are quite inaccurate whereas the results for 3-21G are much better. Hence, Dewar50,65 concludes that since 3- 21G calculations take little more computing time than STO-3G, the latter should not be used. (Of course, the results from such a comparison cannot be taken too literally, since the mean errors depend on both the number and type of molecules considered for each method).

Previous comparisons16,66 0f MNDO with other semi-empirical methods (particularly those methods parametrised to reproduce minimal basis set ab initio calculations) showed MNDO to be superior in accuracy to these, as well as economical in computing time required. As discussed earlier (Section 1.3.1), the new AMI method^ already shows signs that it is superior to MNDO, especially in the region of calculating non-bonded repulsions in sterically crowded molecules. Calculations^ of proton affinities and

30 deprotonation enthalpies by AMI show that the errors for protonated and deprotonated species are generally of the same order as for their neutral precursors and are smaller than in the case of MNDO.

Recent^ comparisons of the transition states for MNDO and MNDO/C calculations with those from state-of-the-art ab initio calculations show satisfactory agreement for geometries, frequencies and zero-point vibrational energies. The ab initio energies were reproduced more closely by MNDO/C than by MNDO. However, this comparison reinforces the justification for applying MNDO and MNDO/C to the study of organic reactions. For open-shell systems such as radicals, calculations with unrestricted Hartree- Fock (UHF) orbitals in the MNDO approach^ is much less time consuming than the alternative half-electron (HE) method.^ The energies calculated with UHF MNDO (UMNDO) are generally too negative^ but the comparison^! of thermodynamic properties calculated by UMNDO for radicals agree well with experimental values. Thus, the use of UMNDO for the calculation of radical species is justified.

1.5.1 Choice of methods for investigation of reaction mechanisms

In the light of the previous discussion and the criteria set out in Section 1.1, the MNDO method was chosen initially to investigate reaction mechanisms. The newer AMI method was not available until later on in the research project, but was used in conjunction with MNDO as a check in the areas where MNDO is known to have weaknesses, such as the calculation of small rings and stoically crowded molecules. Since ab initio calculations are much more time consuming than semi-empirical methods like MNDO, they were only carried out after initial MNDO calculations, when the systems were small enough to allow complete optimisation and characterisation of stationary points or when there was disagreement between MNDO and experiment. Indeed, according to Dewar,165 if there is disagreement between the ab initio and MNDO methods, then, it does not always follow that the latter is in error, unless a high level ab initio method is used, or unless the area is one in which MNDO is known to have weaknesses.

31 1.6 Potential Energy Surfaces and the Location of Transition States

The nature of the potential surface of energy is of prime importance in the understanding of reaction mechanisms. Indeed, reaction mechanisms could be predicted unambiguously if the corresponding potential energy surfaces could be calculated with sufficient accuracy. In particular, three points on the potential surface are of special interest, namely, the minima corresponding to the reactants and products, and the intervening saddle point(s) corresponding to the transition state(s). These stationary points can be distinguished by the fact that at a minimum, all the normal vibrations or eigenvalues of the force-constant matrix, are positive whilst for a transition state, there is one and only one negative eigenvalue. The potential surface for a molecule with N atoms is 3N-6 dimensional and hence, is extremely complex.

The location of minima on the potential energy surface is a much easier task than the corresponding search for saddle-points and hence, methods for energy minimisation are quite common. For example, the Davidon-Fletcher-Powell algorithm^ used by the MNDO and AMI programs, where full optimisation with respect to all geometric variables leads to a minimum in an automatic procedure. However, the resulting minimum would have to be characterised as such by the calculation of the second derivatives of energy (with respect to the atomic positions) to make sure that they are all positive.

There are several basic approaches in the location of transition states. The simplest method of obtaining a saddle-point is by selecting an appropriate reaction co-ordinate and optimising the geometry with respect to the other 3N-7 variables, as the reaction co­ ordinate is varied. The approximate transition state so located can then be refined, by for example, minimising the gradient norm through a non-linear least-squares optimisation technique.73 However, the efficiency and even the success of this technique is critically dependent upon the choice of the variable against which the potential energy is plotted. The transition state so located would again need to be characterised by the calculation of the second-derivatives to show that there is only one negative eigenvalue.

A more fool-proof method of locating transition states (and minima) would be the calculation of potential energy surfaces (contour maps) by the use of two reaction co­ 32 ordinates. In this method, the geometry is fully optimised with respect to the remaining 3N-8 variables whilst the two reaction co-ordinates are varied. The construction of a contour map then allows the location of the approximate transition states and the minima corresponding to reactants, products and even intermediates. These stationary points could then be refined further by optimising the full 3N-6 variables in, say, a least squares method^ for transition states and by an energy minimising algorithm for the minima. The calculation of such two-dimensional energy grids is time consuming but is becoming much more feasible for semi-empirical methods with the advent of floating point accelerators (FPAs). The advantage of such a method is that, not only are stationary points able to be located, but that the contour map reveals qualitative information about the nature of the reaction mechanism. Hence, this has been the preferred method in the investigation of reaction mechanisms by MNDO or AMI in this thesis.

Of course, various algorithms for the location of transition states are also available and so a few will be discussed. These algorithms can search for transition states in an automatic procedure and are quite essential for ab initio methods, where the use of contour maps is prohibitively time-consuming. One of the earliest algorithms is due to Mclver and Komornicki74 in which, for a starting guess to a transition state geometry, the gradient norm of energy is iteratively reduced to zero (a necessary condition for a stationary point). The calculation of the force constant matrix then allows the condition that there is only one negative eigenvalue to be checked. In a modification by Poppinger,75 the Hessian matrix (second-derivatives of energy) with its eigenvalues and eigenvectors is repeatedly evaluated, and if convergence occurs, then a transition state is located. An alternative procedure due to Halgren and Lipscomb^^ interpolates between reactant and product minimum points. In the same vein, Dewar et. alJ7 have produced an algorithm for locating transition states automatically once the reactants and products have been characterised. These methods are based on the assumption that the structural variations of a molecular system along a reaction path are not very different from geometry variations generated by a quadratic interpolation between 'reactant* and 'product' geometries. Such a simple strategy works well for relatively simple energy hypersurfaces where the interpolation will lead to a transition state. However, such a procedure can fail unexpectedly for more complicated reactions, eg. where there is considerable nuclear and

33 electron re-organisation. In these cases, non-convergent loops will be set up and so a transition state will not result. For this reason, such methods were not used in this thesis.

A different approach due to Schlegel^^ is currently used in the GAUSSIAN82 package for ab initio calculations. In the geometry optimisation, this procedure uses the first derivatives of energy (ie. the atomic forces) which are calculated analytically. A guessed force constant (second-derivatives of the energy) matrix is then constantly updated using the gradients. At each step, a one-dimensional minimization using a quartic polynomial is carried out, followed by an n-dimensional search using the second derivative matrix. By controlling the number of negative eigenvalues, both minima (no negative eigenvalues) and transition states (one negative eigenvalue) can be calculated.

An even more sophisticated algorithm has recently been reported by Baker^9 designed to be used with GAUSSIAN82. It is capable of locating transition states even if started in the wrong region of the energy surface. In addition, transition states for alternative rearrangement/dissociation reactions can be located from the same initial starting point. Again, the method is not limited just to transition states and so is also capable of locating minima.

Such powerful algorithms have obvious advantages in that they are: completely general and not dependent on the choice or number of reaction co-ordinates, whereas contour maps are limited just to reaction co-ordinates; they are fully automatic once the initial geometry or geometries have been specified; and they are quicker than contour map calculations. In this respect, they are the only means by which to easily locate transition states at the ab initio level. Also, for those algorithms that involve the use of second-derivatives of energy (either the force constant or Hessian matrices) the stationary points are already characterised. However, the calculation of potential energy contour maps or surfaces has a certain irreplaceable advantage in that they lead directly to the reaction mechanism (only where a reaction is governed by two reaction co-ordinates, though). In particular, the potential energy surface (contour map) can reveal the important lack of certain transition states as well as their presence. The absence of a transition state for a particular reaction mechanism cannot be inferred from the failure of an algorithm to locate it, since this failure could be

34 due to genuine problems in achieving convergence. For this reason, whenever possible contour maps were used in this thesis to directly gain information about reaction mechanisms.

1.7 Some Examples of Calculations on Pericyclic Reactions

At this point, it seems appropriate to discuss examples of calculations based on the theoretical methods and techniques just discussed, to set the work carried out in this thesis in context. To do this, the subject of pericyclic reactions has been chosen since some of the reactions studied in this thesis can be classified as such. For example, the benzilic acid rearrangement (Chapter 2) and also some hydride transfer reactions in Chapter 3 can be considered as [1,2] sigmatropic rearrangements. Whilst, the ring openings of the oxirane carbanion (Chapter 4) and of 1-aminocyclopropanecarboxlic acid (Chapter 5) can be considered as electrocyclic reactions. Hence, calculations involving [1,2] rearrangements will be discussed with the proviso that the examples chosen exclude electron deficient systems (like cations) since the reactions studied here involve electron-rich systems.

Bentley*^ has investigated the [ 1 ,2 ] hydride shifts from boron to carbon in a series of organoborates, BH 3 CX, where X = O, NH and CH 2 , by ab initio , MNDO and MINDO/3 calculations. Ground state geometries were calculated for the species I-IV shown in Scheme 1.7.1. For ab initio calculations, the GAUSSIAN76^^ program was used to fully optimise geometries at the STO-3G level by interpolation of three points on a parabola to the energy minimum using small increments in all geometrical parameters. (Such an energy minimisation method is obviously time consuming and has its limitations so nowadays GAUSSIAN76 has been replaced by GAUSSIAN80 and GAUSSIAN82 which use the algorithms for energy minimisation mentioned in Section 1.6), Single-point energy calculations were then carried out with the larger basis sets 4-31G and 6-31G*. Such a practice lends itself to criticism in two ways : firstly, the errors50>65 in a small basis set like STO-3G are quite large whilst secondly, any error in initial geometry optimisation are reflected and magnified in the re-calculation of energy at a different basis set. 16 This second effect is especially important for STO-3G geometries. For MNDO and MINDO/3 however, geometries were optimised independently using derivative procedures (ie. like that in reference 72). No transition states were located nor were any of the species

35 calculated characterised as ground states by the calculation of force constants.

Scheme 1.7.1

H H 3 B-=— c +=x X=B — CR3 I IV y hydrolsis oxidation oxidation

X H 0 = ^ HOCH 3 H H

The MNDO and ab initio results agreed qualitatively with differences in energy between the 6-31G* and MNDO results being usually less than 9 kcal mol-1. On the assumption that the calculated heats of reaction paralleled trends in activation energy, the results for X = 0 were interpreted to be consistent with a reversible reaction between borane and carbon monoxide followed by a rate determining 1,2-shift. For the first hydride shift to form lib, the results indicated that the heat of reaction for X = NH was less endothermic than X = 0 whilst the reaction was calculated to be highly exothermic for X = CH2. The relative ease of the second rearrangement was predicted to be in the order : X = O ~ NH > CH2, whilst for the third rearrangement, the order predicted was : X = O > NH > CH2. Rotational barriers for planar species (Ha) were calculated by MNDO, MINDO/3 and single-point calculations at the 4-31G and 6-31-G* though MINDO/3 predicted some unlikely geometries.

Rzepa et. applied the MNDO method to the study of the mechanism of [1,2] radical migrations as a model for coenzyme B i2 mediated rearrangements. The general rearrangement in the radical system R'CH-CHXR to R'CHX-CHR was investigated for a

36 wide range of substituents, X, and for R = R’ = H. Also, R and R' were varied including R = H, R' = OH and R = COSH, CO 2 H, C0 2 ", R’ = H. The radicals were calculated using the MNDO UHF procedure for open shell systems with full optimisation of all geometrical variables. Transition states were located by calculating reaction paths using one reaction co­ ordinate (Rj) and by calculating potential energy surfaces using two reaction co-ordinates (Rj and R2) as in Figure 1.7.1. Unlike in the previous example, the transition states so located were characterised by the calculation of force constants ( ie. were shown to have just one negative eigenvalue).

R'HC * H— CHR — 1 Figure 1.7.1 Such calculations revealed three possible mechanistic routes : for X = -CH(NH 2 )C0 2 H by dissociation-recombination, in 1,2 diols by stepwise migration of a protonated OH group via an intermediate TT-allyl complex, and acyl groups by either concerted migration or dissociation-recombination. Groups such as X = SiH 3 , CHO, CN and CS 2 H were predicted to be good migrating groups in such reactions.

Schlegel et. al.%3 have applied the configuration interaction (Cl) and multi-configuration interaction (MC) SCF ab initio methods to the study of [1,2] and [1,3] sigmatropic shifts in propene using minimal STO-3G and extended 4-31G basis sets. The molecular orbitals were constructed from the three n orbitals of allyl and the Is orbital of H for the valence space. A preliminary Cl analysis was used to interpret the sigmatropic shifts in terms of the interaction and crossing of diabatic energy surfaces. On the basis of this analysis, transition states were optimised at the MC-SCF level by using gradient methods and were characterised by the calculation of the Hessian matrix. The results showed that the SCF level was inadequate in a large region of the potential energy surface. It was found that if a [1 ,3 ] suprafacial hydrogen migration is attempted in propene, the hydrogen crosses into a region where the trimethylene diradical is more stable and hence, a single determintantal SCF calculation cannot describe the wavefunction properly. Hence, it was concluded that at least two configurations (which correlate with an excited state of allyl) are needed. As for the transition states, the [1,3] supra transition state was found not to exist whereas the [1,2] 37 supra transition state was found to be ca. 1 0 kcal mol -1 lower than the antara transition state but both were found to be in strong competition with dissociation.

Frenking and Schmidt^ have applied the MNDO method to the investigation of the [1,2] rearrangements of singlet carbenes and nitrenes as in Scheme 1.7.2. A variety of migrating groups were calculated (eg. R = H, F, Cl, CH3 , C2 F5 , OCH3 and SCH 3 ). In the MNDO method, all geometries were fully optimised and transition states were characterised by the calculation of the force constant matrix. From the theoretical studies, it was concluded that in the [1 ,2 ]-rearrangements of saturated carbenes, carbonylcarbenes, saturated nitrenes and carbonylnitrenes, the transition state preferred is one in which the C-R bond of the migrating group R is eclipsed to the empty p -orbital of the carbene or nitrene. This was particularly demonstrated by the calculation of the transformation matrix between the MO's of the educt and the transition state. Migratory aptitudes calculated, in general, agreed with experimental results and were rationalised in terms of nucleophilicity and leaving group character of the rearranging group. Such reactions were considered to be intramolecular substitutions, being more S^2 or S^l type as they were more or less concerted. The factors considered important in determining migratory aptitudes were recognised as the mutual influence of competing groups at the P position and conformational constraints especially for groups owning lone-pair orbitals.

Merkelbach et. al.%5 have applied the MNDO method the study of the stereochemistry of the carbon-skeleton rearrangements dependent on coenzyme B^. These workers investigated the stereochemistry in the enzyme-catalysed carbon-skeleton rearrangements of methylmalonyl-coenzyme A to succinyl-coenzyme A, methylaspartate to glutamate, and methylitaconate to methylene glutarate via intramolecular [ 1 ,2 ] shifts, by calculations based on anionic cyclopropane intermediates shown in Scheme 1.7.3.

38 Scheme 1.7.2

R 1 R 1 (1) r "/L2\ 4 R3" V \ r 4 ^ R2 ^R 4 r2/ \ r 4 R 2

R 1 R 1 R 1 -- o=c=< (2) 0v ~ ^ S r 2 c / \ r 2 \ r 2

R 1 R 1 V R 3 Rl A (3) -N --- R3— ^ = N R 3 I 2 R 2 R R R R (4) N / - N ■ o = c = n '/ 0 ^ o

Scheme 1.7.3

39 Potential energy surfaces were calculated for the ring closures in intermediates 1, 2, and 3 (Scheme 1.7.3) by the use of the two reaction co-ordinates T\ and T2 with full optimisation of the remaining 3N-8 variables. The minimum energy reaction paths were located from these contour maps, though transition states were not reported to be characterised by force constant calculation. The charge distribution was monitored for migration as well as the evolution of the coefficients of the atomic orbitals in the HOMO of the cyclopropane intermediates. The inversion of configuration in the methylasparate isomerisation and the retention of configuration in the methylmalonyl-coenzyme A rearrangement, were rationalised in terms of the charge distribution and HOMO characteristics.

Finally, the application of ab initio calculations by Goddard^^ in the [1,2]-fluorine or [1,2]-methyl shifts in methylfluorovinylidene to 1-fluoropropyne is reported. Calculations were carried out with GAUSSIAN82 programs and geometries were optimised at the 4- 31G SCF level by gradient methods for transition states and minima. Single-point energy calculations were carried out on the 4-31G level geometries at the 6-31G** level. As mentioned earlier such a procedure invites criticism since errors in geometry calculation accumulate in the energy calculation . 1 6 Corrections for electron correlation were included through Moller-Plesset perturbation theory (MP2, MP3) and through singles and doubles configuration interaction (CISD) with the 4-31G basis. The CISD results were adjusted for unlinked cluster effects through a size consistency correction (CISD + SCC). MP2 and MP3 calculations were also carried out at the 6-31G** level. The stationary points calculated were characterised by calculation of the vibrational frequencies at the 4-31G level which additionally allowed prediction of vibrational frequencies for unknown stable species and evaluation of the zero-point energy corrections on reaction energies and barrier heights. The results for barrier heights with respect to the vinylidene isomer were ~ 30 kcal mol'l for [1,2]-fluorine shift and =18 kcal mol ' 1 for the corresponding methyl shift. It was observed that the assumption of the additivity of polarisation and electron correlation effects proves useful for the reaction energy and the methyl shift but leads to errors for the fluorine shift.

40 THE MECHANISM OF THE BENZILIC ACID

REARRANGEMENT 2.1 INTRODUCTION

2.1.1 Mechanism

The benzilic acid rearrangement is one of a general class of molecular rearrangements which involves the hydroxyl anion catalysed conversion of a 1 ,2 -diketone ( 2 .1 ) to an a hydroxy carboxylic acid:

Scheme 2.1.1.1

This reaction was first discovered by von Liebig^ in 1838 and was subsequently the target of numerous synthetic and mechanistic investigations. These early studies were the subject of a review by Selman and Eastham^ in 1960.

The currently accepted mechanism for this rearrangement is one which resulted from these earlier studies and was proposed by Ingold^^ in 1928 :

Scheme 2.1.1.2 O O OH" OH "°. OH HO o- ^ ---- C ■aF=te' ^ ---^-O- x-^ ^ X R x R R ° R O 2.1 2.2 2.3 2.4

The first step is the reversible addition of a nucleophile such as OH" to a carbonyl group to give the intermediate 2 .2 followed by a rate limiting intramolecular [ 1 ,2 ] migration of a formally nucleophilic R" group to the second carbonyl group. A rapid proton transfer then completes the reaction to give the salt of the final a-hydroxy acid (2.4).

The evidence for this mechanism is two-fold, consisting of a combination of direct

42 supportive evidence and indirect evidence which discounts alternative possibilities. Firstly, of the evidence supporting the rapid and reversible formation intermediateA 2.2 (as opposed to a concerted mechanism) is as follows : i) It is known^Oa that benzil forms an adduct with potassium hydroxide in pyridine solution that contains only one molecule of base. On heating, the adduct rearranges rapidly to potassium benzilate. Other work90b,c has ajso shown that only one molecule of base is required to rearrange one molecule of benzil. ii) Also for benzil, it has been shown^l that exchange of oxygen in 'heavy' water (H2180) is much more rapid in alkaline than in neutral solution thereby implying that the first step is a rapid, reversible addition of hydroxyl ion to benzil, the rate determining step being rearrangement of the ion thus formed.

Secondly, the evidence supporting the rearrangement of intermediate 2.2 to 2.3 in the rate limiting step is as follows : i) The kinetics of the reaction of benzil with base92 show that the reaction is second order overall, being first order with respect to both base and benzil. This is consistent with the above mechanism, although by itself, it is not conclusive. ii) The alternative possibility of 2.2 undergoing a concerted proton transfer with migration to lead directly to 2.4 can be eliminated by the fact that rearrangement of benzil93 occurs about 85% faster in deuterated water than in hydrogenated water. This difference arises due to the enhanced basicity of deuteroxide ions in D 2O relative to hydroxide ions in H 2O. Additionally, the concerted mechanism would require specific hydroxide ion catalysis whereas, rearrangement with bases other than hydroxide is known.94

For glyoxal^^ and phenylglyoxal^ the migration of hydrogen has been established (for the latter by isotopic labelling with 14C). Such a rearrangement of monosubstituted glyoxals could be envisaged as proceeding by a proton abstraction mechanism after the initial formation of intermediate 2.2 :

43 Scheme 2.1.1.3 IIO o- O O OH- o OH OH- Oil o- H X > - < « y - 4 - o . — x h x XH X OH a o i

1 OH __/ OH

However, experimental evidence from kinetics and labelling experiments discount this possibility. The kinetics^ of the rearrangement of phenylglyoxal show that the reaction is second order overall, first order with respect to phenylglyoxal and with the base. Also, rearrangements of glyoxal^ and phenylglyoxal^^ in deuterated water fail to lead to rearranged products that contain any deuterium, thereby implying that the transfer is intramolecular which is consistent with the classical mechanism.

The role of the metal cation of the base MOH upon the rate of the benzilic acid rearrangement in non-polar solvents has been investigated by several workers : i) Pfeil et. al.9% showed that the cation of the hydroxide base in 50% aqueous dioxane significandy enhances the rate of rearrangement of 2,2'-dichlorobenzil. They found that the speed of the rearrangement decreased from thallium hydroxide > barium hydroxide > sodium hydroxide and the kinetics varied likewise, from second order overall for alkali hydroxides to intermediate between second and third order for alkaline earth hydroxides to third order for thallium hydroxides. Hence, some change in the mechanism is implied. This cation effect is highly dependent upon the solvent, being obscured in highly polar water media. They suggest that co-ordination of the metal cation with the negative oxygen in the intermediate 2.2 weakens the neighbouring carbon-phenyl bond by 'ionfield catalysis.' ii) Puterbaugh and Gaugh^^ have similarly investigated the effects of the alkali metal cation upon the rate of rearrangement of benzil in 67% dioxane- 33% water mixtures. They found that the lithium effected the reaction faster than the other alkali cations. They propose that this is due to the greater coordinating power of lithium over the other alkali hydroxides. Lithium could participate in a ring mechanism that facilitates the migration of the phenyl group ie:

44 Scheme 2.1.1.4 Li+

o ' " ' O \ // P h ^. / c — c \ nr! Ph iii) Most recently of all, Poonia et. all®® have investigated the coordinative role of alkali cations for the rearrangement of benzil in ethanol/water mixtures. They were able to isolate solid complexes between benzil and the metal hydroxides that could be rearranged to the metal benzilate on heating. The benzil was shown to coordinate to the metal cation in the ethanol / water mixtures. They also showed that the presence of a Lewis acid is necessary for the rearrangement of benzil. Hence, they proposed a modified version of the classical mechanism for rearrangements in low polarity (poor-ionising) solvents where M4* coordination is feasible:

Scheme 2.1.1.5 Ph ^ Ph M - 0 Ph 0 1 +MOH 1 1 % w C1 — \ C — Ph HO —C - C —Ph C C Ph V*— ^ II 1 Hydrolysis II 1 p » / Ph 11 11 0 O M + O 0 ( v ° of 0 ‘ M+ \ / O H ---M + H

2.1.2 Migratory Aptitudes

For the classical mechanism, the kinetics of the rearrangements can be expressed by Scheme 2.1.2.!(where 2.1 is the starting diketone and 2.2 is the intermediate formed by OH" attack): Scheme 2.1.2.1

k -i Under steady state conditions, the observed second order rate constant is given by the

45 expression : ^obs =------

( l + k . l / k 2) If k _i / k2 » 1, this reduces to ^obs = ^cq x k2 ... (2.1) where the equilibrium constant KCq = k\! k

For an unsymmetrical diketone RCOCOX, R refers to the migrating group and X is the non-migrating substituent, this convention is adopted throughout this The chapter. rate of rearrangement depends both on, the ability of R to enhance the electrophilic nature of the a carbonyl group for attack by hydroxide ion ie. Keq, and also on the ability of the intermediate thus formed to rearrange before reversal of the hydroxide ion attack ie. k2. The first factor, Kcq, would then be expected to be more favourable for electron- withdrawing migrating groups. The second factor k2, however, entails the migration of a nucleophile towards an electrophilic centre, which it has been assumed will be enhanced if the migrating group is a good nucleophile, ie. electron releasing.

Such a combination of factors affecting the rate constant means that it is difficult to predict substituent effects in terms of a single constant. Nevertheless, a wide variety of substituent effects for the rearrangement of an unsymmetrical benzil^S 0n the overall rate of reaction and the identity of the migrating group R for pairs of substituents has been established, the latter by means of isotopic labelling to distinguish the final products.

In general, for substituted benzils, electron withdrawing substituents at meta and para positions have been shown to exhibit enhanced^, 101-3 rates 0f migration, whilst electron-releasing substituents at these positions exhibit diminished^, 101,103-5 rates relative to the phenyl ring. These effects have been rationalised^ by proposing an early transition stately, 106} such that the equilibrium constant, Keq, rather than the rate constant for migration, k2,, is the dominant term. As consistent with this postulate, electron withdrawing substituents at ortho positions have been shown^S to behave anomalously by preferential migration of the unsubstituted ring due to stericl^’ 107,108 an(j electronic^ factors.

46 It has been argued 101,107 that since the rate determining step in the classical mechanism involves the migration of a nucleophile towards an electron-deficient centre that aryl groups carrying electron-releasing substituents might be expected to migrate to a greater extent than phenyl. In fact, as noted above, the opposite is observed.^8 in addition, the migratory preferences in the rearrangements of substituted benzils and chlorophenanthraquinones can be correlated by a Hammett plot.^8 These two factors have led some workers*0*»*07 t0 postulate a different mechanism whereby attack by hydroxide occurs in the rate determining step to lead to a concerted migration. However, this mechanism is not consistent with the observed oxygen exchange between benzil and water^l and also with the evidence of Hine and Haworth^ ^ that there is no proton-transfer in the rate determining step.

Now, since the overall rate of rearrangement depends both on the initial pre-equilibrium involving attack by base and the rate constant for migration, it follows that a faster rearrangement may not necessarily lead to an overall faster reaction. Also, the Hammond postulate of an early transition state*05-6 is consistent with the observed Hammett correlation, making it unnecessary to propose that hydroxide ion attack occurs in the rate limiting step. Apart from studies on substituted benzils, the migratory preferences have been investigated for a wide range of reactions in order to establish the 'driving force’ for migration. A wide variety of formally nucleophilic groups have been observed to migrate including R = H, alkyl, aryl, acyl, aroyl, ester, amide and acid. The results of these investigations are summarised in Table 2.1.2.1.

41 Table 2.1.2.1

Summary of Migratory Preferences O O System ^ __(( Migratory Preferences References X R R, X

Ph, H H 96 Ph, p-OMePh Ph > p-OMePh 104

CH3 CO^t CO2 > C02Et pH <10 109,115 C02Et > C02 pH>11.5

Ph, p- unsubstituted ring 108

p-OMe,p-CH3Ph,p-ClPh,m-ClPh,Ph m-Cl > p-Cl > p-CH3 > p-OMe 101 O O 2-Cl > 7-C1 > 3-C1 > Ph 107

Ph 105 F m-F > o-F > p-F > 102

o N ^ N complex mechanism involving mono-, di- and tri-anions. 110 o s#*'y ^ , o O 0 0 - N - C — 111 v s = 0 H H

48 CH3; CONPhCH3, CONPh2 CONPhCH3, CONPh2 112 113 CH3, C 021Bu COi'Bu o o H P . °H 114 t f ROH l ^ C 0 2R C02' > C02Et pH < 10 116 C2H5, C 02Et CO^Et > C02" pH >11.5

CH3; C 02‘Bu, low pH CO^u; C02 117 CCyPr, C 02Et high pH C 02 Bu, C 02'Pr, C 02Et

Benzyl, CONH2 c o n h 2 118

V.O R-CMejCcycl.) 119

R-CMejCcycl.) 120 o 0

A comparison^8 0f the rates of migration of the groups in Table 2.1.11 show for normal rearrangements (ie. those not involving ortho effects) that migration of aryl or alkyl groups are significantly slower than those of ester and amide groups. For an unsymmetrical diketone, electron-attracting groups, like ester and amide, migrate in preference to alkyl or aryl groups. In terms of migratory aptitudes, this is surprising, since electron-rich groups (ie. good nucleophiles) could be considered to be more apt to rearrangement. However, this is consistent with the observations i) that in symmetrically substituted benzils and in arylglyoxals, electron-attracting groups accelerate the rate of migration whilst electron­ releasing groups decelerate the rate of rearrangement and; ii) that in unsymmetrical benzils the more electron attracting aryl group migrates preferentially. From these observations it has been inferred88,118 that the effect of electron attracting groups on facilitating the initial attack by base (ie. Keq) is more important than the intrinsic ability of a group to migrate (ie. Jc2).

49 2.1.3 Single Electron Transfer

In the classical mechanism for the benzilic acid rearrangement, the involvement of any free radicals was eliminated on the basis that the rate^2 of rearrangement is not affected by the addition of peroxides. However, recently, evidence has been presented for single-electron- transfer (SET) as the major pathway in reactions previously thought to proceed via classical S^l and S^2 mechanisms.

The reactions of various nucleophiles with aromatic aldehydes and ketones have been reported to involve SET. For example, there is evidence^ 0f a SET pathway in the reaction of Grignard reagents with aromatic ketones. Similarly, the reactions of alkali metal amides 122 ancj alkoxides-^ with alkyl halides and polynuclear hydrocarbons, which were classical examples of S^l and S^2 reactions, have been reported to involve SET as the main pathway for reaction. EPR evidence again, has suggested SET in the reactions of aromatic ketones with lithium am ideslithium alkoxides*^ and in the reactions of thioalkoxides with other organic substrates. 126 A ldol^ an(j Claisen^ condensation reactions involving aromatic ketones, which had previously thoroughly accepted mechanisms, have also been shown to involve SET.

More relevant to the benzilic acid rearrangement, an investigation129-30 0f the closely related Cannizzaro reaction has shown that this may involve an intermolecular SET followed by hydrogen atom migration, as an alternative to the transfer of a formal H" moiety. Such mechanisms involving a SET have not hitherto been suggested for the benzilic acid rearrangement.

A theoretical study of the benzilic acid rearrangement, including this possibility of SET is reported here (Scheme 2.1.3.1). Also, the migration of formal R' groups was investigated to determine the relative importance of the pre-equilibrium and intrinsic migrating ability on the rearrangement. Since it is difficult to predict migratory preferences experimentally due to the composite nature of the observed rate constant (equation 2.1), a theoretical approach was necessary, as in this way, it is possible to separate out the effect of the pre-equilibrium and the rate of migration, by keeping one group constant (X) whilst migrating the other (R)

50 for all combinations of R and X. The effect of other mechanisms ie SET on these migratory preferences was also investigated.

The investigation was then widened to include thioglyoxals and thioketones. Although there is no experimental evidence reported for the rearrangement of thioglyoxals by a benzilic acid-like process, such species have been the target of theoretical and synthetic studies. 1^1 in the case of a thioketone it would be interesting to see how the classical mechanism would compare with the alternative possibilities, particularly that of single­ electron-transfer since radical centres would be expected to be sensitive to the replacement of an oxygen atom in a diketone by a sulphur atom in a thioketone.

Scheme 2.1.3.1

51 2.2 RESULTS AND DISCUSSION

2.2.1 Rearrangement of glyoxal to glycolic acid (R = X = II) 2.2.1.1 Mechanism

This rearrangement is the simplest possible and is known to occur via an intramolecular hydride shift^. Phenylglyoxal (2.1, R = H, X = Ph) is also known96 to rearrange via a hydride shift rather than migration of the phenyl group. Hence, the reaction of glyoxal was studied initially in order to establish the general features of the MNDO potential surface for this type of reaction.

By analogy with the closely related Cannizzaro reaction a mechanistic scheme can be postulated in which not only a classical hydride transfer route can be envisaged (Scheme 2.1.3.1, path a) but also alternative routes involving a single electron transfer to the carbonyl oxygen atom, either before (path b) or after (path c) a proton transfer between the oxygen atoms (see Section 2.1.3). In this case, attack of the alkoxide oxygen atom (2.2, R = X = H) to form an epoxide could be yet another alternative (Scheme 2.2.1.1).

Scheme 2.2.1.1 O k O x o- ? OH O R n 2.1 2.2 II O O X ^ O H R ■o? x 2.13 2.14 2.15 96 2.16 *

-C> O HO O XH x H n X R OH R O- 2.3 2.4

52 Energy Contour Map for Hydride Migration

+ * * 2 (H)(0)C---- 1— C(0H)(0-) “------

R j

Separation between contour levels is 3,6 kcal mol"1 VTS-

J Figure 2.2.1.1

1 Energy Contour Map for Hydrogen Migration

(H)(0-)C.-----1— C(0H)(0.) Cn ------> - R i

Separation between contour levels is 2.4 kcal mol-1

* T S Figure 2.2.1.2 1.1 2.2

i Energy Contour Map for Hydrogen Migration H

R:

Figure 2.2.1.3 (H O )H d '- C ( 0 - ) ( 0 ~ )

R»

3.99 kcal mol1 Firstly, for the classical mechanism, a potential energy contour map for path a (Figure 2.2.1.1) reveals that the rearrangement of (2.2, X = R = H) to (2.3, X = R = H) is a concerted process occurring via transition state 2.7, with a calculated barrier 28.81 kcal mol“l rather higher than that found for the Cannizzaro reaction itself (Table 2.2.1.2). This is to be expected for what is a highly non-linear hydride transfer, although the magnitude of the barrier is not inconsistent with the known rearrangement of glyoxal.95 The contour map reveals no dissociative pathway corresponding to formation of the isolated H- ion, in contrast to the results previously reported for the rearrangement of the ethyl radical, 82 where two pathways corresponding to dissociative and concerted migration were apparent.

For the single-electron-transfer (SET) routes, the first one (Scheme 2.1.3.1, path b) corresponds to intramolecular electron transfer to the carbonyl group to give an excited singlet electronic state 2.5, followed by migration of R and then proton transfer. This route was modelled by calculating (2.5, X = R = H) as a triplet state using the spin unrestricted UHF approximation, 69 finding this species to be 39.4 kcal mol-1 higher in energy than 2.2. Since MNDO is known to predict excitation energies to be too low,70 this is likely to be a lower bound on the energy of the SET process, suggesting that a SET is improbable for the reaction of glyoxal itself. It is interesting to compare the triplet potential surface (Figure 2.2.1.2) for the conversion of 2.5 to 2.3 with the singlet surface previously calculated (Figure 2.2.1.1). A purely dissociative mechanism operates, with no corresponding concerted pathway available for rearrangement of 2.5. During the conversion of 2.5 to 2.3, a changeover from the triplet (2.5, = 2) to singlet (2.3, = 0) manifold also occurs, hence, a UHF procedure cannot be used to accurately locate transition states.

The second SET route (Scheme 2.1.3.1, path c) corresponds to initial proton transfer to give the singlet biradicaloid species 2.6, followed by migration of group R = H. For this singlet biradical 2.6 ( =1) unlike the triplet species 2.5, the migration to give 2A ( = 0), occurs just on the singlet manifold, so that such a process was able to be a* studied within the UHF method. SpeciesA6 was found to be higher in energy than 2.5 by 22.3 kcal mol-1. The potential surface for rearrangement to 2.4 shows a concerted pathway

56 for reaction via an extremely early transition state (Figure 2.2. 1.3). Figure 2.2. 1.3 also shows a surface for the expectation value of the spin operator S2 ( ie. ), where the change in value from = 1 for the biradical species 2.6, to = 0 for the closed- shell system 2.4, is depicted.The barrier to migration for hydrogen is 8.0 kcal mol'1. Despite this low barrier, the prohibitively high energy of 2.6 relative to 2.2 and to the transition state for classical hydride migration, 2.7, makes this route most unlikely compared to the classical mechanism. An alternative possibility, of electron transfer to the migrating group R itself, is excluded for the specific case of R = H.

For the alternative epoxide mechanism outlined in Scheme 2.2.1.1, the energy of the epoxide intermediate (2.13, 2.14 R = X = H) was found to be 15.56 kcal mol-1 higher than 2.2, with barriers of 33.34 kcal mol"1 and 49.90 kcal mol-1 to form 2.3 and 2.4 respectively. Again, these values are too high to be feasible alternatives relative to the classical mechanism. A proton abstraction mechanism involving intermediate 2.2 is known not to occur^,96,97 as outlined in Section 2.1. Nevertheless, abstraction by base of the proton a to the carbonyl group in intermediate 2.2 would result in the formation of enolate anions as shown in Scheme 2.1.1.3, (see Section 2.1), which could then reprotonate to give glycolic acid.

Table 2.2.1.1 Energies of enols (2.34,2.35, 2.36) relative to 2.2 in kcal mol-1 H OH HO OH -o OH > = < HO H ^ O - H OH 2.34 2.35 2.36 Method ^^enol-2.2

MNDO -15.66 -15.96 -13.21 3-21G -9.70 -9.44 +12.59 RMP4// -3.83 -3.61 +16.37 3-21G 6-31G -2.35 -1.00 +15.00 6-31+G -0.41 -1.28 16.20

57 The energies of the enol intermediates formed by proton abstraction from 2.2 are shown relative to the energy of 2.2 in Table 2.2.1.1. Surprisingly, these energies vary significantly between MNDO and ab initio methods and also between the different basis sets. MNDO predicts all three enol intermediates to be more stable than 2.2 whereas this as relative stability decreases on going to ab initio results as wellAwith increase in the size of the basis set. In fact, the order of stability between the enols 2.34, 2.35 and 2.36 also varies between MNDO and ab initio. At the MNDO level, isomers 2.34 and 2.35 have very similar energies but 2.35 is the most stable and is lower in energy than 2.2 by 15.96 kcal mol-1. At the ab initio 3-21G level, 2.34 and 2.35 again have very similar energies a- but both are more stable thanA2 by a smaller degree and this time, 2.34 is the most stable isomer. The largest difference is for 2.36, MNDO predicts this to be more stable than 2.2 by 13.21 kcal mol'1 whereas, the 3-21G levels predicts the same isomer to be less stable than 2.2 by about the same amount, ie. 12.59 kcal mol'1. At the larger basis sets levels, 6- 31G and 6-31+G, enols 2.34 and 2.35 are very close in energy to that of 2.2, whilst enol 2.36 is quite unstable relative to intermediate 2.2.

Hence, the failure of proton abstraction to occur in practice may be due any number of reasons. For instance, the failure may be due the higher energy of the enols than 2.2 as predicted by ab initio methods. Alternatively, if the MNDO results apply, then, this implies that either the barrier to reaction is a high one (due to electrostatic repulsion between the negatively charged 2.2 and eg OH") or that 2.2 is more effectively solvated than any of the enol tautomers.

2.2.1.1.1 Conclusion

From the energetics calculated for the various mechanisms for rearrangement in glyoxal, it is concluded that glyoxal involves an intramolecular hydride transfer and occurs on the ground state singlet surface, with a low probability of eg. any single electron transfer process or epoxide ring formation, occurring.

58 2.2.1.2 Kinetic Isotope Effects for the Hydride Transfer in Glyoxal (2.1, R = X = II) relative to the Cannizzaro Reaction of Formaldehyde

There has been much recent speculation about the degree of linearity of hydride transfer reactions and whether tunnelling is important in such reactions^2 (see section 3.1). The rearrangement of glyoxal is of some interest since it can be considered as an almost unique example of a highly non-linear hydride transfer. In order to be able to compare the reaction of glyoxal with other types of hydride transfers, the intramolecular conversion of 2.2 to 2.3 via transition state 2.7 was chosen in the reaction of normal and labelled glyoxals :

Scheme 2.2.1.2 O O f + OH ' ^eq J| O- OH OH o ^ f o i i H ^ ^ O H H H H O O OH OH y-f +oH' + OH O H ^ r -

Scheme 2.2.1.3

O O- O OH + OH ‘ H A h ^ o h OH H H n H

For both these systems, the observed rate (kobs) is the product of the rate constant for the second step (kj) and the equilibrium constant for the pre-equilibrium step (Keq). It follows that the observed isotope effect (&Hobs / &Dobs) *s product of the two ratios KeqH / KeqD and 2/^D2- ^ was previously shown^O for this reaction also that the involvement of any single electron transfer mechanism is unlikely.

59 In addition to MNDO studies, calculations were extended to include ab initio methods in order to compare with other recent studies 132a,b on the subject. The AMI method was also employed since it is superior to MNDO in the region of non-bonded interactions^ which could be very important in determining the linearity of hydride transfers in these systems particularly the Cannizzaro reaction.

The calculated barriers for the hydride transfer step in each reaction are shown in Table 2.2.1.2. For formaldehyde, the barriers to hydride migration are clearly method and basis set dependent, as is the geometry of the transition state (Figure 2.2.1.4, overleaf). The transition state for hydride migration in formaldehyde shows pronounced asymmetry in the C-H bond lengths at the 3-21G basis level, but not at the higher 6-31+G level, or indeed with MNDO^O or AMI. It is interesting to compare these results with those of Houk and WU132aj wh0 studied the hydride transfer from methoxide to formaldehyde. These workers report a similarly asymmetric transition state at the ab initio 3-21G level, where the corresponding C-H bond lengths, to those shown in Figure 2.2.1.4, were 1.55 A and 1.35 A. The barrier to migration found by these workers is also very similar to ours, with a value of 7.8 kcal mol-1 compared to our value of 7.2 kcal mol-1 at the the 3-21G level. Other barriers reported by Houk and Wu,132a with larger basis sets are not comparable with our results, since the former are only single-point energy calculations with the 3-21G geometry. Houk and W u^2a ajs0 report geometry optimised results with large basis sets for model structures with two-fold symmetry. However, these structures were shown to have two negative vibrational frequencies and hence, do not represent true transition states.

Our investigation of the linearity of the transition state for the Cannizzaro reaction also reveals a large basis set dependency as reflected in the value of the C-H-C angle in the transition state : 176.6° // MNDO, 175.6° // AMI, 136.5° // 3-21G, 148.2° // 6-31G and 162.2° // 6-31+G (Figure 2.2.1.4). Such an effect was also noted in the study by Houk and Wul32a who report similar values for their symmetrical model of the transition state, ie. angle C-H-C was 152° // 3-21G, 142° // 6-31G, 159° // 6-31+G, 147° // 6-31+G* and 159° // MP2 / 6-31+G. In contrast, Williams et al.,132b jn their study of the hydride en c transfer from methylamine to the methylammonium cation, report an essentially linear linkage in a symmetrical transition state at the ab initio 3-21G level.

60 Table 2.2.1.2 Barriers to Hydride Transfer for Glyoxal and Formaldehyde in kcal mol-1

AH MNDO AMI 3-21G 6-31G RMP4// 6-31+G RMP4// 6-31G 6-31+G

0 0 H H 28.81 27.89 27.36 34.98 28.78 38.61 34.92

0 17.58a 12.48 7.24 13.78 4.10 17.01 7.86 a From calculations reported by J. Miller and H. S. Rzepa. 130

Figure 2.2.1.4 : Transition States for Hydride Migration in Glyoxal and Formaldehyde

50.5

Bond lengths are in A at the 6-31+G basis set level and at the (3-21G) level.

61 Of course, such a difference may be due to inherent differences in the behaviour between the two different kinds of hydride transfer systems ( ie. methylamine and formaldehyde) involved, making generalisations about all hydride transfers difficult. It has previously been noted that hydride transfers are more easily bent than the equivalent proton transferl34 (Chapter 3). Such bent geometries for hydride transfer in formaldehyde are reminiscent of the agosric interactions found in organometallic species 135 ie% Scheme 2.2.1.4 H HO v X

/\ H O H

H O Alternatively, this non-linearity may be due to significant interactions between the incipient alkoxide oxygen atom and the carbon atom of the hydride donor ie. Scheme 2.2.1.5 H H H ° ^ c / O H For glyoxal, the value of the barrier is not so sensitive to method or basis set, with the basic geometry (Figure 2.2.1.4) eg.angle of transfer changing only slightly. In this case, the angle of transfer is predicted to decrease with increasing basis set size, whereas in the previous case, the larger basis set predicted the larger angle. The calculated barriers for the hydride transfer step in the reaction of formaldehyde (Table 2.2.1.2) for all the methods, MNDO, AMI and ab initio, are similar to those reported for other hydride transfer reactions. 132a,b, 134-6 The barriers for hydride migration in glyoxal are uniformly higher than this, as is consistent with the significantly more bent transition state for glyoxal (see Figure 2.2.1.4).

Calculated isotope effects based on the uncorrected normal vibrational frequencies obtained at the MNDO, 3-21G and 6-31+G levels are shown in Table 2.2.1.3. The calculated harmonic rate ratios (HRR as defined in Chapter 6) are for 2 / &D2> an<^ are typical of large primary effects. The 6-31+G values tend to be intermediate between the MNDO

62 and 3-21G values for the observed isotope effect, although HRR tends to have higheT values for the ab initio rather than the MNDO results for glyoxal, whilst the calculated Bell tunnelling correction 137a (as defined in Chapter 6) has the higher values for the MNDO results. The latter vary much more since they are very sensitive to the magnitude of the calculated imaginary frequency, which in turn is highly basis set dependent. 132a,b

The ratio KcqH/ KcqDfor the pre-equilibrium step was calculated and a small inverse isotope effect was obtained for formaldehyde and glyoxal. Analysis of the factors!37bc contributing to the equilibrium isotope (see Chapter 6) effect shows that the zero point energy difference between the H and D, in the reactants and products is the main contributor to the inverse equilibrium isotope effect, see Table 2.2.1.4. The small value (ie. close to 1) and inverse nature of the zero-point energy contribution can be rationalised in terms of two opposing factors affecting the zero-point energy difference. Namely, on the one hand, there is a change in hybridisation from sp* to sp3 on going from reactants to product at the a-carbon atom. This would lead to an increase in the frequency of the carbon-hydrogen out-of-plane bending mode 137c so tending increase the zero-point energy difference in the product. Hence, this factor would account for an inverse isotope effect. On the other hand, there is an 'oxy-anion effect’l l weakening of the carbon-hydrogen bond adjacent to the alkoxide substituent in the product. This second factor would tend to decrease the zero-point energy difference in the product relative to the reactants and so would tend to favour a 'normal’ isotope effect. The final inverse zero-point energy contribution (ZPE) indicates that the first factor dominates but the opposing second factor is reflected in the magnitude of the overall ZPE which is close to one. The overall situation is more complex because in this case, the zero-point energy difference is not the only dominant factor contributing to the equilibrium isotope effect. Another factor, namely the vibrational product contribution (see Chapter 6) to the isotope effect is of similar magnitude, but in the opposite direction, (being greater than 1) to the zero-point energy contribution. Hence, the overall isotope effect is inverse but close to 1 in magnitude. Normally, values of secondary inverse isotope effects due to such changes in hybridisation tend* 37b,c to be somewhat more inverse, with values of between 0.46-0.71.

63 Table 2.2.1.3 Kinetic Isotope Effects for Glyoxal and Formaldehyde at 373K

System Method HRR TUN COR ^k h eq ^Hobs *Hobs x TUN COR

K^ d eq ^obs A^obs

O h H i MNDO 2.980 1.450 0.940 2.801 4.062 3-21G 2.652 1.494 0.967 2.565a 3.832 6-31+G 2.480 1.940 0.892 2.212a 4.292

o 0 H f JH H MNDO 3.453 1.998 0.896 3.095b *6.183 3-21G 4.737 1.172 0.885 4.192b 4.913 6-31+G 4.771 1.534 0.844 4.026b 6.176

O O Hr D HD H MNDO 3.871 1.894 0.867 3.356° 6.357 3-21G 5.786 1.154 0.797 4.612° 5.322 6-31+G 5.410 1.476 0.810 4.380° 6.464

O O V i f H D MNDO 3.808 1.917 0.858 3.268d 6.264 3-21G 5.615 1.162 0.818 4.593d 5.338 6-31+G 5.222 1.489 0.832 4.343d 6.466

For T = 373-700K : akHobs/k Dobs = 1.1011 xe317-64/T(3-21G), 1.334xe251-70/T(6.31+G) bkHobs/kDobs = 1.0654 xe399.32/T (MNDO), 0.9412 x e556.98/T (3-21G), 0.9651 x e532.07 / T (6-31+G). c kHobs / kDobs = 1.0139 x e447-23 7 T (MNDO), 0.8782 x e619-127 T (3-21G), 0.9072 x e587-82 / T (6-31+G). 4 kHobs / kDobs = 1.0324 x e430-6 8 1T (MNDO), 0.8939 xe61U 8/ T (3-21G), 0.9196 xe579.77 /T (6-31+G).

64 For glyoxal and formaldehyde, the inverse isotope effect decreases with increase in basis set size, hence, optimisation at RMP4/6-31+G level may reduce this even further so decreasing the overall isotope effect. Despite this inverse value, the observed isotope effect, kHobs / kD0bs, is still substantial and the values obtained are very similar to the experimental hydride transfer isotope effects recently reported by Watt et alA?>6 jn particular, the semi- classical isotope effects are predicted for all three levels to be larger for glyoxal than for formaldehyde. This is surprising since it has long been accepted that non-linearity decreases the expected magnitude of a simple proton transfer reaction. 139 The present result may indicate that hydride differs radically in this respect from proton transfer.

Table 2.2.1.4 Equilibrium Isotope Effects for Formaldehyde and Glyoxal at 373K

Vpa EXCb ZPEC EIEd

3-21G 1.2301 0.9820 0.8006 0.9671 6-31+G 1.2325 0.9804 0.7384 0.8923

0 0 V f H H Vpa EXCb ZPEC EIEd

MNDO 1.0725 1.0601 0.7883 0.8963 3-21G 1.1032 1.0200 0.7866 0.8851 6-31+G 1.1038 1.0232 0.7472 0.8438 a VP refers to the vibrational frequency productcontribution to the isotope effect, b EXC refers to the contribution to the harmonic ratio due to thermal excitation into the upper levels of the oscillators. 137b c ZPE refers to the zero-point energy contribution to the isotope effect, d EIE is the equilibrium isotope effect and is (VP x EXC x ZPE). 137b

65 The calculated tunnelling corrections show the opposite trend (Table 2.2.1.3). For MNDO (and for AMI), tunnelling is predicted to be more important in the reaction of glyoxal than in the reaction of formaldehyde. Intuitively, this might be as expected for what is normally regarded as a relatively tightly bound hydride transfer in an intramolecular reaction as opposed to a looser transfer in an intermolecular reaction. At the ab initio level, however, this trend is reversed, the tunnelling being more important for formaldehyde at both 3-21G and 6-31+G levels. A further striking difference between the two kinds of hydride transfer is again manifested in the different temperature dependence of the isotope effects. The Cannizzaro reaction of formaldehyde shows a much smaller effect than the intramolecular hydride shift of glyoxal.

Results for the labelled glyoxals are also included since this provides one means of measuring these effects, by for example, monitoring the intensities of the 2H or 12C NMR signals of the two labelled products formed from either labelled glyoxal. The ratio of the intensities leads to the kinetic isotope effect as indicated in Figure 2.2.1.5. Competing reactions such as hydrogen exchange via a proton abstraction are known95,96 not t0 occur in either the reactant or the product glycolic acid. In fact, monitoring of the or l^C NMR signals ensures that only the wanted labelled products are detected.

From the calculations, the effect of labelling, ie. the secondary isotope effects tend to increase the predicted magnitude of HRR, but to decrease the isotope effect on the pre­ equilibrium! Hence, the overall effect of the use of 13C labels is to slightly increase the observable isotope effect for the hydride transfer.

2.2.1.2.1 Conclusions

In summary, the transition state for intermolecular hydride transfer in the Cannizzaro reaction of formaldehyde is found to display a large method and basis set effect concerning the barrier to migration and the linearity of the transition state. MNDO and AMI predict almost linear geometries whereas a bent transition state is predicted by the ab initio method where the angle of transfer increases with basis set size. The symmetry of the transition state is also method dependent : where MNDO, AMI and 6-31+G ab initio methods

66 predict similar C-H bond lengths in the transition state, whilst, unsymmetrical bond lengths are predicted at the ab initio 3-21G level.

Surprisingly, the calculated semi-classical isotope effect for hydride transfer is found to be larger for glyoxal than formaldehyde by both MNDO and ab initio methods, despite the highly bent geometry of the transition state for glyoxal. In this respect, hydride transfer seems to differ from proton transfer and goes against the accepted view that non-linearity decreases the isotope effect.*39 Tunnelling in hydride transfer seems to be much more important for the Cannizzaro reaction of formaldehyde than the benzilic acid rearrangement of glyoxal by the ab initio method and not by MNDO and increases with basis set size. The Cannizzaro reaction is predicted to have a much lower temperature dependence on the kinetic isotope effect than the rearrangement of glyoxal. Such a prediction should be able to be verified experimentally. Figure 2.2.1.5 Measurement of the Kinetic Isotope Effect for Glvoxal ■ A Possible Experiment Dnmr Signal o o O \\ // OH o o- HO c—c wc- / \ --->~kHobs / * \ / *9\\ OH \ H D D H H OH

o O “ HO O \\ / \ ---► kDobs -C s — ,c* \ SOH D-'-yj \ H D H OH OR,

0 0 % w // OH" 0\\ HO\ o 1 c-— C — c-1 f t r - , C kHobs / *\ / * » ^ / c* \ H D D \SOHH H OH O O ‘ HO O \\L" / \ // .__^kDobs / *Vs \ H \D OH H OH

67 2.2.2 Migration of Group R via Transition State 2.7 and with X = II

There has been considerable discussion^, 118 as t0 t^e controlling factors determining the rate of rearrangement in the benzilic acid-type reactions ie. the rearrangement of 2.1 to 2.4 (Scheme 2.1.3.1, see Section 2.1). The equilibrium between 2.1 and 2.2 depends on the ability of R to enhance the electrophilic nature of the a carbonyl group. On the other hand, the rearrangement of 2.2 to 2.3 entails the migration of a nucleophile towards an electrophilic centre, which it has been assumed will be enhanced if R is a good nucleophile. The observed enhancement in rate for electron withdrawing substiuents on the migrating group R has been rationalised^^8,118 by proposing an early transition state, such that the equilibrium constant Keq rather than the rate constant &2 is the dominant term. However, such a simple Hammond type model may be oversimplified, particularly if other mechanistic pathways involving eg. electron transfer are possible, or if the transition state is a very 'tight' one in which the nucleophilic characteristics of the migrating group are less important.

The specific substituent effect on the rate constant for migration, k2, was studied a. theoretically by calculating barriers for the conversion of 2 tox3 by migration of group R whilst maintaining the second substituent, X, constant (X = H) via the classical mechanism, Table 2.2.2.1. These results for formal R- migration can be compared with those for the migratory properties of the corresponding electrophilic R+ groups, as known from the molecular rearrangements of carbocations and related species, and with a third category of migratory group formally intermediate to R- and R+, the neutral radical species R*.

In general, for the groups studied in Table 2.2.2.1, migration is concerted and does not involve the type of cyclic intermediates that were found previously for the corresponding migrations of eg. vinyl and phenyl groups at the radical^ 1 or cation oxidation level. Also, the range of activation energies is much smaller than was found^ for eg. the migration of R- or R+ groups. The transition state for migration of R", 2.7, was not particularly sensitive to stereochemical changes such as those resulting from proton exchange between the alkoxide and hydroxy groups. The two possible isomers resulting from such a process differed in energy usually, by less than a kcal mol-1. They are shown below :

68 Scheme 2.2.2.1

R R 2.7 H t.yj \ ..i OH H\-»«< O- O o- o ■ 011

For consistency, the energies in Table 2.2.2.1 refer to isomer i, which for most R groups was the lowest energy isomer. Figures 2.2.22 and 2.2.2.3 show the energy contour maps for the migration of phenyl and vinyl groups. Comparison of these with the energy contour map for hydride migration (Figure 2.2.1.1) shows that all these are qualitatively similar.

The calculated entropies of activation for the migration step (Table 2.2.2.1, overleaf) tend to be similar in value and generally negative (with the exception of the COSH group), suggesting a relatively tight and symmetrical transition state (see Figure 2.2.2.1). The calculated overall charges on R range from -0.38 for R = H to -0.85 for R = COSH, with R = Ph having an intermediate value of ca -0.6. In general, the larger negative charge is found on the better electron withdrawing groups.

Unactivated alkyl groups such as methyl are predicted to have relatively high barriers to migration, although if the alkyl group is contained within eg. a four membered ring the barrier is significantly reduced. Indeed, it is known that cyclobutane 1,2 dione rearranges in water without any added OH' catalyst. ^ 4 Cyclohexane 1,2 dione is also reported^ to undergo ring contraction slowly, but in general methyl groups are observed not to readily migrate.88,109,112-3,115,117 Such migration is predicted to occur with retention of configuration at the carbon centre (Figure 2.2.2.1). The other substituent where MND0 predicts a large barrier to migration is OH. In this case, the method may be partly in error, since the calculated energy of an isolated OH' is too high* 40 by 36 kcal mol"1. Experimentally, it would be difficult to prove that hydroxyl migration ever occurs, since the product would be indistinguishable from the species formed in the reversible pre­ equilibrium.

69 Table 2.2.2.1 Calculated MNDO Transition State Properties For the Benzilic Acid Rearrangement AH3_2 ac Bond 0 R AH*a AS*1’ AG*a AH4.2 ac qd Length Anglef H 28.81 -5.96 30.55 -9.45 -0.38 1.55 58.8 (-20.11) (1.50) c h 3 36.18 -1.07 36.49 -10.27 -0.41 2.08 42.3 (-24.23) (2.05) c h =c h 2 30.36 -4.07 31.55 -12.09 -0.45 2.00 44.7 (-23.69) (1.94) c o 2h 21.62 -0.84 21.87 -7.00 -0.69 2.26 39.7 (-14.64) (2.18) C3H5 33.44 -0.99 33.73 -14.99 -0.59 2.19 39.9 -(eye) (-28.95) (2.20) -CH2CH2 26.26 4.11 25.06 11.47 2.41 36.4 (2.69) (2.51) CN 26.77 -2.11 27.39 -13.15 -0.65 1.98 45.4 (-21.01) (1.94) CHO 28.76 -2.90 29.61 -12.39 -0.50 2.09 42.7 (-25.07) (2.03) CONH2 21.69 -0.58 21.86 -8.45 - 0.68 2.26 39.9 (-20.02) (2.16) OHS 48.58 -7.58 -0.63 2.03 44.7 (-15.49) (1.91) COSH 17.61 5.27 16.07 -9.56 -0.85 2.66 34.4 (-15.46) (2.41) c o 2c h 3s 22.59 -13.10 -0.79 2.39 37.7 (-24.94) (2.29) Ph 27.53 -3.06 28.43 -12.82 -0.57 2.11 42.3 (-22.82) (2.06) p-PhCN 25.32 -1.46 25.75 -12.13 -0.63 2.16 41.5 (-24.30) (2.10) p-PhOH 27.67 -1.79 28.19 -11.78 -0.58 2.12 42.2 (26.19) (2.06) a In kcal mol"1. b In cal mol ’1 K' 1 at 293K. c AH3.2 = AHf(2.3) - AHf(2.2). Values in parentheses correspond to AHf(2.4) - AHf(2.2). d Charge on the migrating group in the transition state. e Bond length Cl-R and (C2-R) in the transition state, in Angstroms. f Angle C1-R-C2 in the transition state. S Transition states for OH and CO 2CH3 transfer were not characterised by force constant calculation due to problems with hydroxy and methyl group rotations leading to the presence of extra negative vibrational eigenvalues.

70 H Energy Contour Map for Phenyl Migration

.PH a /

R, (H)(0)C----1— C(0II)(0-)

R,

Separation between contour levels is 2.8 kcal mol-1

* TS Figure 2.2.1.2 Energy Contour Map for Vinyl Migration* „ CH=CIIi ’’ A

/ ' *2 (II)(0)C---- 1----C(0II)(0-)

R j

Separation between contour levels is 2.7 kcal mol-1

* TS Figure 2.2.23 1.4 2.4 Groups such as ester, acid and amide are predicted to have relatively small barriers and indeed experiment confirms these to be good migrating groups.! !8 The best such group is thiolacid (or ester) (Table 2.2.2.1), for which experimental results appear not to have been reported. Such groups were also predicted to migrate readily in radical reactions.^! Previously^’! 18 jt was assumed that these groups migrated well not because any intrinsic aptitude to migration but because of favourable pre-equilibrium. The barriers to migration calculated clearly indicate that such groups do have favourable intrinsic migratory aptitudes as well.

The most revealing trend is to be found for three para substituted aryl groups (Tables 2.2.2.1 and 2.2.2.2). It is known experimentally88,118 that electron withdrawing substituents (modelled here with pCN) on the migrating group R significantly enhance the observed rate of rearrangement, although again the assumption has been made that this is due largely to the effect on the equilibrium constant, Keq, rather than on the rate constant, The MNDO results indicate that, for phenylglyoxal at least (X =H), both Kcq and ^ are favoured by such substitution. For example, a /?CN substituent on the group R = Ph is predicted to promote the equilibrium in favour of 2.2 (by AH = 7.6 kcal mol-1, Table 2.2.2.2), to decrease the barrier to migration (by 2.2 kcal mol-1), and to increase the calculated overall negative charge on R, the entropy of activation, the bond lengths in the transition state and the formal resemblance of the migrating group to R- (Table 2.2.2.1). The change in entropy in particular is in such a direction as to favour AG* for the electron withdrawing group (Table 2.2.2.1). The calculated effect of an electron donating substituent on R such as p OH is more complex, increasing the barrier to migration and the bond lengths in the transition state.

2.2.2.1 Conclusions

In summary, for the migration of group R, for a constant substituent, X = H, the above results illustrate the dangers of simplifying assumptions regarding the nature of the transition state in such reactions. In other words, the migrating group appears not to behave as a formal nucleophile in terms of the substituent effects. Certainly there is no theoretical evidence here to support the accepted interpretation of an early transition state.88

74 To reiterate, for the groups studied in Table 2.2.2.1, migration is concerted and the range of activation energies is much smaller than was found^l for the migration of R’ or R+. The calculated entropies of activation tend to be negative (with the exception of the COSH group) and the C-R bond lengths in the transition state tend to be similar, suggesting a relatively tight and symmetrical transition state. The calculated overall charge on the migrating group, R, in the transition state varies between -0.38 for R = H, to -0.85 for R = COSH and the larger negative charge is found on the better electron withdrawing groups. Such groups tend to be the best migrating groups, as in agreement with experiment. Hence, groups such as ester, thiolester, acid and amide are predicted to have small barriers to migration.

Such a finding is in direct contrast to the p r e v i o u s ^ , 118 ideas concerning the reasons for migratory preferences, since it was believed that electron withdrawing groups migrated well, not because of any intrinsic aptitude to migration, but because of favourable pre­ equilibrium. The barriers to migration calculated clearly indicate that such groups do have favourable migratory aptitudes as well.

2.2.3 The Effect of Substituent X on the Migration of R

Due to the composite nature of the observed rate constant (equation 2.1, Section 2.1.2), comparison of substituent effects on Keq or £2 is directly experimentally complex (see Sections 2.2 and 2.3). Nevertheless, it can be readily established for a pair of substituents R and X from isotopic labelling experiments which one will migrate in preference to the other. It also follows from equation (2.1) (Section 2.1.2) that the relative rates of the two isomeric reactions are related to the difference in free energy between 2.1 and 2.7, and not directly to the barrier for the rearrangement step 2.2 to 2.3. Since 2.1 and OH- are common to both reactions, only the relative free energies of the two isomeric transition states 2.7 need to be compared. Under these circumstances, it becomes apparent that the group X may have a significant role to play in determining the relative stability of transition state 2.7. Initially, calculations (see Table 2.2.2.2, overleaf) for two specific pairs of substituents (R / X = H or Ph^S and cyclopropyl or CO 2HI 16)} for which migratory preferences have been experimentally established by isotopic labelling, are discussed.

75 Table 2.2.2.1 Calculated MNDO Energies for Different R and X Substituents in kcal mob 1

X R 2.1 2.2 AH2.Rcaa 2.7 AH7.2 b 2.5 AH5.2 C (2.10) (AH30_2c) H H -62.64 -135.45 -31.04 -106.63 28.81 -96.06 39.39 H Ph -38.94 -104.97 -24.26 -77.43 27.53 -68.52 36.45 (-72.95) (32.02) Ph H -38.94 -112.02 -31.31 -70.96 41.06 -88.54 23.48 H p CNPh -6.28 -79.88 -31.83 -54.56 25.32 -45.02 34.86 (-57.91) (21.97) p CNPh H -6.28 -85.79 -38.76 -47.63 38.16 -67.87 17.92 H p OHPh -87.19 -153.10 -24.14 -125.43 27.67 -121.31 31.79 (-123.55) (29.55) p OHPh H -87.19 -160.59 -31.63 -120.84 39.74 -138.35 22.24 Ph Ph -13.18 -78.80 -23.85 -38.21 40.59 -53.31 26.16 pCNPh Ph 19.20 -52.57 -30.00 -9.24 43.33 -31.78 20.80 Ph pCNPh 19.20 -54.23 -31.66 -13.84 40.39 -26.11 28.12 (-30.90) (23.33) pOHPh Ph -60.65 -127.34 -24.92 -85.80 41.54 -102.60 24.74 Ph pOHPh -60.65 -127.44 -25.02 -85.97 41.47 -101.91 25.53 pOHPh pCNPh -29.34 -102.78 -31.67 -63.07 39.71 -75.90 26.88 pCNPh pOHPh -29.34 -101.12 -30.01 -59.59 41.54 -81.33 19.79 C3H5 co2H -128.71 -215.29 -44.81 -187.58 27.71 -178.84 36.45 c o 2h C3H5 -128.71 -209.32 -38.84 -164.75 44.57 -172.66 36.66 a AH2.Rca = AHf (2.2) - AHf (2.1) - AHf (OH') b AH7.2 = AHf (2.7) - AH 1 (2.2) c AH5.2 = AHf (2.5) - AHf (2.2), similarly values in parentheses correspond to AH10.2 = AHf (2.10) - AHf (2.2).

76 2.2.3.1 The Rearrangement of Phenylglyoxal via Transition State 2.7 (R / X = H / Ph)

The hydroxyl anion catalysed rearrangement of phenylglyoxal to phenylglycolic acid has been established^ as proceeding via hydrogen migration in preference to phenyl migration. The results in Table 2.2.2.1 with X = H indicate little difference between R = H and R = Ph in enthalpic contribution to the rate constant k2. The classical explanation for the observed specificity would be that an aldehyde (ie. 2.2, R = H, X = Ph) is more susceptible to nucleophilic attack than a ketone (ie. 2.2, R = Ph, X = H), and that therefore the migration is determined by the value of the equilibrium constant and not the rate constant k2. The MNDO calculations indeed predict the isomer R = Ph, X = H to be 7.1 kcal mol ' 1 less stable than R = H, X = Ph. However, the barrier for [1,2] migration (ie. AH7 _2) for R = H, X = Ph is 13.5 kcal mol ' 1 higher in energy than for R = Ph, X = H, a difference that arises largely from the substituent effect of the group X! Overall therefore, the absolute energy of (2.7, R = Ph, X = H) corresponding to migration of the phenyl group via path a in Scheme 2.1.3.1, is 6.5 kcal mol ' 1 lower than that for hydride transfer (2.7, R = H, X= Ph, Table 2.22.2), in apparent contradiction with experiment.96 A similar result was also obtained for the pair of substituents R / X = H and p- cyanophenyl.

2.2.3.1.1 Conclusions

The classical mechanism predicts that the phenyl group should migrate in preference to hydrogen, in apparent conflict with experiment where the opposite is observed. 96 Although such results are within the limits of accuracy of the MNDO method, this does suggest that alternative explanations such as those involving single electron transfer (Scheme 2.1.3.1) or an epoxide ring mechanism (Scheme 2.2.1.1) should be considered.

2.2.3.2 The Rearrangement of Phenylglyoxal involving Epoxide Ring Formation

The results for the epoxide mechanism outlined in Scheme 2.2.1.1 for phenylglyoxal are shown in Table 2.2.3.1. As in the previous example of glyoxal, the energies of the epoxide intermediates, 2.13 and 2.14, are higher than intermediate 2.2 by 17.85 and 16.30 kcal

77 mol "1 for the combination R = H, X = Ph, and by 8.73 and 10.28 kcal mol "1 for the alternate combination R = Ph, X =H. In this case, the corresponding barriers to migration of R are also very high (Table 2.2.3.1), sufficiently high in fact, to effectively exclude this mechanism relative to the classical pathway where the barriers to migration of R (= PI / Ph) are much lower (by tens of kcal mol'1). Interestingly, this route would also predict the migration of the phenyl group in favour of hydride migration, again in apparent contradiction to experiment.

2.2.3.2.1 Conclusions

A mechanism involving epoxide ring formation as in Scheme 2.4.1.1, is excluded for the case of phenylglyoxal since the intermediates and transition states involved are much higher in energy than the corresponding species in the classical route. However, both these mechanisms so far, fail to explain the observed^ migration of hydrogen in preference to phenyl. Hence, the possibility of SET is investigated.

Table 2.2.3.1 Calculated MNDO Energies and Barriers for the Mechanism in Scheme 2.2.1.1 for Phenylglyoxal in kcal mol-1 X R 2.2 2.13 2.14 2.15 2.16 Ph H -112.02 -94.17 -95.72 -31.68a -45.22a H Ph -104.97 -95.72 -94.17 -65.10a -37.57a XR AHb13.2 AH‘14.2 AH*d15.13 AH*e16.14 AH*f7.2 Ph H 17.85 16.30 62.49 50.50 41.06 H Ph 9.25 10.80 30.62 56.59 27.53 a These transition states had extra negative vibrational eigenvalues of the order of 28-55 cm-1 due to rotations of the OH and phenyl groups. b AH13.2 = AHf (2.13) - AHf (2.2) c AH14.2 = AHf (2.14) -AHf (2.2) d AH* i5.13 = AHf (2.15) - AHf (2.13) e AH*16.14 = AHf (2.16) - AHf (2.14) f AH*7.2 = AHf (2.7) - AHf (2.2)

78 2.2.3.3 The Rearrangement of Phenylglyoxal involving Single Electron Transfer

If the migrating group is R = H, only one mode of SET is possible, ie. the one representing transfer of an electron from the alkoxide oxygen atom into the adjacent carbonyl group, giving 2.5. However, if R = Ph, an SET can occur to give either biradical 2.5, or the species 2.10 via electron transfer to the aryl group itself (Scheme 2.2.3.1).

Scheme 2.2.3.1 O R SET -O R X OH ^ ^ OH O- i)R = H X O* 2.2 2.5

Indeed, it was possible to locate two triplet states corresponding to 2.5 or 2.10 with X = H, R = Ph, and one state corresponding to 2.5 with X = Ph, R = H (Table 2.2.2.2). These triplets were distinguished by differences in the charge distribution (Table 2.2.3.1). As consistent with the two different kinds of SET possible, the charge distribution for the biradical 2.10, showed that most of the negative charge was located in the aromatic ring of the migrating group R. For the other isomer 2.5, the charge was located mainly on the portion C/(0)(0H) or for particularly electron withdrawing groups, X, like /?-CNPh, the charge would be concentrated on the portion C 2XO. (Table 2.23.2 , see overleaf) Also, the C2-O bond for the isomer 2.10 is much shorter than for isomer 2.5.

Discussing firstly the specific case of X = H, the intermediate biradicals 2.5 or 2.6 are not significantly stabilised compared with glyoxal, irrespective of the nature of the migrating group R. Thus triplet 2.5 is 39.4 kcal mol -1 higher than 2.2 when R = H, and 36.5 kcal mol -1 higher when R = Ph, values that effectively exclude the possibility of such electron transfer. The triplet state 2.10 (R = Ph), representing electron transfer into the phenyl ring,

79 is also high in energy, 32.02 kcal mol -1 relative to 2.2. The corresponding transition state 2.7 is 8.9 and 4.5 kcal mol ' 1 lower than 2.5 and 2.10 respectively, indicating that neither SET pathway involving the migration of the phenyl group is favoured. The situation is different when X = Ph, since the phenyl group can stabilise the adjacent radical centres in 2.5 or 2.6, see Scheme 2.2.3.2. (overleaf).

Table 2.2.3.2 Division of Charge in Triplet Species 3 2.5 and 2.10 i O

XR C2XO C;(0)(OH) R AHlb & Type of Triplet

H Ph -0.18 -0.64 -0.19 -68.52 1.23 2.5 Ph H -88.54 2.5 H pCNPh 0.02 -0.12 -0.90 -57.91 1.22 2.10 H pCNPh -0.17 -0.63 -0.20 -45.02 1.23 2.5 pCNPh H -0.84 -0.23 0.06 -67.87 1.24 2.5 H pOHPh -0.01 -0.12 -0.88 -123.55 1.22 2.10 H pOBPh -0.18 -0.63 -0.36 -121.31 1.23 2.5 pOHPh H -138.35 2.5 Ph Ph -0.79 -0.18 -0.03 -53.31 1.25 2.5 pCNPh Ph -0.80 -0.17 - 0.02 -31.78 1.23 2.5 Ph pCNPh -0.70 -0.19 -0.05 -26.11 1.25 2.5 Ph pCNPh -0.02 -0.09 -0.90 -30.90 1.22 2.10 /?OHPh Ph -0.94 -0.19 0.13 -102.60 1.24 2.5 Ph pOHPh -0.77 -0.19 -0.04 -101.91 1.24 2.5 pOHPh pCNPh -0.75 -0.19 -0.05 -75.90 1.25 2.5 /?CNPh /?OHPh -0.80 -0.17 -0.02 -81.33 1.24 2.5

R X s / \ "OH o ' O b In kcal mol-1.

80 Scheme 2.2.3.2 -O R n R OH

In this case (2.5, X = Ph, R = H) is now only 23.5 kcal mol ' 1 higher than 2.2, a stabilisation of 15.9 kcal mol -1 relative to (X = R = H). The energy of (2.5, X = Ph, R = H) is now calculated to be lower than that of the transition state (2.7, X = Ph, R = H) by as much as 17.5 kcal mol -1 (Table 2.2.22).

The subsequent fate of a biradical such as (2.5, X = Ph, R = H) is also of some interest, since the process resembles quite closely a [1,2] hydrogen atom migration. It has been shown^l that such a process in a simple radical system has a prohibitively high energy. It was not possible to directly study the [1,2] hydrogen atom migration of 2.5 to 2.3 on the singlet surface since the excited wavefunction was modelled using a triplet state (see Chapter 6) and hence, a conversion from the triplet to singlet manifold occurs on going from 2.5 to 2.3. However, the related conversion of singlet (2.6, R = X = H) to 2.4 has a relatively low barrier (8 kcal mol-1, Section 2.2.1). This latter process is probably facilitated by the 'oxy-anion' effect,138 and therefore the barrier for [ 1,2] hydrogen atom migration in 2.5 is probably somewhat higher, but not so large as in a conventional radical .**1 If this is true also for the singlet conversion of (2.5, X = Ph, R = H) to 2.3, then paths b or c may indeed constitute viable routes for the migration of hydrogen rather phenyl. It is therefore suggested that the observed migratory preference in phenylglyoxal might be rationalised by a mechanism involving an intramolecular SET from the oxy-anion substituent to the carbonyl group followed by a [ 1,2] hydrogen transfer.

2.2.3.3.1 Conclusions

The energetics of a single electron transfer when R = H and X = Ph, are such as to favour the formation of biradical species such as 2.5 relative to the transition state for classical migration when R = H, X = Ph. If the corresponding barrier to [1,2] hydrogen migration is

81 low, as it was found to be in the biradical 6 for R = X = H, then such a mechanism would explain the observed migratory preference in phenylglyoxal.

An important point that emerges from this example is the effect of substituent X on migration. The ability of substituents X, to stabilise or not a particular intermediate or transition state has a crucial role to play in controlling the mechanism. In this case, X = Ar can stabilise intermediates like 2.5 formed by single electron transfer for any migrating group R.

One approach to testing the hypothesis of SET for arylglyoxals experimentally, might be to investigate the effect of a para substituent attached to group X = Aryl (Table 22.2.2) on the rate of migration of the group R = H, via the effect on the two constants and k2. The entries in Table 2.2.2.2 include the enthalpy of reaction of (2.1 + OH") giving 2.2. Changes in this quantity should reflect the effect of substituent X on the equilibrium constant Keq (assuming no entropic differences). The pCN substituent on X has a surprisingly large effect on the stability of 2.2, promoting its formation by 7.4 kcal mol -1 relative to X = Ph (with R = H) and by 6.2 kcal mol -1 (with R = Ph). Such (3 activation of a dicarbonyl compound should be verifiable experimentally. The pCN group on X is also predicted to act on &2 by reducing the barrier to [1,2] hydride migration by 2.9 kcal mol"1. However, such a group also promotes the SET process via 2.5 by 5.6 kcal mol’1, which would also favour Hence, it is predicted that electron withdrawing groups on the non­ migrating substituent X should enhance the rearrangement of arylglyoxals, but that this effect would not differentiate between paths a,b or c in Scheme 2.1.3.1.

In contrast to these results, an electron donating substituent on X such as p-hydroxy appears to have only very small effects on Keq, the barrier to migration, and the SET process leading to 2.5.

2.2.3.4 The Rearrangement of R / X = Cyclopropyl / C02H

It has been noted experimentally 1 ^ for this system that the ester (or acid) group migrates in preference to the cyclopropyl group, and also that the cyclopropyl substituent slowsdown

82 the rate of rearrangement compared with a simple alkyl substituent (eg. X = CI-I3, R = CO2H). MNDO calculations for this system are consistent with both these observations. The barrier for the conversion of2 toA3 with R = CO 2H, X = cyclopropyl is 6.1 kcal mol ' 1 higher than the corresponding barrier with R = CO 2H, X = H. The intermediate 2.2 is also more stable by 6.0 kcal mol -1 for the combination (R = CO 2H, X = cyclopropyl) than for the alternative (R = cyclopropyl, X = CO 2H), due to enhancement of the electrophilic characteristics of the a carbonyl group by the ester substituent. Overall, the transition state 2.7 is 22.8 kcal mol "1 higher in energy for the combination X = CO 2H, R = cyclopropyl than for the isomeric X = cyclopropyl, R = CO 2H and clearly indicates that only the ester or acid group should migrate. The energy difference between R =C 02H or cyclopropyl for the migration step (ie AH 7.2) is actually much smaller (11.8 kcal mol-1) when X = H in both cases, again clearly illustrating that both substituents have a very important joint role to play in controlling the rate of this rearrangement. There is no reported experimental evidence that this specific reaction occurs with any opening of the cyclopropyl ring. 116 it is therefore unlikely that an SET mechanism is occurring with this combination of substituents, since the formation of a biradical such as (2.5, X = cyclopropyl, R = CO 2H) should result in the formation of products corresponding to opening of the ring. Calculations (Table 2.2.2.2) also show that the SET process is not favoured in this case.

2.2.3.4.1 Conclusion

This example illustrates the joint importance of both R and X groups in deciding the rate and preference of migration.

2.2.3.5 The Benzilic Acid Rearrangement Proper (R = X = Ph)

The preceding results for phenyl glyoxal suggest that an SET mechanism involving the formation of a species such as 2.5 or 2.10 may be particularly favourable for the rearrangement of benzil itself (2.1, R = X = Phenyl). There are however several important differences to be expected between the migration of the group R = H and that of R = Aryl. Previous studies^ 1 indicated that in simple radicals, [1,2] hydrogen migration was a relatively high energy concerted process, whereas migration of a group such as

83 phenyl was predicted to be a comparatively facile stepwise reaction, proceeding via a cyclic intermediate. The analogues of these intermediates for the benzilic acid reaction would be species such as 2.8 or 2.9.

Scheme 2.2.3.3

Table 2.2.3.3 Calculated Energies of Intermediate Species For R = Ar in Paths b and c, in kcal mol"1

X R 2.8 2.9 ah8. / AH9.2b

H Ph -89.43 15.54 H pCNPh -64.76 -75.99 15.12 3.89 H pOHPh -139.10 -150.70 14.00 2.40 Ph Ph -79.78 -78.48 -0.98 0.32 pCNPhPh -60.66 -51.79 -8.09 0.75 Ph pCNPh -54.04 -51.76 0.19 2.47 pOHPhPh -129.82 -127.86 -2.84 -0.52 Ph pOHPh -130.41 -128.89 -2.97 -1.45 pOHPhpCNPh -103.82 -102.99 -1.04 -0.21 pCNPhpOHPh -110.83 -102.09 -9.71 -0.97 a AH8.2 = AHf (2.8) - AHf (2.2) b AH9.2 = AHf (2.9) - AHf (2.2)

84 For phenyl migration in phenylglyoxal, MNDO does indeed predict such intermediates to occur on the pathway for conversion of triplet (2.5, R = Ph, X = H) to 2.3 and for singlet (6, R = Ph, X = H) to 2.4 via 2.8 and 2.9 respectively (Table 2.2.3.3). Thus (2.8, R = A Ph, X = PI) was found to be 15.5 kcal mol "1 less stable than 2.2, and the barrier to its formation from 2.5 was quite high (35 kcal mol-1). It is noted at this point that the charge and spin distribution clearly indicated that the negative charge was located on the oxygen atom shown for 2.8 (as opposed to other representations involving location of the negative charge on the phenyl ring or the other oxygen) and that therefore 2.8 should be susceptible stabilisation by the substituent X. This is indeed found to be true for benzil itself, where (2.8, R = X = Ph) is now 1.0 kcal mol -1 more stable than 2.2 and 26.5 kcal mol -1 more stable than triplet 2.5. The latter itself is now 15.1 kcal mol ' 1 lower in energy than the transition state 2.7 (Table 2.2.2.2). The isomer 2.9, differing only in the position of the proton, is similar in energy to 2.8, but as expected shows a smaller substituent effect due to X (Table 2.2.3.3). For 2.8, the stabilising effect of electron withdrawing substituents (ie pCN) on the substituent group X or electron donating substituents (ie /?OH) the migrating group R is quite marked, though the effect is more dramatic for the former. Hence, the most stable of the intermediate species 2.8 (relative to 2.2) studied is for R = pOH, X = pCN, where 2.8 is now more stable than 2.2 by 9.71 kcal mol-1.These results do raise the possibility that species such as 2.8 or 2.9 might be capable of being trapped under suitable circumstances.

Since there is a great deal of information regarding substituent effects available where R = X = aryl, three such systems were studied as models (Table 2.2.2.2) ie. R = pCNPh, pOHPh, Ph, X = Ph, /?CNPh, pOHPh. The results for these systems will be discussed in terms of their effect on K^, on &2 and on the SET and the species resulting from this. The effect of replacing phenyl by p-cyanophenyl is to favour the formation of 2.2 by 7.8 kcal mol'l when on the group R and only by slightly less when on group X (6.2 kcal mol" *), as was noted for the arylglyoxal system. In contrast, little effect is predicted on hi (AH7.2, Table 2.2.2.2) when the substitution is on R, whilst an increase in the barrier is calculated when such substitution is on X. This is in contrast to the previous calculations (Table 2.2.2.1) for the case of X = H rather than phenyl, which indicated that substituents on the R group had a rather greater effect on the barrier to [1,2] migration.

85 Two triplet states of (2.2, X = Ph, R = / 7-cyanophenyl) were characterised (Table 2.2.3.2) , corresponding to single electron transfers to give 2.5 and 2.10, the latter being the more stable species (by 4.8 kcal mol-1). For the isomeric combination (X = p- cyanophenyl, R = Ph), only 2.5 could be characterised and not 2.10, presumably due to the relative stabilisation of 2.5 by group X. These results mean that if an SET to give 2.5 occurs, electron withdrawing substituents are favoured on X and not R, contrary to experiment. Such behaviour can be rationalised in terms of stabilisation of 2.5 by increased delocalisation of the negative charge (by resonance as in Scheme 2.2.3.2 and/or inductively) for electron withdrawing X substituents. On the other hand, an SET to form 2.10 shows little discrimination between R and X in terms of the para substitution (Table 2.2.2.2) . In fact, the formation of 2.10 by a SET into the migrating group R should be encouraged by electron withdrawing substituents capable of stabilising the negative charge. An electron donating group such as pOH has a much smaller effect on Keq, and the energy of the SET process.

2.2.3.5.1 Conclusions

In summary, these results imply that electron withdrawing substituents in the rearrangement of substituted benzils act principally by influencing the equilibrium constant Keq, with a much smaller effect on the rate constant ^ • These results are to be contrasted with those previously discussed for arylglyoxals, where it was predicted that both Keq and k2 are subject to substituent effects. Clearly, the group X does not play a passive role in such reactions! It is also predicted that there may be two types of SET possible, with differing substituent effects. Electron transfer to give 2.10 is the most consistent with experimental observation. The energies of the electron transfer appear to indicate that such mechanisms have to be seriously considered as an alternative or complementary process to the classical reaction mechanism.

Some possible ways in which such SET mechanisms may be able to be detected are suggested here. Firstly, since for aryl systems the energies of the cyclic intermediates, 8 a* andA9, are comparable to that of intermediate 2.2, it may be possible to trap these species under suitable conditions. Secondly, a suitable para substituent attached to an aryl group

86 may be another possibility. For example, a cyclopropyl substituent would ring open if SET occurred and the products so formed would provide a means of detecting such a process. A better alternative would be to use a hindered cis double bond as a substituent. This would, tend to isomerisel^l and so again would provide a means of distinguishing such a pathway from the classical mechanism ie. Scheme 2.2.3.4

Additionally, spectroscopic techniques could also be applied (eg. EPR) to detect the biradical intermediates involved. Radical inhibitors may also affect the reaction, though it is known that the addition of peroxides does not affect the rate of reaction.92

2.2.4 The Role of the Positive Counter-Ion on the Mechanism of Rearrangement

In solvents such as water, the role of the positive counter-ion to the hydroxyl ion appeals not to be important. However, when the reaction is carried out in less polar solvents, it has been suggested that the positively charged ion does indeed play an active role by coordination to the two carbonyl oxygens, prior to nucleophilic attack by OH' and concominant R' migration (see Section 2.1). Such a possibility was modelled by calculating the barriers to migration of two groups R = H and CO 2H with X = H in both cases and with Li(H20)+2 coordinating to the two oxygen atoms of the erstwhile carbonyl groups as in 2.11 and 2.12 :

R Scheme 2.2.4.1 2.11 2.12 The calculations show that the intrinsic barrier to migration is actually increased, by 4 kcal mol ' 1 in the case of R = H and by 15 kcal mol -1 in the case of R = CO 2H. The reason for the- this can be seen in Acalculated overall charge on the whole of the migrating group (Table 2.2.2.1). A group with little opportunity to delocalise negative charge such as methyl typically has a charge of ca. -0.41 at the transition state, compared with a CO 2H group with a value of -0.69. The addition of a positive counter ion such as Li(H 20)+2 reduces the negative charge on the migrating group quite significantly, the acid group for example, now having the value -0.47 and with a corresponding barrier to reaction quite similar to a methyl group. If the counter ion appears to play no role in promoting the intrinsic ability of a group to migrate, then its effect must be to displace the equilibrium away from 2.1 and towards the coordinated system 2.2. This hypothesis was investigated by calculating the enthalpy of reaction for the two equilibria (reactions 2.2 and 2.3).

2.1 + OH- = 2.2 ... (2.2) 2.11 + H20 = 2.12 ... (2.3)

Firstly, it is noted that the heat of formation of OH" is predicted by MNDO to be too high by 36 kcal mol -1 whilst the corresponding values for alkoxide anions are correctly reproduced.110 If this correction is applied, it is found that AH for reaction (2.3) (-34.5 kcal mol-1) is 3.5 kcal mol ' 1 more exothermic than for reaction (2.2) (-31.0 kcal mol'1).

2.2.4.1 Conclusions

Although these calculations on the role of the positive counter-ion do not take into account any entropic factors or solvation effects, they do provide a possible indication that coordination to a counter-ion might affect the value of the equilibrium constant and hence the observed kinetics of benzilic acid type rearrangements.

2.2.5 The Benzilic Acid-like Rearrangement of Thioglyoxal Systems 2.2.5.1 Rearrangement of Mono- and Di-Thioglyoxal (R = X = H)

As the previous investigation of the mechanism of glyoxal rearrangement to glycolic acid showed that a single-electron-transfer mechanism (SET) was unlikely compared to the

88 classical mechanism, the study was extended to include thioglyoxals. In the thioglyoxal systems the radical intermediates postulated in a SET mechanism have the possibility of extra stabilisation by adjacent S atoms.

For mono-thioglyoxal (2.17 and 2.18), there are three possible intermediates (2.19, 2.20 and 2.21) and transition states (2.22,2.23 and 2.24) for the symmetric case of R = X = PI, leading to two different products (2.28 and 2.29) stemming from initial attack of the base (OH-) at either the sulphur carbonyl group or the oxygen carbonyl group in the classical mechanism (see Scheme 2.2.5.1, overleaf). For thioglyoxal (2.17) (R = X = H, Scheme 2.2.5.1) in the initial base attack at the oxygen carbonyl group, the energy of reaction of (2.17 + OH') to form intermediate 2.19 is similar to that in glyoxal with a value of -30.05 kcal mol -1 (Table 2.2.5.1, 3 pages overleaf). However, the barrier to hydride migration for this system is now reduced from 28.81 kcal mol -1 for glyoxal to 18.29 kcal mol-1. The energy required to form the biradical intermediate 2.30 (Scheme 2.2.5.2, 2 pages overlef) in the alternative SET mechanism is also reduced relative to the simple glyoxal case to just 14.23 kcal mol -1 and in fact, the energy of this biradical intermediate is now 4 kcal mol -1 lower than that of transition state 2.22 for classical mechanism. Hence, in this case, SET is now a feasible alternative route to reaction over the classical mechanism.

ta For the case of initial base attack at the thio carbonyl group, the situation is quantitively different. The energy of intermediate 2.20 so formed is 28.85 kcal mol -1 more stable than intermediate 2.19 formed by initial attack at the oxygen carbonyl group, whilst the energy of the corresponding transition state (2.23) is only slightly higher than the isomeric species 2.22 by 1.37 kcal moH. Similarly, the energy of biradical 2.32 is also slightly higher than that of the corresponding isomeric biradical 2.30 by 2.33 kcal mol-1. Hence, in this case, due the extra stability of intermediate 2.20, the barrier to hydride transfer is elevated to 45.51 kcal mol-1, whilst the energy of biradical 2.32 is 42.51 kcal mol -1 higher than intermediate 2.20.

89 Scheme 2.2.5.1 Classical Mechanism

S O m r - C O- R s v^Vo X R X R X OH

2.17 2.19 “ 2.22

-S I O HS 0 x-V-f x-V-f R OH R O- 2.25 2.28

-o s x yf R OH 2.26 O S ™ _ O, s- R 0=7£“V s X R X R X OH 2.18 2.20 - 2.23 J

HO ^ X an I R 0 - R o SH I \ 2.29 O =r SH R X O ■ 2.24 / ' X -O O X ^R f SH 2.27

90

2.21 Scheme 2.2.5.2 SET Mechanism S ( 3 OH' S\ /°' SETJS \ / O’ IIS O* y < 7— V~ OH -=*Srv. > — p OH ^ f - o - X I * X R A R A R 2.17 2.19 2.30 2.31

-S V O HS I' O x V ( X -^ — C R 0H R 0 - 2.25 2.28

-o 4r,s HO S , X- R-^---- (.<■ ' R OH X ° ' 2.26 2.29 A A 1 O | S* HO S' OH- °V_X S- SET "O v w 7----f-O H ^5=^ ~ OH ^ W o ' x i X R X R X R 2.18 2.20 2.32 I O t SH .0 SH HO S v-fo. S.'Vr -fo- ► V ^ O * X R X R X R 2.21 2.33

-O> SH HO * S . X X -^ — < < -' R R O ' 2.27 2.29

91 Table 2.2.5.1 MNDO Calculated Energies for the Rearrangement of Thioglyoxal in kcal mol-1

AHf2.„ AHf2_i9 AHf2.20 AHf2.22 AHf2.23 AHf2.30

-3.80 -75.62 -101.48 -57.34 -55.97 -61.30

AHf2.32 AHai9_Rca AHb2()-Rea AH~ 22.19 a h « '23.20

-58.97 -30.05 -55.91 18.29 45.51 a AH19.Rea = AHf (2.19) - AHf (2.17) - AHf (OH') b AH20-Rca = AHf (2.20) - AHf (2.17) - AHf (OH') c AH*22-19 = AHf (2.22) - AHf (2.19) d AHit23 20 = AHf (2.23) - AHf (2.20)

2.2.5.1.1 Conclusions

For the monothioglyoxal system, the energies of both the classical route and the alternative SET are very high though comparable with each other. Overall, it can be concluded that if migration does take place then both classical hydride transfer and SET are feasible energetically. The kinetic isotope effect for the migration step calculated for both initial attack at thio-carbonyl and at oxy-carbonyl routes shows a marked difference between these routes. At 373K, the kinetic isotope effect as based on calculated harmonic rate ratios (HRR) for kH / kD for migration via transition state 2.22 is 1.65, whilst the corresponding value for transition state 2.23 is 6.96. The observed isotope effect would involve the pre­ equilibrium isotope term which is complicated by the different isomers, 2.19 and 2.20 and tautomers formed by proton shifts, and hence this was not able to be calculated. However, the observed isotope effect would still be expected to quite be different for the two isomeric transition states possible. The products isolated would distinguish whether the initial attack involved thio- or oxygen carbonyl group attack but would not be able to distinguish between the classical or SET mechanisms.

92 For di-thioglyoxal, the difference between these two routes is more marked. In this case, like that of glyoxal there is only one intermediate, analogous to 2.2 (Scheme 2.1.3.1), is possible by attack of base. This reaction is highly exothermic, with an enthalpy change of - 55.53 kcal mol"1, compared to-31.04 kcal mol -1 for glyoxal, the difference being due to the relative instability of thioglyoxal. The barrier to hydride migration from such an intermediate is 34.16 kcal mol-1, rather higher (by 5.35 kcal mol-1) than in the case of glyoxal. This time however, the energy of the first biradical intermediate, formed by SET into the thio-carbonyl group, is only 16.13 kcal mol "1 higher than the intermediate formed by attack by OH'. Hence, in this case, if rearrangement occurs then SET is the more likely pathway (providing of course, that the barrier for [ 1,2] radical migration of hydrogen is less than 18 kcal mol'1).

2.2.5.2 The Rearrangement of Monosubstituted Mono-thioglyoxal (R, X = H)

As in the previous case of unsubstituted glyoxals, the most stable intermediate (2.20) is formed by hydroxyl attack on the thiocarbonyl group for all the different migrating groups investigated (Scheme 2.8.1.1 and 2.8.1.2). The tautomer of this intermediate (2.21) is higher in energy but lower than the intermediate formed by attack of base at the oxygen carbonyl group. The transition states for classical nucleophilic R' migration (2.22 and 2.23), are much closer in energy for most groups except CN, CHO, Ph, p-OHPh, p- OHPh and CH 3, where 2.23 is the most stable isomer. The energies of all the species reported in Table 2.2.5.2 are for the most stable configuration. For the substituted glyoxals discussed in Section 2.2.2, the stereochemical effect on the transition state was less than 1 kcal mol*1. For the transition states and biradical species in the monothioglyoxals, the different stereoisomers are usually separated by 1-5 kcal mol ' 1 except for vinyl (where the stereoisomers for 2.24 differ by 12 kcal mol'1) and p-CNPh and p-OHPh (where the stereoisomers of 2.30 differ by much more).

For rearrangement via intermediate 2.19, the barrier to migration via transition state^22 is similar to the energy required to form the biradical 2.30 and in fact for most systems the latter has the smaller energy, the exception being COSH, where the difference between the two quantities is only .8 kcal mol'1. Again, these energies are less than or similar to the barriers to migration in the classical mechanism for the monosubstituted glyoxal systems 93 (AH*7-2 in Table 2.2.5.3).

Table 2.2.5.2 Calculated MNDO for Different R Substituents (X = II) in kcal mol'1 < 0 R AI-lf2.I9 AHf2.20 AHf2.2i AHf2.22 AHf2.23 AH*2.24 ro AHf2.32 AHr2.33

H -75.62 -101.48 -87.08 -58.28 -57.43 -49.09 -61.34 -61.15 -45.48 c h =c h 2 -51.53 -77.00 -62.72 -32.47 -30.07 -22.30 -36.92 -36.01 -20.08 CN -48.54 -72.17 -59.86 -27.53 -68.99 -57.77 -29.31 -30.80 -15.02 CHO -108.25 -134.24 -118.76 -88.10 -130.63 -114.71 -92.98 -92.13 -75.79 Ph -43.54 -68.35 -53.78 -22.57 -55.91 -37.78 -25.18 -37.76 -17.96 pOHPh -92.14 -116.90 -102.28 -71.68 -110.09 -98.92 -74.40 -85.90 -70.54 /?CNPh -18.95 -42.68 -28.91 1.46 -9.70 -26.15 -0.54 -22.73 -20.82 COSH-111.01 -134.55 -117.53 -92.53 -90.43 -89.69 -91.69 -90.14 -73.32 c o n h 2 -116.03 -139.37 -123.56 -98.99 -99.45 -95.26 -97.45 -94.45 -102.50 OH -131.28-153.28 -139.60 -88.58 - 88.11 -85.33 -109.76 -103.26 -92.06 u o -162.45 -183.54 -170.76 -141.91 -139.23 -141.10 -142.95 -140.66 -124.26 C3H5 -49.67 -76.17 -61.06 -22.74 -19.70 -20.87 -36.10 -35.36 -19.26 c h 3 -75.81 -102.70 -88.29 -50.08 -42.20 -40.78 -62.43 -61.65 -45.66 c o 2h -172.32 -194.43 -177.51 -154.66 -154.91 -152.20 -148.85 -149.01 -133.38

For rearrangement via intermediate 2.20, the barrier to migration via transition state 2.23 and the energy required to form biradical 2.31, are much larger than in the previous system for all the R groups except cyanide, aldehyde, phenyl, p-hydroxyphenyl and p- cyanophenyl. In the latter systems the barrier to migration via transition state 2.23 is much smaller than in the previous system and also much smaller than the energy required to form biradical 2.31. For the other R groups, the energy required to form biradical 2.31 from intermediate 2.20 is comparable and less than the activation energy for migration via a* transition stateA23.

94 Table 2.2.53 Calculated Barriers to Migration for Substituted Mono-Thioglyoxals (X = II) in Real mol"’

s ° - 0 s “ 0 0 “ o n Oil v > — f o i l x R x R 2.19 2.20 R 2.2

R AH^22-19 AH?td30-19 ^ ^23-20 a h ^ 31.20 AH*g 7.2

H 17.35 14.39 44.05 40.32 28.81 c h =c h 2 19.07 14.61 46.94 41.00 30.36 CN 21.01 19.23 3.18 41.37 26.77 CHO 20.15 15.27 3.62 42.12 28.76 Ph 20.97 18.35 12.44 30.58 27.53 p OHPh 20.46 17.75 6.80 30.99 27.67 /?CNPh 20.41 18.41 16.53a 25.32 COSH 18.48 19.32 44.12 443.41 17.61 c o n h 2 17.04 18.58 39.92 36.86b 21.55 OH 42.69 21.52 65.17 50.02 48.58 c o 2c h 3 20.53 19.50 42.44a 42.85 22.59 c 3h 5 26.93 13.57 55.30a 40.81 31.84 c h 3 25.73 13.38 60.50 41.05 36.18 c o 2h 17.66 23.47 39.52 45.42 20.94 a The energy of transition state 2.24 was used as this was the lowest energy isomer. b The energy of biradical 2.32 was used as this was the lowest energy isomer. c AH-22-19 = AHf (2.22) - AHf (2.19) d AH*3o.i 9 = AHf (2.30) -AHf (2.19) e AH*23-20 = AHf (2.23) - AHf (2.20) f AH*31.20 = AHf (2.31) - AHf (2.20) S AH*7.2 = AHf (2.7) - AHf (2.2)

95 2.2.5.2.1 Conclusions

Overall, the effect of sulphur substitution on the mechanism of rearrangement^substituted thioglyoxals, is complex and depends on the type of migrating group. The balance of factors resulting in good and bad migrating groups is altered by such a substitution. For example, for the three aryl systems, the selectivity for migration in the classical route for the glyoxal system was /?-CNPh > Ph > /?-OHPh. For the sulphur substituted systems however, in migration via transition state 2.22 the selectivity is virtually lost and the three aryl systems have almost the same barriers. For migration via transition state 2.23, the selectivity is quite markedly reversed so that p-OHPh has the lowest barrier of the three aryl groups.

96 CHAPTER 3

A MNDO-SCF MO STUDY OF PROTON,

HYDRIDE AND RADICAL HYDROGEN

TRANSFER REACTIONS

97 3.1 INTRODUCTION

3.1.1 The Nature of the Transition State and Isotope Effects for Hydride Transfer Reactions

The transfer of hydrogen whether as radical, proton or hydride are amongst the simplest of all bond-making / bond-breaking processes and the study of such reactions has been of theoretical as well as general interest. Despite the great number of papers published on the subject of such reactions, there is still a gap, particularly in the details concerning hydride transfer reactions relative to proton transfers. For example, concerning the transition state, there is much interest in the angle of hydride transfers. It is generally accepted that proton transfers are linear, whereas it is not so firmly established as to whether hydride transfers are bent or linear. However, there is little doubt as to the importance of understanding the hydride transfer process since such reactions are widespread in both organic as well as biochemical reactions. 142

One particular biochemical hydride transfer system which has received widespread attention is that of coenzyme nicotinamide adenine dinucleotide (NAD+/NADH). Several studies report linear transition states whilst others advocate bent transition structures. Considering the theoretical investigations first, Donkersloot and Buck^2e carried out a study on NADH analogue reactions consisting of the reduction of the cyclopropenium cation by cycloprop ene, 1,4-dihydropyncKne and tropilidene in turn. They calculated contour maps by the choice of the two bond distances of the migrating hydride from the oxidant and reductant as reaction co-ordinates by the MINDO/3 method. Transition states and reactants were located by optimisation with both MINDO/3 and STO-3G but were not characterised by force constant calculation. All the reductions involved a linear C—H—C linkage in the transition state, with concerted and gradual breaking of one C-H bond whilst forming the other one and with simultaneous transfer of negative charge. No transition state involving a bent C—H--C linkage was able to be detected.

Still on NADH, Verhoeven et. alX^2d,143 report a MNDO study on 1,4-dihydropyridine as the model for NADT, with substrates as the pyridinium cation and 1,1-dicyanoethene. They too, employed a reaction co-ordinate scheme similar to Donkersloot, 132e, but with

98 some symmetry restrictions, to calculate contour maps. Again, transition states were located by full geometry optimisation. Transition states with linear hydride transfer were preferred to the bent transition structures also found.

So far, these two theoretical studies on NADH analogues have revealed a preference for linear hydride transfer. However, bent transition structures are reported in a recent ab initio study by Houk et. tf/.132a on the hydride transfer from the methoxide anion to formaldehyde. The transition state for this intermolecular reaction was optimised at the 3- 21G level, where the angle of transfer was found to be 133.8°. A symmetrical model of the real transition state was optimised at higher basis set levels where the angle of transfer was shown be highly basis set dependent. A similar relationship was noted in our studies on the transition state for formaldehyde in the Cannizzaro reaction (see Section 2.2.1.2) where the angle of transfer varied from near linear at the MNDO and AMI levels to 136.5° for 3-21G, 148.2° for 6-31G and 162.2° for 6-31+G ab initio levels.

These bent transition structures are consistent with some calculations on non-linear transition states reported by McKee et. al. 144a,b The reduction of formaldehyde by lithium methylamide was studied!44a at the MNDO and ab initio 3-21+G levels. Transition states were located and characterised by force constant calculation, for intra- and intermolecular (for dimeric species) hydride transfer where the angles of transfer were reported to be 149.1° and 172.4° respectively. Similarly, in another investigation 144b involving di -hydrogen transfer between methanol and formaldehyde, the C-H-C angle was found to be less than the corresponding O-H-O angle in the cyclic six-membered ring transition state at MNDO, 3-21G and 6-31G* levels of theory.

In contrast, Sheldon et. alM$> report a linear transition state (ie. linear C-H-C fragment) with C2h symmetry at the 6-311G** level for the reaction of the methoxide anion with formaldehyde. However, such a structure has been found not be a true transition state by Houk et. al.132a who report that it has three negative vibrational eigenvalues. (This example illustrates only too well the argument for characterising stationary points). Likewise, Williams et. al. 132b report a linear hydride transfer for the reaction between methylamine and the methyleneammonium cation (CH 2NH2+) at the ab initio STO-3G and

99 3-21G levels. The transition states, in this case, were characterised by the calculation of vibrational frequencies.

Experimental investigations of hydride transfer in the NAD+/NADH and other systems tend to include the calculation of isotope effects. Lewis and Symons ^ 6 suggested a triangular ie. non-linear transition state for hydride transfer where electrophilic agents react with a C-H bond. Low kinetic isotope effects are generally associated with such non-linear transfer as rationalised by 0 'Ferralll 39b and by Westheimer.l39a Kinetic isotope effects*39b fork^/kj) = 1 -2 were suggested for sufficiently bent transition structures whilst it was noted that experimentally observed values for some 1,2-hydride transfers tend to go up to about 3. In fact, Stewart and T o o n e^ report a maximum value in the kinetic isotope effect for the hydride transfer in the reaction of triarylcarbonium ions with the formate ion when the pH is varied. The value of k-^/kd varying between 1.8 and 3.2 in this reaction.

A popular method to investigate bent hydride transfer reactions has been the determination of the temperature dependence of kinetic isotope effects. *47 jn particular, a temperature- independent kinetic isotope effect coupled with an anomalous ratio of the pre-exponential term (in the Arrhenius rate equation) Ajj/Ae), has been taken as a probe of a nonlinear transition state for hydrogen transfer. 147 Qn closer examination of the theory underlying such assumptions, such generalisations have come under considerable criticism from several sources, 148-50 which do not recommend the use of such simplifications to gauge the non-linearity of hydrogen transfers. Nevertheless, experimental studies of non-linear hydride transfer are numerous. For example, Watt and Crazed 1 have investigated the barriers to intramolecular hydride transfer in some polycyclic hydroxy-ketones where hydride transfer occurs via a six-membered ring transition state. The relative ease of hydride transfer in such a non-linear arrangement has been used as additional evidence to support bent transfers in similar systems. 132a The calculation of small kinetic isotope effects 1^2-4 has led to the inference of non-linear transition states in the past, though such evidence is by no means full-proof.

Quantum mechanical tunnelling 137 in hydrogen transfer (ie. proton, hydride and radical

100 system) reactions is also of interest. Tunnelling is inversely related to mass (and temperature), and hence its particular importance to hydrogen systems. Such tunnelling can lead to non-linear Arrhenius plots and to kinetic isotope effects larger than the semi- classical values based on the loss of vibrational zero-point energy in the transition state. The extent of tunnelling depends sensitively on the curvature of the potential-energy barrier of the reaction, which is a function of its height and width (ie. the narrower the barrier the greater the tunnelling). Tunnelling in hydrogen atom systems in the solid-state!55-8 ancj recently, in the gas phase 159 has been observed.

For tunnelling in solution, there will be additional solvent molecules to consider. Caldin and Mateol^O have investigated the effect of various aprotic solvents on the extent of tunnelling (for proton transfer) and found that tunnelling is greater in the less polar solvents. It is also known that tunnelling is larger when there are bulky substituents near the reaction site and for reaction in aqueous solvents. These effects were rationalised by Kurz and Kurzl61 in terms of solvent re-organisation. They postulated that due to the high di-electric constant of aqueous solutions, and to the steric hindrance of bulky substituents, hydrogen transfers in such systems should involve little coupled solvent re-organisation.

Similarly, the findings of Caldin and M a t e o 160 can be explained by coupled re­ organisation of the solvent with proton transfer in the polar solvents, but only electron- polarisation in the non-polar solvents ie. in the former case, coupled solvent motion increases the effective mass of the migrating proton.

Tunnelling has been shown to be important in various hydride and hydrogen transfer reactions. For example, hydride transfer in the NAD+/NADH system has been reported to involve significant tunnelling by calculations 162 an(j by measurements of the primary kinetic isotope effects in model systems. 163,4 por a rigid cyclic hydroxy ketone, Watt et. al. 136 have calculated the primary kinetic isotope effects and tunnelling correction via Bell's model approximation,!37 at the STO-3G ab initio level, with complete geometry optimisation and characterisation of transition states. The calculated results predict an important contribution to the kinetic isotope effect from quantum mechanical tunnelling (ica. 40% at 25° C ). These workers also measured the kinetic isotope effect for the same system at several temperatures and found good agreement between theory and experiment in the kinetic isotope effect, if tunnelling was ignored. In other words, for their system,

101 tunnelling in solution seems to be decreased over that in the gaseous phase.

3.1.2 Effective Concentrations and Entropy in Hydride Transfer Reactions

Effective concentrations or molarities are used in the comparison of the rate constant of an intramolecular reaction, k\, with that of the corresponding intermolecular process, k2. Formally, an effective concentration (EC) is the ratio of these two rate constants ie. EC = ki/k^. Since, the rate constant for an intramolecular reaction is first order, whilst that for the corresponding intramolecular reaction is generally second-order, the ratio of rates, EC, has the dimensions of molarity. In other words, an effective concentration is that concentration of the catalytic group required to make the intermolecular reaction go at the observed rate of the intramolecular process.

In a review by Kirby, 165 effective concentrations for nucleophilic reactions involving ring formation are generally found to be much greater (by many powers of ten) than for acid- base catalysed reactions. This contrast between the two kinds of reaction has been rationalised in terms of the entropy changes involved. That is to say, the main advantage of the intramolecular reaction over the corresponding intermolecular process is seen to be entropic since more entropy is lost in a bimolecular reaction than in a unimolecular reaction if the transition state is 'tight' ie. has low residual entropy. Transition states corresponding to nucleophilic reactions are regarded as such, thus explaining the high values of effective concentrations. On the other hand, transition states for acid-base catalysed reactions (proton transfer reactions) are regarded as loose, ie. the transition state has high residual entropy. Hence, the entropy of activation for the bimolecular process is less unfavourable in the proton transfer case, so there is a smaller possible advantage of the intramolecular process. This explains the smaller ECs for proton transfer systems.

Watt et a/. 166a have suggested that since hydride transfer reactions show behaviour consistent with large negative entropy changes in the gas phase, 167 then intramolecular hydride transfers should show large effective concentrations. To test their hypothesis, they measured the rate of intramolecular hydride transfer in a rigid hydroxy ketone and compared that to the intermolecular hydride transfer from some alcohols to some ketones.

102 The high effective concentration resulting was then rationalised in terms of the above entropy argument.

In order to study the differences between proton, hydride and radical hydrogen transfer reactions, in terms of the angle of transfer, kinetic isotope effects, entropy changes and effective concentrations, we decided that theoretical calculations were appropriate for all these factors. For intramolecular reactions, we chose to study the models based on the hydroxy ketone studied by W a t t , 166a Scheme 3.1.2.1, and reactions with a variable chain of carbon atoms linking the sites involved in transfer as in Scheme 3.1.2.2.

Figure 3.1.2.1: R = II

103 Scheme 3.1.2.2 : R = (CH2)n, n = 0, 1, 2, 3 O- 0 O 0 - 1 II Hydride II 1 Transfer c c—,H H —,C/ N ^ C s^ I I ... 1 H

OH OH Hydride OH OH 1 1 1 1 C+ C — ij Transfer u ^ C c+ ...2 / V R n H n ' ' r ' \ H H OH OH OH OH 1 1 Proton 1 1 L — H r C— ... 3 H ^ S R ' \ Transfer 11" / ' ' R / S H / H H OH OH OH OH 1 1 Radical 1 1 C* C —. n H — C C- ... 4 H ^ S R ^ ^ Transfer / S R / S H H H The corresponding intermolecular processes, where the chain linking the two sites of transfer can be considered to be infinite ie. R = ©o, in analogy with the intramolecular systems, are shown in Scheme 3.1.2.3.

Scheme 3.1.2.3 0- 1 0 O- O H " ? 'H + x Hydride r A Me H ' 'M e Transfer H Me ••• $ OH OH OH OH 1 Hydride J. + I + c + + H \ H •------II l 11 C .. 6 H " 'Me Me Transfer Me H ' * Me OH OH OH OH i1 1 I I Proton C TT .. 7 C- + H \ H ■------H \ 11 ✓ C- ' n ' 'Me Me Transfer jyje H Me OH OH OH OH 1 l l I .. 8 c* + .C siT Radical C* H \ H - H l H H / * H " * Me Me Me Me

104 Owing to the size of the molecules in these reactions schemes, the MNDO method was chosen in preference to the ab initio method. This method has been recently shown^S to predict transition state stnictures for a wide variety of molecular systems in reasonable accord with results obtained from more time-consuming ab initio calculations. At the time of this research, the AMI method was not yet available.

3.2 RESULTS AND DISCUSSION

3.2.1 Effective Concentrations and Entropy Effects on the Nature of the Transition State for Proton and Hydride Transfers

Table 3.2.1.1 ( two pages overleaf) shows thermodynamic properties, including the free energy of activation, AG*, for the proton and hydride transfer reactions depicted in Schemes 3.1.2.1 and 3.2.1.2. Effective concentrations (which are ratios of rate constants of the intramoleculat reaction with respect to the intermolecular reaction) were calculated from the values of the free energy of activation in the following manner:

According to the Eyring equation, 166b rate constant, k = K (kT / h) K* where k is the transmission coefficient, k is Boltzmann's constant, T is the absolute temperature, h is Plank's constant, and K *1 is the equilibrium constant for the formation of the activated complex. Now the free energy of activation, AG* = -RT In K * , (c 0 )l-m where R is the gas constant, T is the absolute temperature, c is the concentration in the standard state to which the thermodynamic parameters are referred, and m is the molecularity of the reaction. The factor (c 0)l~m is necessary to make the argument of the logarithm dimensionless, ie. this is the units of K*. Such a factor was proposed by Robinson. 166c Hence, k = (ce)l~m k (kT/ h) exp (-AG* / RT) If k\ is the rate constant for the intermolecular reaction (m = 1) and &2 is the rate constant for the intermolecular reaction (m = 2), and the subscripts 1 and 2 are used to denote these

105 reactions respectively, then : k\ = (c0)l~ 1 Ki(kT/ h) exp (-AG!* / RT) and k2 = (cO)1’2 k2 (kT/h) exp (-AG2*/RT) Now, effective concentration, EC - k \ l k^ Hence, EC = ce exp ((AG2* - AG^) / RT), assuming that the transmission coefficient ratio is unity. Now, AG* = AH*-TAS*» Therefore, EC = c 0 exp ((AH2* - AH^) - T ( AS2* - AS i*))

Effective concentrations for the proton and hydride transfer reactions (as in Scheme 3.1.2.1 and reactions 1-3 in Scheme 3.2.1.2) are shown in Table 3.2.1.2. With the exception of proton transfer in the case of R = (C H ^ , the effective concentrations of hydride transfer reactions are much larger than those of the corresponding proton transfer reactions by several powers of ten. For those systems in which n < 2, the effective concentrations for both proton and hydride transfer reactions are less than one. In these cases, intramolecular transfer would involve the formation of three- or four-membered rings in the transition state and hence would involve unfavourable enthalpy changes for the intramolecular transfers relative to the intermolecular cases. These results are consistent with the experimental findings of Watt et. a/., 166a in which the effective concentrations of hydride transfer reactions in the hydroxy ketone in Scheme 3.1.2.1 were measured and found to be large (6.5 x 1O0 M, compared to 7 x 10^ M calculated for same system). The poor quantitative agreement between calculated and experimental values of effective concentrations is not surprising, but the qualitative effects in effective concentrations between proton and hydride transfer reactions are well reproduced by the calculations. Watt et. a/. 166a postulated that hydride transfer reactions should have large effective concentrations relative to proton transfer reactions due to dominance of favourable entropy as a result of 'tighter' transition states for hydride transfer.

Such a hypothesis is put to the test by our calculations of entropy (of activation) and other thermodynamic properties of proton and hydride transfer systems. Entropies, enthalpies and free energies of activation for the proton and hydride transfer reactions depicted in Schemes 3.1.2.1, 3.1.2.2 and 3.1.2.3 are shown in Table 3.2.1.1 (overleaf). From the results it can be seen that intermolecular transfer, for both proton and hydride cases,

106 Table 3.2.1.1 Thermodynamic3 Properties on Proton and Hydride Transfer Reactions at 323K

R = (CH2)0 (CH2)[ (CH2)2 (CH2)3 lib oo^ Reaction

AH* 26.88 30.05 21.20 19.18 19.78 15.59

AS*vib -4.17 -4.79 -5.41 -10.31 -1.93 +15.63 AS*rot -1.55 -1.46 -1.40 -0.23 -0.04 -17.70 1 AS*int -5.72 -6.26 -6.81 -10.54 -1.97 -2.08 AS** 0 0 0 0 0 -35.62 AS* tot -5.73 -6.26 -6.81 -10.53 -1.96 -37.70 AG* 28.73 32.07 23.40 22.58 20.41 27.76

AH* 30.24 38.80 22.98 24.13 22.62 19.09

AS*vib -4.78 -5.47 -7.40 -7.15 -3.20 +12.91 AS*r0, -1.47 -1.48 -1.43 -0.07 -0.03 -18.06 2 AS*int -6.24 -6.95 -8.83 -7.08 -3.24 -5.14 AS*ir 0 0 0 0 0 -35.69 AS* tot -6.25 -6.95 -8.84 -7.08 -3.24 -40.83 AG* 32.26 41.04 25.84 26.42 23.67 32.28

AH* 56.57 42.13 19.69 11.38 20.31 8.09

2.44 -3.22 -5.45 -5.75 -1.96 +16.15 AS*rot -1.44 -1.51 -1.48 0 -0.01 -17.95 3 AS*jnt -3.89 -4.74 -6.93 -5.75 -1.97 -1.79 AS** 0 0 0 0 0 -35.69 AS*Tqt -3.88 -4.74 -6.94 -5.75 -1.97 -37.48 AG* 57.82 43.66 21.93 13.24 20.95 20.20 a AH* and AG* in kcal mol-1, AS* in cal mol -1 K-1. bFor systems in Scheme 3.1.2.1. cFor intermolecular transfers as in Scheme 3.1.2.3.

107 Tabic 3.2.1.2 Effective Concentrations for Proton and Hydride Transfer Reactions

R = Reaction (c h 2)0 (CH2h (CH2)2 (CH2)3 IF

1 0.2 lO-3 9x 102 3x103 9 x 104

2 1 10-6 2 X 104 9x103 7 x 105

3 10-26 10-16 10"1 5x 104 0.3 o For systems in Scheme 3.1.2.1

involves large negative entropy changes : -38 cal mol -1 for hydride transfer in reaction 5, - 41 cal mol -1 for hydride transfer in reaction 6 and -37 cal mol '1 for proton transfer in reaction 7. Since the entropy of activation is much less unfavourable in all the intramolecular systems studied, on this basis alone, intramolecular transfer should be favoured for both hydride as well as proton transfer. Since this conclusion is not borne out in the effective concentrations, where intramolecular transfer is only more favourable for the hydride transfer cases, other factors must be necessary to explain the results.

One important factor not yet mentioned is the enthalpy of activation. Consider firstly the caged structures in Scheme 3.1.2.1, (used in the study by Watt et. a/.166a)# por proton s and hydride tranfer reactions, the entropy of activation is much less negative than in the intermolecular case and the values are similar for proton and hydride transfer. Interestingly, for these intramolecular reactions, the enthalpy of activation is also similar for both the hydride and proton transfer systems. This is in stark contrast to the intermolecular systems, where proton transfer has a much lower enthalpy of activation, 8.1 kcal mol"1, than either of the hydride transfer reactions where the corresponding values are 15.6 and 19.1 kcal mol-1. Hence, overall for intramolecular transfer in the caged structures (Scheme 3.1.2.1), the enthalpy of activation (AH*) is much higher, by 12 kcal mol "1 in fact, for proton transfer relative to the intermolecular case than for the two hydride transfer reactions, where

108 AH* is only 4 and 3.5 kcal mol -1 higher than in the intermolecular reactions.

Hence, the favourable entropy change for proton transfer on going from intermolecular to intramolecular reaction is more than outweighed by the unfavourable increase in enthalpy of activation, thereby explaining its low effective concentrations compared to hydride transfer reactions.This same sort of trend applies to the other systems shown in Table 3.2.1.1. For R = (CFl2)n where n = 0, 1, however, the highly bent transition states result in high enthalpies of activation for both hydride and proton transfer systems relative to the intermolecular cases, resulting in low effective concentrations ( « 1). Nevertheless, the effective concentrations for hydride transfer are still much larger than the corresponding proton transfer reactions.

3.2.1.1 Conclusions

In order to rationalise the much larger effective concentrations for hydride transfer compared to proton transfer reactions, the enthalpy of activation plays the deciding role rather than the entropy of activation. The entropy of activation does not discriminate o between protn and hydride transfer reactions, it is much less unfavourable for both intramolecular proton and hydride transfer reactions relative to the intermolecular case. In other words, the favourable entropy change for proton transfer, on going from intermolecular to intramolecular, is more than outweighed by the unfavourable increase in enthalpy of activation, thereby explaining its low effective concentration compared to hydride transfer reactions. This conclusion is contrary to the postulate of Watt et. a/, 166a who believed that entropy, ie. degree of 'tightness' or 'looseness' was the deciding factor discriminating between proton and hydride transfer reactions in this respect. In fact, the similar entropies of activation and C-H bond lengths (Table 3.2.2.1, overleaf) in the transition state for proton transfer in reaction 3 and hydride transfer in reaction 2, indicate that there is little difference between the two in terms of 'tightness'.

3.2.2 The Angle Dependency of the Enthalpy of Activation for Proton and Hydride Transfer Reactions

109 Table 3.2.2.1 Transition State Properties and Kinetic Isotope Effects for Proton and Hydride Transfer Reactions at 323K

R = Reaction (CH 2)o (CH2h (CH2)2 (CH2)3 IF ooh

1 C-HBond 1.50 1.50 1.44 1.43 1.43 1.44 Length 0 Angle C-H-C 59.7 98.7 131.6 155.3 115.9 173.9

Charged -0.36 -0.38 -0.29 -0.28 -0.25 -0.29

HRR° 3.42 3.53 3.29 3.31 3.17 3.47

2 C-HBond 1.41 1.42 1.39 1.38 1.39 1.39 Length 0 Angle C-H-C 62.5 99.7 130.8 153.8 112.5 174.3

Charged -0.01 -0.17 -0.18 -0.18 -0.12 -0.19

HRRe 2.81 3.07 3.01 3.23 3.07 3.46

3 C-HBond 1.33 1.42 1.40 1.38 1.39 1.39 Length 0 Angle C-H-C 70.7 107.4 133.4 153.5 116.4 180.0

Charged +0.23 + 0.22 +0.22 +0.19 +0.18 +0.23

HRRe 2.84 3.94 4.19 4.56 4.04 4.71 a For systems in Scheme 3.1.2.1. bFor intermolecular transfers as in Scheme 3.1.2.3. °C- H bond length in Transition state, in Angstroms. ^Charge on the migrating hydrogen atom in the transition state. eHarmonic Rate Ratio.

110 Tabic 3.2.2.1, shows the transition state properties for proton and hydride transfer reactions like, C-H bond lengths, C-H-C bond angles (ie. the angle of transfer in the transition state) and charges on the migrating hydrogen atom. Consi: dering the angle of transfer ( angle C-H-C) first, it can be seen that as the angle C-H-C increases with n = 0 to oo for the intermolecular cases, then AH* (in Table 3.2.1.2) decreases. For the highly bent transitions states corresponding to n = 0, 1, the enthalpy of proton transfer is, for the first time in the series, much greater for proton transfer than the corresponding hydride transfer reaction. In fact, for all except n = 3, AH* is much higher for intramolecular proton transfer than for the linear intermolecular transfer compared with the difference between intra- and intermolecular hydride transfer reactions. These results lend support to the view that hydride transfer reactions can tolerate bending more readily than proton transfer reactions. 132a, 146

For both proton and hydride transfer reactions, the charges on the migrating hydrogen are relatively small and fairly constant throughout the series as n varies from 0, 1,2, 3, II and oo. For the two hydride transfer systems however, the charges for reaction 1 are consistently higher than those for reactions 2. Similarly, the enthalpy of activation for reaction 1 is consistently smaller than for reaction 2 throughout the same series, and the C- H bond length in the transition state is longer for reaction 1 than for reaction two and effective concentrations for reaction 2 tend to be higher than those for reaction 1. In fact, for hydride transfer in reaction 2 and proton transfer in reaction 3, where the transition states differ only in the charge carried, the C-H bond lengths are very similar. Hence, there seems to be little evidence to support the idea of discrimination between proton and hydride transfer reactions in terns the degree of 'tightness* in the transition state.

3.2.2.1 Conclusions

For the proton and hydride transfer systems studied, the enthalpy of activation for highly bent hydride transfer reactions (as in the case where n = 0, 1) is actually smaller than for the corresponding proton transfer reactions. In fact, for all non-linear transfer the difference between the intermolecular and intramolecular enthalpies of activation is smaller for hydride transfer compared to the analogous proton transfer reactions. These findings lend support to the view that hydride transfer reactions can tolerate bending more readily than proton 111 transfer reactions. 132a, 146

3.2.3 The Anomalous Behaviour of Systems where R = (CH2)3

For the reactions 2 and 3 where R = (CH^ there are anomalies in the transitions state properties calculated. For example, the effective concentration for hydride transfer in reaction 2 appears to be lower than would be expected, whilst the enthalpy of activation, seems higher than expected. Conversely, for proton transfer in reaction 3, the effective concentration appears to be higher than expected from the general trends, whilst the enthalpy of activation seems lower than expected. For these systems where the transition states involve six-membered rings, anti-periplanar interactions can be important. Hence, potential energy contour maps were constructed from the two H-O-C-H dihedral angles in the transition states for proton and hydride transfer, for di-equatorial and equatorial-axial hydroxyl substituents. The resulting contour maps are shown in Figures 3.2.3.1, 3.2.3.2, 3.2.3.3 and 3.2.3.4.

The contour maps in Figures 3.2.3.1-4, show that the rotations of the two hydroxy substituents ie. anti-periplanar interactions, have important energetic consequences for the transition state. In fact, plots of the enthalpy of activation against the dihedral angle H-O-C- H for proton and hydride transfer reaction are shown in Figures 3.2.3.5, 3.2.3.6, 32.3.1 and 3.2.3.8. These plots show that the rotations of the two hydroxyl substituents in the transition state are clearly inter-dependent. Comparison of the plots for di-equatorial and equatorial-axial hydroxyl rotations reveal very little changes in pattern and intensity between these situations, for any one kind of transfer.

There is a clear difference in behaviour between the interactions of the two hydroxy groups in proton and hydride transfer reactions. For hydride transfer, there are two energy minima, at 90° and 270°, which are lower in energy and a maximum, at 180°, which is higher in energy when the two hydroxyl group dihedral angles are equal compared to the case when these dihedral angles are varied independently. In other words, coupled rotation of the two hydroxyl groups is favoured for hydride transfer in reaction 2. In contrast, for proton transfer, there are two maxima, at 126° and 234°, and a minimum, at 180°. All of

112 these are higher in energy when the dihedral angles are equal, compared to the case when these vary independently. In other words, coupled rotation of the two hydroxyl groups is not favoured for proton transfer in reaction 3.

3.2.3.1 Conclusions

For proton and hydride transfer in reactions 2 and 3, the case of R = (CH 2Xbehaves anomalously in terms of effective concentration and enthalpy of activation when compared to the other values in the series obtained by varying R. The cause of this behaviour is probably the result of the importance of the hydroxyl group rotations or anti-periplanar interactions in the six-membered ring transition states. For hydride transfer, the coupled rotation of the two hydroxyl groups is favoured, resulting in minima when the two dihedral angles equal 90° and 270°. In contrast, for proton transfer the independent rotations of the two hydroxyl groups is favoured, resulting in an energy minimum when one angle is 180° whilst the other is 0°.

113

Figure 3.2.3.1 Separation between contour Separation levels is 2.1 kcal mol'1 •* •* TS Anti-periplanar Interactionsin a ProtonTransfer TransitionState

114

2... c h H Figure S.2.3.2 TS * Separation between contour Separation levels is 3.0 kcal mol'1 Anti-periplanarInteractions in a HydrideTransfer TransitionState

115

CH H Figure 3.2.S.3 * T S Separation between contour Separation levels is 2.1 kcal mol'1 Anti-periplanarInteractions in a Proton TransferTransition State

116 Anti-periplanar Interactions in a

Hydride Transfer Transition State +

max coax

* T S - Separation between contour levels is 3.0 kcal mol'1

max 360 Figure 3.2.3.4 H H Rl=R2 Rl^R2 Figure 3.2.3.5 •

-t X10 R Anti-periplanar Interactions in a in Interactions Anti-periplanar Proton Transfer Transition State Transition Transfer Proton Plot ofAHfAgainst the Reaction Co-ordinate, R

118 Figure 3.2.3.6 Rl=R2 RI54R2

Anti-periplanar Interactions in a in Interactions Anti-periplanar Hydride Transfer Transition State Transition Transfer Hydride Plot ofAHfAgainst the Reaction Co-ordinate, R

119

Anti-periplanar Interactions in a in Interactions Anti-periplanar State Transition Transfer Proton Plot ofAHfAgainst the Reaction Co-ordinate, R

120 Plot of AHf Against the Reaction Co-ordinate, R Anti-periplanar Interactions in a Hydride Transfer Transition State HO \/ /

Rl ^ R2 H R2

Rl= R2 H'

Figure 3.2.3.S 3.2.4 The Effect of Bending on the Transition States for Proton, Hydride and Radical Hydrogen Transfer Reactions

To investigate further the angle of transfer required for proton, hydride and radical hydrogen transfer reactions, the effect of bending on the linear transition states for reactions 5-8 was tested. The original linear transition states are shown Figure 3.2.4.1. As a comparison, the transition states for transfer in the rigid caged systems, R = n, are shown in Figure 3.2.4.2. Figure 3.2.4.3 shows plots of the enthalpy of activation for proton, hydride and radical hydrogen transfers against the C-H-C angle in the transition states. From the plots, proton transfer in reaction 3 is revealed to be the most sensitive to bending. The enthalpy of activation for proton transfer is the lowest compared to both hydride and radical hydrogen transfers when the transfer is linear ( ie. angle C-H-C = 180°). However, the enthalpy for proton transfer rapidly increases to overtake the hydride transfers at lower angles (ie. angle C-H-C less than 120°). Of the two hydride transfer reactions, reaction 2 is less sensitive to small angles than reaction 1. Radical hydrogen transfer seems to behave more like hydride transfer on bending, the enthalpy of activation for this process rising slowly, as angle C-H-C is lowered, though this enthalpy is always much greater than for the other charged transfer reactions.

3.2.4.1 Conclusions

Overall, intermolecular proton, hydride and radical hydrogen transfer reactions are predicted to proceed by linear transition states by the MNDO calculations discussed here. Ab initio calculations by Houk et. a/. 132a and by us in Chapter 2, have suggested some degree of bending for hydride transfer reactions. The results here suggest that hydride and radical hydrogen transfer reactions can tolerate bending more easily than proton transfer reactions.

122 Figure 3.2.4.1

123 Figure 3.2.4.2 Transition States For R = II ForR = States Transition

124 Figure 3.2.4.3 Hydride Transfer Proton Transfer Radical H TransferHydride Transfer Energy In The TS xio Angle in C—H—C TS Variation Of Activation With Angle Of Transfer

125 3.2.5 Molecular Orbital Effects on Proton, Hydride and Radical Hydrogen Transfer Reactions

In order to rationalise the fundamental differences in behaviour between the different kinds of hydrogen transfer, for example, the different responses to bending, we looked at the molecular orbitals of these reactions. For proton and hydride transfers, the HOMOs (highest occupied molecular orbitals) were studied, whilst SOMOs (singly occupied molecular orbitals) were studied for radical hydrogen transfers. Figure 3.2.5.1 and Figure 3.2.5.2 show the HOMOs for hydride transfer in the transition state for the linear case, R = oo, and for the highly bent transition state, R = (CH 2)q for reactions 1 and 2. The HOMO for the linear transition state for both hydride transfer systems, has considerable electron density with spherical symmetry, on the migrating hydrogen. This spherical symmetry of the HOMO for hydride transfer may be a clue to explaining the tolerance of hydride transfers to bending. Indeed, comparison of these HOMOs with those for hydride transfer in the case R = (CH 2)o shows that for the latter highly bent transition states, the orbital pictures are relatively unaltered. In fact, comparison of the two different hydride transfers of reaction 1 and 2, for R = (CH 2)o> shows that in the former, the electron density is very much localised on the migrating hydrogen, whereas in the latter, the density is more delocalised to include the neighbouring carbon atoms. This difference may account for the higher tolerance of the transition state for reaction 2 to bending than that of reaction 1.

The HOMOs of proton transfer in the two cases when R = and when R = 0, are shown in Figure 3.2.5.3. Not surprisingly, these orbitals are quite different to the previous ones for hydride transfer. This time, there is no electron density on the migrating hydrogen but instead, two p-type orbitals aligned towards the C-H-C axis, on the two axial carbon atoms. Such an arrangement is no longer so resilient towards bending, since bending would lead to destructive interference between the two p-type orbitals. Such effects are illustrated by a comparison of the linear transition state with that of the highly bent transition structures for R = (CH 2)q (Figure 3.2.5.3). The LUMO (lowest unoccupied molecular orbital) for proton transfer is very similar to the HOMO for hydride transfer. This is as expected since if occupied, the LUMO for proton transfer would then become the HOMO for hydride transfer.

126 The SOMO for radical transfer for R = is shown in Figure 3.2.5.4. For the linear transition state, the SOMO is quite similar to the proton transfer case, in that there is no electron density on the migrating hydrogen. Instead, there are two p-type orbitals on the carbon atoms of the C-H-C axis. However, unlike in the proton transfer case, the p-orbitals are oriented perpendicular to the C-H-C axis. Such an arrangement is more resilient to bending than in the proton transfer case as can be seen fromthe SOMOs of transition states for R = (CH 2)0 and (CH2)i (Figure 3.2.5.5).

3.2.5.1 Conclusions

The differences in behaviour between proton, hydride and radical hydrogen transfer can be rationalised in terms of the differences in shape of the calculated molecular orbitals of these reactions.

127 R = 0 -3.80 eV Figure 3.2.5.1 H H — H— Transfer HOMOs / > f r H H = oo c / R H s / H -3.68 eV

128 Figure 3.2.5.2 H- Transfer HOMOs

129 f X f H H R = 0 -.96 eV HOM'Os Figure 3.2.5.3 H+ Transfer R = oo -1.77 eV

130 Radical Hydrogen Transfer SOMO

\

Figure 3.2.5.4 Radical H Transfer SOMOs

-8.23 eV -8.06 eV R = 0 R = 1

Figure 3.2.5.5 3.2.6 Kinetic Isotope Effects for Proton and Hydride Transfer Reactions at 323K

As a measure of the kinetic isotope effect, harmonic rate ratios (HRR) were calculated from vibrational frequencies within the ideal gas, rigid rotor, harmonic oscillator approximation (See Chapter 6). Table 3.2.2.1 shows the HRRs for proton and hydride transfer reactions. Considering the classical contribution to the kinetic isotope effects only (ie. HRRs), the kinetic isotope effects are much larger for proton transfer than for hydride transfer as expected, 139 since the transition states for hydride transfer are always more bent than in the corresponding proton transfer systems. However, the HRR for both proton and hydride transfer systems are very similar for reactions 2 and 3 for n = 0, 1 where R = (CH2)n- For hydride and proton transfer within reactions 2 and 3, the HRRs increase slightly with increase in angle of transfer, whereas for the hydride transfer in reaction 1, there is not so much variation of HRR with angle of transfer. Figure 3.2.6.1 shows the variation of the kinetic isotope effect (ie. HRR) with angle of transfer in the transition state, for proton and hydride transfer reactions.

Our calculated HRRs for hydride transfer in reaction 1 for R = II, can be compared to experimental kinetic isotope effects measured by Watt et. a/.136 These workers studied similar hydride transfers to that for reaction 1 for R = II, where the models differed only by the presence of one or more methyl groups substituted for hydrogen. There is good agreement between our results for hydride transfer for reactions 1 and 2 and those of Watt et. fl/.,136 despite differences due to the methyl groups and secondary isotope effects for pre-equilibrium in some of the Watt models. This suggests that tunnelling is not important for these reactions in solution and so reinforces our disregard of it in the present context. In fact, Watt et. al.136 \n their work, also carried out some calculations at the ab initio STO- 3G levels for these reactions, where they calculated HRRs and tunnelling corrections. Their calculations predicted that tunnelling should be important (eg. being 40% at 25 °C) though agreement between their calculated and measured kinetic isotope effects was only achieved if tunnelling was disregarded.

133 Figure 3.2.6.1 For Reaction 2 -For Reaction 1 - -For Reaction 3 in the Transition State Angle C—H—Cxio-, Plot of HRR Transition Against Angle State of Transfer in the

134 3.2.6.1 Conclusions

Calculated harmonic rate ratios for proton and hydride transfer reactions predict the kinetic isotope effects of proton transfer to be greater than the corresponding hydride transfer reactions, except for the most highly bent transition states, where HRRs are predicted to be similar for both reactions. In general, our calculated HRRs for hydride transfer for the system, R = II, are similar to those measured by Watt et. alA36 jn their study on similar models.

135 CHAPTER 4

An SCF-MO Study of the Relative Barriers to Inversion and to Ring Opening in Three- membered Ring Carbanions

136 4.1 INTRODUCTION

The study of three-membered heterocyclic rings, containing oxygen, nitrogen and sulphur, has been of considerable theoretical as well as practical interest. Such studies have not only elucidated the nature three-membered heterocyclic compounds but have also made an important contribution to the widespread application of such compounds in organic synthesis. Particularly, investigations on inversion barriers provide useful information as to the stereochemical outcome of reactions involving three-membered rings. Such information is vital to the syntheses where the setting up of chiral centres is of importance.

The questions concerning the structure of three-membered cyclic compounds have been the subject of many papers. In particular from the earliest studies, 167 the similarity between cyclopropane and its heteroanalogues, and alkenes had been pointed out. These similarities were supported by force constant comparison by Linnett*^ between cyclopropanes and heterocycles, and ethene. Such a study led to the conclusion that there was a greater similarity between the valence states of the carbon atoms in cyclopropane and its heteroanalogues to those in alkenes compared with the corresponding states in alkanes.

In fact, the results of electron diffraction studies on aziridine, 169-70 oxirane and thirane^O suggested that the transformation of an acyclic compound into a three-membered heterocycle was accompanied by a rearrangement of the hybrid states of the atoms forming the ring. The C-C bond lengths in all these compounds were found to be similar and intermediate between the C-C bond length in diamond (1.554 A) and the C=C bond length in ethene (1.344 A). In particular, the distance between the carbon atoms in cyclopropane heteroanalogues is close to the length of the central bond in butadiene (1.483 A), which can be regarded^ as a simple sp^-sp^ bond. From such evidence, it is inferred*^ that there are two types of endo bonds in cyclopropane heteroanalogues. The two-carbon skeleton having an enhanced ^-character compared with the saturated C-C bond, whilst, the two remaining endo-bonds to the heteroatom having overlap of orbitals which is intermediate between lateral 7t-bonding and terminal G-bonding.

In addition, there is indirect evidence172 to suggest that in three-membered heterocyclic rings, the heteroatom has an enhanced ^-character of its lone-pair electrons compared to

137 heterocyclic four- and five-membered compounds and acyclic amines, ethers, and sulphides. Such .y-character could be interpreted as evidence 172 for conjugation in cyclopropane heteroanalogues. In other words, the differences in strain energy between cyclopropane 173 (25 kcal mol'1) and aziridine, oxirane and thirane (14, 13 and 9 kcal mol" *) could be rationalised 172 jn terms of stabilisation of the cyclic states by the 7C-electrons of the heteroatom. From the order of stability, the 7t-bonding would be greatest for the least strained heterocycle ie. thirane.

There have been a number of quantitative SCF-MO calculations as well as experimental studies for oxaziridines, aziridines and cyclopropyl systems. Those studies dealing with cis-trans isomerisation will be discussed here. Wayner et. al174 investigated the nature of the one-electron two-centre bond in cyclopropyl radicals by calculating the cis-trans isomerisation by ab initio calculations at the STO-3G and 4-31G levels. Geometries were optimised with some symmetry constraints and the resulting structures were not characterised by force constant calculation. Nevertheless, from the barriers to cis-trans isomerisation calculation for various conformations and electronic states for the cyclopropyl radical, these workers concluded that there was substantial bonding between the carbon termini of the cyclopropyl radical.

Paquette et al. 175 have studied the configuration stability of silyl substituted cyclopropane radicals and carbanions. They found that a-silyl substituted carbanions underwent reaction with retention of configuration whereas, a-silyl substituted radicals underwent reaction with racemization. From this result, they concluded that d^-p^ overlap is not as important is for a-silyl substituted cyclopropane carbanions as itfor the corresponding radicals. Other studies with l-chloro!76> l-fluoro^^ l-isocyanol77} l-methoxy!76} and l-methyl!78 cyclopropyl anions and oxirane carbanion!79 also report retention of configuration. Similarly, other workISO confirms that cyclopropyl radicals are not usually configurationally stable.

For nitrogen, it is well established that inversion barriers at that centre are substantially increased if the nitrogen is part of a three-membered ring.l^l in fact, Lehn et.al.^%2 carried out a theoretical study on the inversion barriers at nitrogen in aziridine and

138 oxaziridine, at the ab initio SCF-LCAO-MO level of theory. They used a basis set with 9 s and 5 p Gaussian orbitals for carbon, nitrogen and oxygen and 4 s orbitals for hydrogen. The calculated barriers to inversion at nitrogen were 18.3 and 32.4 kcal mol -1 for aziridine and oxaziridine, respectively, indicating that an oxygen substituent in the ring raises the barrier. Similar conclusions were reached in a study by Ono et. al.,183 who investigated the effect of the phenyl substituent on the nitrogen barrier in substituted oxaziridines. These workers deduced that the inversion barrier at nitrogen decreased in the order oxaziridines > in aziridines > amines. In fact, the barriers in certain oxaziridine derivatives are sufficiently high to permit resolution of enantiomers. 184

Kostyanovsky et. a/. 185 measured the inversion barriers at nitrogen for N-acyldiaziridines and N-acyloxaziridines, by NMR. Their results indicated that the rate of inversion is quite slow and was consistent with an earlier observation 186 that amide conjugation diminishes when the nitrogen is incorporated in a three-membered ring. From the NMR signals, values of the free energy of activation was calculated for nitrogen compounds, the temperature varying with the system studied. Further details of the chemistry of oxaziridines and nitrones can be found in a review by Sliwa.187

The order of nitrogen inversion in aziridines can be rationalised!72 in terms of the increased repulsion between the lone-pair electrons on the adjacent nitrogen and oxygen atoms in the transition state for inversion. In addition, the necessarily small C-N-C valence angle in the three-membered state favouring sp3 rather than sp2 hybridisation at the nitrogen atom, must also play a part in the high barrier. Such strain can also be used to rationalise the configurational stability of cyclopropyl carbanions which generally react with retention of configuration, 175-9 as discussed earlier. However, also mentioned earlier, cyclopropyl radicals are generally not configurationally stable 180 and hence other factors besides strain must be important in controlling the barrier to inversion in three-membered rings. 181

139 Scheme 4.1.1 0 N il L-----XH L/\-----XH Ax„ A 4.1 4.2 4.3 4.4

a ; X = C' b ; X = N c ; X = 0 +

In the specific case of three-membered ring systems (see Scheme 4.1.1), alternative reactions involving ring opening are possible, and if reversible, they would also lead to loss of configuration at the tri-substituted centre. See Schemes 4.1.2 and 4.1.3.

Scheme 4.1.2

Y ~ H2C = X / 2>XH 4.5 4.1a,b, Y = O a X = C, Y = O 4.3a, Y = S b X = N +,Y = 0 c X = C, Y = S

For example, oxaziridines (4.1b) are known to undergo electrocyclic ring-opening under thermal or photochemical conditions to give nitrones (4.5b) by cleavage of the C-01^7 bond. In a theoretical s t u d y 188 of the relative stability of carbonyl imines (R 2C=0-NR), it has been speculated that such species could under favourable circumstances, be formed by C-N cleavage in oxaziridines. For oxirane and thirane carbanions (4.1a and 4.3a), cleavage of the C-0 or C-S bond would result in the formation of an enolate or thioenolate anion (4.5a and 4.5c). An apparently less likely alternative is C-0 bond cleavage giving the oxyanion carbene (4.6).

140 Scheme 4.1.3

H 4.1a 4.6

Although a number of quantitative SCF-MO calculations have been carried out for oxaziridines, aziridines and cyclopropyl systems, no such study of oxirane carbanion (4.1a) has been reported. In particular, no comparative study of the barriers to inversion and ring opening have been made. Hence, we decided to carry out such a theoretical study for the iso-electronic series of heterocycles shown in Scheme 4.1.1, ie. structures 4.1-4.4, using both the MNDO and ab initio SCF-MO procedures. AMI calculations were also carried out for cyclopropyl carbanion (4.4) as a means of assessing the conflicting results obtained by MNDO and ab initio methods for this system. All the species were studied in their unsolvated states, no effects of solvation with counter-ions such as Li+ were considered at this stage.

141 4.2 RESULTS AND DISCUSSION

4.2.1 Barriers to Inversion at the Centre X in Compounds (4.1)-(4.3)

Table 4.2.1.1 Calculated Barriers to Inversion (in kcal mol'l) at the Centre X in Compounds (4.1)-4.3)

Method x = c- Barrier X = N Barrier X = 0 + Barrier

MNDO 9.17 31.96 =14° 0 0 0 /\ L— OH MNDO// /\ 42.03 ^— NH 28.79 + 3-21G*

MNDO 1.38>> 22.28,a 28.45b 16.91b NH NH NH /\ L—OH MNDO// /\ 27.46b t-— NH 17.84,a 26.99b + 16.35b 3-21G*

MNDO 1.03 23.32 9.24 S S S /\ f\ £— OH MNDO// ZA 19.76 t-— NH 15.65 + 5.21 3-21G* a Refers to the cis isomer. b Refers to the trans isomer.c 0 -0 distance not optimised.

The barriers to inversion in the isoelectronic series^compounds shown in Scheme 4.1.1 were calculated at the MNDO level with single-point energy calculations at the ab initio 3- 21G* level. From the results in Table 4.2.1.1, good agreement between the two methods is seen in the inversion barriers at X = N and 0 +, whereas there is considerable disagreement

142 between the two methods for the carbanion systems. Basis set quality is known to be particularly important in such negatively charged systems, and it is possible that the minimal valence basis set employed in MNDO has serious deficiencies in calculations for such carbanions. Indeed, it has been previously notedly that the electron affinities of carbanion systems can be seriously in error if the negative charge is localised predominantly on one carbon.

Comparing the inversion barriers at centre X, the order of decreasing barrier height is X = C" > N > 0 +, for the same substituents comparing across the table. Such behaviour can be rationalised in terms of the repulsion between the centre X and ring substituent (O, N or S) in the planar transition state. This repulsion would be expected to be greatest for the negatively charged carbanion systems in the planar transition state and would be expected to be the least for the positively charged 0 + systems. For inversion at any one centre, the order of barrier heights decreases from O > NH > S as ring substituents. Again, this trend follows the order of decreasing electronegativity and hence decreasing repulsion in the transition state between the inverting centre and the ring substituent.

4.2.1.1 Conclusions

Single-point calculations at the the ab initio 3-21G* level (with MNDO optimised geometries) show considerable disagreement in the calculated barriers to inversion at carbanionic centres (for systems 4.labc). In contrast, there is agreement between the corresponding results for inversion at isoelectronic nitrogen (N-H) and oxygen (+0-H) centres. The MNDO calculated inversion barriers for the carbanionic systems, 4.labc, seem to be too low in comparison to the ab initio 3-21G*//MNDO results and experimental studies which indicate that such species are configurationally stable. 175-9

4.2.2 The Relative Barriers for Inversion and Ring Opening for the Carbanion Systems (4.1a)-(4.3a),(4.4)

For the oxirane carbanion, 4.1a, loss of configuration at the carbanion centre could proceed in three ways, (i) by direct inversion at this atom, (ii) by the reversible ring opening to give the enolate 4.5a, or (iii) by the formation of the carbene, 4.6. Figure 4.2.2.1, shows a 143 MNDO potential energy contour map where the processes (i) and (ii) are clearly distinguished. The lower of the two pathways corresponds to direct inversion at the carbanionic site via a planar transition state. There are two transition states of higher energy which lead to the formation of the enolate, 4.5a, from both reactant and product, which in this case are chemically identical. For pathway (iii), a reaction path study with the H 2C-O bond length as reaction co-ordinate, shows that the formation of the carbene, 4.6, is a relatively high-energy pathway, AH* = 33.7 kcal mol'1. In addition, this reaction is significantly endothermic, AH = +28.7 kcal mol-1, compared with the enol anion 4.5a, which is formed exothermically, AH = -61.5 kcal mol-1. It should be noted, however, that the presence of elements such as lithium can stabilise carbenoid systems ^ 0 and hence, the presence of a Li+ counter-ion may make the formation of the species such as 4.6 more favourable.

In accordance with the trends discussed in section 4.2.1, the barrier to inversion in the related aziridine carbanion, 4.2a, is predicted to be much lower by both MNDO and 3- 21G*//MNDO results. For the thirane carbanion, 4.3a, the MNDO potential energy contour map is shown in Figure 4.2.2.2. Although, this map is qualititavely similar to that for oxirane carbanion, this time the transition states for both inversion and cleavage to the thioenol, 4.5c, are very reactant-like and both barriers are very small. For the cyclopropyl carbanion, 4.4, the MNDO potential energy contour map as seen in Figure 4.2.2.3 is quite different from the previous cases of oxirane and thirane carbanions discussed. In this case, there is no transition state corresponding to direct inversion but instead, a minimum in energy corresponding to a planar configuration for the carbanion in the ground state. This last result is surprising to say the least, since numerous derivatives of cyclopropane carbanions have been experimentally demonstrated to be configurationally stable. ^5 p0T this system, the calculations were repeated at the AMI level. Figure 4.2.2.4 shows the AMI energy contour map for inversion and ring opening in the cyclopropyl carbanion. In fact, this contour map is chemically identical to the previous MNDO one ie. even AMI predicts a minimum in energy corresponding to a planar configuration for the carbanion in the ground state. The AMI calculated barrier to ring opening of the cyclopropyl carbanion of 19.12 kcal mol -1 is again similar to the MNDO calculated barrier, 18.58 kcal mol"1.

144 Figure 4.2.2.1 Separation between contour levels is 2.8 kcal mol'1 * T S 270 „ 100 Energy Contour Map ForInversion and Ring Opening

1 4 5 Energy Contour Map For Inversion and Ring Opening !

146 Figure 4.2.2.3 MNDO Results Separation between contour T* S levels is 3.5 kcal mol'1 Energy Contour Map ForInversion and Ring Opening

147 148 For the ab initio studies, single-point calculations were initially carried out at the fully optimised MNDO geometries, using a 3-21G* basis set (Table 4.2.1.1). As discussed earlier, a qualitative difference between MNDO and these ab initio results occurs only in the case of the carbanion systems. The MNDO calculated barriers to inversion are much lower than those from the ab initio study. This is probably due to the inadequacy of the minimal valence basis set employed for the MNDO method. Indeed, it has been previously noted 189 that the electron affinities of carbanion systems can be seriously in error if the negative charge is localised predominantly on one carbon.

To investigate the case of carbanion systems further, geometry optimisation at the single determintantal ab initio level was carried out at the 3-21G* and 6-31+G basis set level. Corrections for zero-point energy and for electron correlation by Moller-Plesset^ theory up to the fourth order (RMP4) were also included. The results for the barriers to inversion and ring opening for systems 4.1a-4.3a, and 4.4 are shown in Table 4.2.2.2 (overleaf). For the MNDO results, the barriers to ring opening are much higher than those corresponding to direct inversion for all the systems and the height of the barrier to inversion decreases from oxirane (4.1a) > aziridine (4.2a) > thirane (4.3a) > cyclopropyl (4.4) carbanions. For the ab initio 3-21G //3-21G level, both the barriers to inversion and cleavage (to give 4.5a,b,c) are much higher than the MNDO values. In the case of the oxirane carbanion (4.1a) both barriers to inversion and ring opening in the enolate path, have similarly high values. For aziridine and cyclopropyl carbanions, the barrier to direct inversion is still lower than that for the ring cleavage process, whereas the opposite now applies in the case of the thirane carbanion (4.3a). In fact, the order of decreasing energy in the barrier to loss of configuration is now different to that predicted from MNDO and is, oxirane (4.1a) ~ aziridine (4.2a) > cyclopropyl (4.4) > thirane (4.3a).

149 Table 4.2.2.1 Calculated Barriers for Inversion at Centre X = C" and for Ring Opening to (4.5) for compounds (4.1)-(4.4) in kcal mol ' 1

O NH S A IX ZA ZA_ A_

Method invb roc invb roc invb roc invb roc

MNDO 9.17 25.39 1.38 13.79 1.03 3.58 0 18.58

3-21G* 45.00 44.50 37.69 43.57 36.08 16.22 20.78 38.54

RMP4/ 46.66 26.94 36.54 26.11 34.22 9.31 19.38 26.89 3-21G*

ZPE/ -1.19 -1.79 -1.47 0.41 - 1.21 -0.35 -1.12 -2.15 3-21G*

6-31+G 36.16 34.71 31.46 39.39 34.11 11.80 17.65 35.34

RMP4/ 35.18 18.23 29.52 23.98 30.15 3.52 16.54 25.36 6-31+G

AS*>298/ -0.68 0.66 -0.14 0.22 -0.36 0.20 -0.88 -0.87 3-21G* a AS^298 cal K- 1mol-1. b Transition-state barrier for inversion at atom X in kcal mol"1. c Transition-state barrier for ring opening to give (4.5a) in kcal mol-1.

150 The effects of the zero-point energy corrections are very similar for both inversion and ring opening at the 3-21G* level. This is not the case for the electron correlation corrections however, single-point calculations at the RMP4 level with 3-21G* geometries, have a much greater effect on the barrier to ring opening than to direct inversion. Inclusion of electron correlation lowers the barrier to ring opening considerably whilst hardly affecting the barrier to inversion at all. This is not so surprising, since direct inversion involves no bond breaking, whereas ring opening involves considerable electronic re-organisation from the c to the k network. In fact, the effect of including electron correlation is great enough to change the order of preference between ring opening and direct inversion. For the RMP4//3-21G* results, for all the carbanion systems except cyclopropyl, the barrier to ring opening is now less that the barrier to direct inversion. The order of decreasing barrier to loss of configuration however, remains the same as for the 3-21G* results which do not include electron correlation.

Optimisation at the higher 6-31+G level was carried out since carbanion species have been shown 191 to require the addition of diffuse p functions to reproduce inversion barriers accurately. The effect of optimisation with this larger basis set is to decrease the barriers to both direct inversion and ring opening compared to the results for 3-21G* optimised geometries. Again the effect of including electron correlation at the RMP4/6-31+G//6-31+G level, is a much more significant lowering of the barrier to ring opening than that to direct inversion. The results remain qualitatively similar to those for the 3-21G* basis set, in terms of the relative order of preference between the inversion and cleavage processes for the various systems.

Finally, the effect of the entropy of activation, calculated for the 3-21G* optimised geometries, is very small on both the inversion and ring opening reactions. Hence, for these reactions, AG* and AH* will be very similar. However, there does appear to^a systematic difference between the entropy of activation for inversion, which is slighly negative, and ring opening, which tends to be positive. The only exception is the thirane carbanion (4.3a), where both entropies are negative.

151 4.2.2.1 Conclusions

The MNDO calculated barriers for loss of configuration at the carbanionic centres in systems 4.1abc, are much lower for direct inversion than for ring opening (via 4.5abc). In fact, for the cyclopropyl carbanion, 4.4, MNDO predicts a planar ground state. This is in direct conflict to experimental studies which indicate that such carbanions are configurationally stable. 175-9 An alternative pathway to ring opening for the oxirane carbanion via the oxy-anion carbene, 4.6, seems unlikely from the high barrier (AH^ = 33.7 kcal mol'1) and significantly endothermic reaction (AH = +28.7 kcal mol-1) compared to ring opening via 4.5.

For the ab initio results, at the highest level of theory (RMP4/6-31+G//6-31+G), the barrier to loss of configuration at the carbanion centres by ring opening is much lower than the barrier to simple inversion, for 4.1abc. The cyclopropyl carbanion, 4.4, is no longer predicted to be planar and in this case, the barrier to simple inversion is less than that for ring opening. The order of decreasing barrier to loss of configuration is aziridine > oxirane > cyclopropyl > thirane, carbanions. The effect of including electron correlation causes a much greater lowering in the barrier to ring opening than in the barrier to simple inversion. Such a result is not surprising since, the process of ring opening involves a much greater degree of electron re-organisation than simple inversion where no bonds are broken. The calculated entropies of activation (at the 3-21G*) level are quite small so that there will be little difference between the enthalpy of activation and the free energy of activation.

The ab initio results predict that for the oxirane carbanion, the barrier to ring opening is much lower than the barrier to simple inversion. This result, of course, applies to the gas phase. In solution, it is highly probable that the carbanion centre will be associated with the positive counter-ion. This is likely to increase the barrier to direct inversion, and to decrease the barrier to ring opening by preferentially stabilising the enol anion product. Similar conclusions can also be drawn for the aziridine and thirane carbanion systems. The barrier to ring opening to the enolate 4.5a, for the oxirane carbanion (4.1a) is predicted to be sufficiently high for the species, 4.1a, to have a significant lifetime at low temperatures. For the sulphur analogue,4.1c, however, the calculations predict very low barriers for both ring opening and direct inversion. Hence, the thirane carbanion 4.3a, is unlikely to have a

152 significant lifetime in solution.

4.2.3 Transition State Properties for the Carbanions, 4.1abc and 4.4

Transition states for inversion and ring opening for the carbanion systems, optimised at the MNDO, and ab initio 3-21G* and 6-31+G basis sets are shown in Figures 4.2.3.1 and 4.2.3.2, respectively. The two ab initio basis sets yield similar transition-state structures for inversion (Figure 4.2.3.1) and for ring opening (Figure 4.2.3.2). However, significant differences between the MNDO and the ab initio structures are found. In particular, the carbanionic centre in cyclopropane carbanion (4.4) is correctly predicted to be non-planar at the 3-21G* and 6-31+G levels. The other major difference is in the calculated lengths of the cleaving bonds at the transition state for ring opening, for which the MNDO values are consistently shorter than the ab initio ones (Figure 4.2.3.2). It is noted that the ab initio geometries are obtained at the non-correlated RHF SCF level, whereas MNDO in principle includes electron correlation effects at the parametric level. It is possible therefore that geometry reoptimisation at the ab initio RMP4 level would give more comparable results, although the computer resources currently required to do this are prohibitive. It is also known47 that the MNDO method overestimates non-bonded nuclear repulsion terms at intemuclear distances of ca. 2.5 A. This tends to result in an overestimation of bond lengths in transition states. This particular failing (apparently corrected at the AMI level,47) does not explain the present differences between the two methods. In the thirane carbanion (4.3a) particularly, the MNDO C-S bond length for ring opening is predicted to be much shorter than the ab initio result. The correlated RMP4/6-31+G and MNDO methods do however agree in predicting very small barriers to ring opening in the thirane carbanion (4.3a).

153 Transition StatesInversionFor

154 Transition ForStates Ring Opening

1 5 5 Interestingly, there are no significant differences in the calculated geometries between the 3-21G* basis, which includes polarisation functions, and the 6-31+G basis set, which is augmented with a set of diffuse p functions. In particular, it is unlikely that d-type functions play a major geometric role in the sulphur system, 4.3a. The larger 6-31+G basis does however, result in lower absolute energies (see Table 4.2.3.1), and in lower barriers to inversion and to ring opening (Table 4.2.2.1).

Table 4.2.3.1 Reactant Energies for X = C' in Compounds 4.1-4.4 Reactant energy 0 NH S Method ZA ZA ZA A MNDOc 25.538 66.837a 45.502 56.927 67.757b

3-21G*d -151.31297 -131.58007a -472.59906 -115.68642 -131.57238b

RMP4/ -151.63053 -131.89048a -472.92318 -115.98494 3-21G*d

ZPE/ 0.04428 0.0577 l a 0.04280 0.06926 3-21G*d

6-31+Gd -152.12534 -132.29322a -474.84425 -116.31765

RMP4/ -152.46941 -132.62652a -475.10514 -116.63534 6-31+Gd a trans. b cis. c kcal mol-1. d Atomic units, 1 atomic unit = 627.52 kcal mol-1.

156 Both the MNDO and ab initio methods predict electrocyclic ring opening of cyclopropyl carbanion to proceed with conrotation, giving an allyl carbanion. This is consistent with the Woodward-Hoffman rules, and is similar to the result previously found for the ring opening of oxadiridine to give a carbonyl imine.175 Although the transition state corresponds to conrotation, it does not have the C 2 axis of symmetry associated with this mode. The strongly pyramidal nature of the C“ atom in the cyclopropyl carbanion (4.4) means that the only element of symmetry common to both reactant and product is the plane bisecting this atom. This precludes C 2 symmetry, and since the selection rules disfavour Cs symmetry, the transition state can only have Ci symmetry. Indeed, when C 2 symmetry is imposed, a stationary point with two negative roots in the force constant matrix is located, the second such root corresponding to out-of-plane motion of the central hydrogen atom.

The charge densities on the carbanionic carbon in systems 4.1-4.4, are shown for MNDO and ab initio optimised geometries in Table 4.2.3.2, overleaf. In contrast to the geometries and energies given by the semiempirical and ab initio procedures, the calculated charge densities are similar for both methods. For oxirane (4.1a), aziridine (4.2a) and cyclopropyl (4.4) carbanions, the calculated charge at the carbanion centre increases for inversion and decreases for ring opening to an allylic system relative to the reactant system. In the former case, the lone pair on carbon becomes orthogonal to the C-C framework and hence more localised, whereas in the latter case, the charge migrates to the two terminal atoms of the allylic system. The one exception is the thirane 4.3a, for which both MNDO and ab initio methods predict an increase in charge on the carbon at the transition state for allylic ring opening. In this respect, as in several others, the thirane is anomalous. However, even in this case, the charge on the carbanionic centre is much greater for the transition state for inversion than for ring opening. In the case of thirane, the enhanced 5-character of the sulphur lone pair and the degree of 71-bonding in the sulphur-carbon bond, are the greatest of all in the series of ring substituents studied for the carbanion series. This may explain the ’anomalous’ behaviour the thirane carbanion relative to the others.

157 Table 4.2.3.2 Charges on the carbon at the X = C” centre in compounds 4.1-4.4 u X 1 II Type MNDO 3-21G* 6-31+G of Charge

0 Or -0.41 -0.31 -0.49 Qin -0.78 -0.48 -0.91 qro -0.33 -0.09 -0.34

NH qr -0.62 -0.38 -0.64 qin -0.78 -0.49 -1.05 qro -0.45 -0.23 -0.38

s /\ qr -0.54 -0.32 -0.41 qin -0.73 -0.65 -0.73 qro -0.57 -0.45 -0.58

A qr -0.78 -0.43 -0.59 qin - -0.60 -1.08 qro -0.44 -0.46 -0.38 qr : Charge on C at inverting centre in reactant. qjn : Charge on C at inverting centre in the transition state for inversion. qjo : Charge on C at inverting centre in the transition state for ring opening to give 4.5.

158 4.2.3.1 Conclusions

There are differences in the predicted geometries of the transition states for inversion and ring opening for the carbanion series of compounds, 4.1-4.4. In particular, the MNDO geometry for the cyclopropyl carbanion is predicted to be planar at the carbanion site, whereas ab initio 3-21G* and 6-31+G methods correctly predict non-planar geometries. In addition, the MNDO calculated lengths of the cleaving bonds in the transition state for ring opening are consistently shorter than the corresponding ab initio calculated bond lengths. In this respect, the ab initio values do not include the effect of electron correlation, whereas MNDO does include correlation effects, albeit at the parametric level. Hence, better agreement may result if the ab initio geometries are optimised at the RMP4 level. In contrast, there is better argeement in the calculated charges on the C' centre between the MNDO and the ab initio 6-31+G level. In general, relative to the carbanions, the charge on the C' centre increases in the transition state for inversion and decreases in the transition state for ring opening. The only exception to this case is in the thirane system, where both transition state charges are greater than in the reactant carbanion. In this case as in the others, the charge on the C' centre in the transition state for inversion is still greater than that for ring opening. The different behaviour of the thirane system compared to the other carbanions, in this case as well as in other instances, may be due to the enhanced s- character of the sulphur lone-pair and hence, the degree of 7t-bonding involved in the S-C bond, relative to the other heterocycles. 172

159 The Mechanism of Ethene Biosynthesis: A MNDO and AMI SCF-MO Theoretical Study

160 5.1 INTRODUCTION

Ethene is a hormone!92 0f vjtai importance to plants since it controls a diverse range of plant functions. In fact, ethene causes seeds to sprout, flowers to bloom, fruit to ripen and fall off, and leaves and petals to shrivel and turn brown. This simple alkene is a natural product of plants and is biologically active in small amounts, ie. less than 0.1 ppm of the gas has been known to cause a response in plants. Since the discovery of ethene as a plant hormone, exogenous ethene has been used in agriculture to ripen produce uniformly, in order to make harvesting more efficient. A better way to achieve such efficiency would be to regulate the plant's own production of ethene. However, such a goal would necessitate the understanding of the mechanism of ethene biosynthesis.

The accepted*^ pathway to ethene biosynthesis synthesis is thought to be :

Scheme 5.1.1 methionine ------> S-adenosylmethionine ------> ACC------> ethene where ACC represents 1-aminocyclopropane-l-carboxylic acid. The role of ACC in the mechanism was first inferred by Adams and Y a n g , 194- who found that 14C labelled methionine was efficiently converted to ethene when apple tissue was incubated in air, but not when incubated in nitrogen. In the latter case methionine was metabolised to ACC instead. They also found that labelled ACC was converted into ethene by apple tissue incubated in air. More rigorous evidence for the involvement of ACC as the precursor to ethene was provided by Baldwin et. a/., 195 who showed that tetradeuterated ACC was converted into tetradeuterioethene in apple slices.

Although much is k n o w n 193 about the first two steps in the biosynthesis of ethene in (Scheme 5.1.1), it is the details of the conversion of ACC into ethene that still remains to be established. For example, to date there is no authentic isolated cell-free ethene-forming enzyme. The characteristics of the conversion of ACC to ethene in vivo suggest that this enzyme is membrane-associated, labile and disrupted by various treatments. 196 However, there is evidence that the reaction is oxygen dependent, 194 and that it is inhibited by Co2+197j by temperatures above 35°C,196 light, and uncouplers such as 161 dinitrophenol.193 Nevertheless, since the discovery that ACC is the immediate precursor to ethene, many mechanisms 198 have been postulated for this step. For example, Adams and Yang, 194 initially postulated that oxidase-derived hydrogen peroxide cleaves ACC's cyclopropane ring, releasing a two carbon framework as ethene. They postulated that the rest of the ACC molecule is converted into carbon dioxide, formic acid and ammonia ie.

Scheme 5.1.2

ACC HOOH-*- [O] + H20 P H+

Later on, 193 these workers also noted that ACC could be oxidised systematically either by hydroxylation followed by dehydration, or by dehydrogenation of the amino group to yield a nitrenium intermediate which can then fragment spontaneously into ethene and products :

Scheme 5.1.3 [O] OH 4- CN ACC V-A COOH COOH

In connection with this mechanism, Pirrung and McGeehan^^ investigated the roles of the

162 nitrenium ion as well as nitrene as possible intermediates for the biosynthesis of ethene by studying the thermal, photochemical and acid catalysed decomposition of 1- azidocyclopropanecarboxylic acid. The latter was found to convert to ethene, carbon dioxide and cyanide via singlet nitrene and nitrenium ion intermediates. Such a process was rationalised by these workers as proceeding by a concerted, chelatropic reaction.

In the meantime, Baldwin et. al.195 who showed rigorously that ACC is indeed the source of ethene, postulated an alternative mechanism involving an enzyme-bound imine intermediate, ie.

Scheme 5.1.3 C02H Oxidation N-Enzyme NII-Enzyme

T HC02H C = N — Enzyme

After these early postulates on the mechanism of conversion of ACC into ethene, the stereochemistry of this reaction was investigated by Baldwin et. a ll®0 and Pirrung^Ol, independently. Baldwin et. showed that the conversion of equal mixtures of the two isomers of cis- or rra«s-2,3-dideutero-l-aminocyclopropanecarboxylate by apple slices gave, in both these cases, a 1 : 1 mixture of cis- and rra«^-l,2-dideuterioethene. In contrast, the chemical oxidation of the same substances proceeded with complete retention of configuration, leading to cz.y-l, 2-dideuterioethene and rm«5-l,2-dideuterioethene, respectively. Hence, these workers concluded that the complete lack of stereospecificity seen in the biosynthetic production of ethene should proceed by a completely different mechanism compared to the stereospecific chemical pathway. Similarly, Pirrung^Ol found that complete scrambling of stereospecificity occurred with cfy-2,3-dideutero-l- aminocyclopropanecarboxylate, both by oxidation in the natural system and by electrochemical means. On the basis of these results, Pimmg^Ol proposed a sequential single-electron-transfer pathway to explain the mechanism of ethene formation in both the

163 natural and electrochemical systems (see Scheme 5.1.4). In this mechanism, the loss of stereochemistry can be explained by the free-rotation of the carbon-carbon bond that evolves into ethene. The products of this mechanism would be ethene and cyanoformic acid which can decarboxylate into carbon dioxide and cyanide. In fact, this is the first mechanism that correctly predicts that cyanide and not formate, as previously believed, is a product of ethene biosynthesis. Evidence^O^ for cyanide formation in plant tissue has recently come to light. This mechanism is also consistent with EPR evidence^OS for carbon centred free-radicals formed in other ACC model oxidations. Pirrung and McGeehan^O^ have further probed the mechanism of ACC to ethene biosynthesis by measuring secondary kinetic isotope effects for 2,2,3,3-tetradeuteriocyclopropanecarboxlic acid in both natural and electrochemical systems. From their results on the electrochemical system, they infer that the rate-limiting step in both these reactions is the production of the amine radical cation from 1-aminocyclopropane-l-carboxylate (Scheme 5.1.4).

Scheme 5.1.4 K > 5x10 s -1 ------

CO e' >-

CO + NCCO 2H NH +.

Several workers205-7 have studied the conversion of alkyl-substituted ACC to alkenes in plant systems. Most notably though, Baldwin et. al.207 have reported the stereochemical outcome of reactions with modified substrates ie. alkyl-substituted ACC. They found that the conversion of a series of specifically 2-alkylated-3-deuterated-l- aminocyclopropanecarboxylates by apple tissue resulted in unequal mixtures of cis- and rra«.y-l-deuterioalk-l-enes, ie. substituted alkenes were formed with net stereochemical 164 bias. This is in contrast to the case of tetra-deuterated ACC where complete scrambling^OO- 1 of stereochemistry was observed. Also, in accord with previous studies by Yang, 20 5 they found that not all stereoisomers of a particular alkyl-substituted ACC were effective substrates. This was explained by Yang205 jn terms of an enzymatic site for alkene formation where the enzyme could only accommodate a certain stereochemistry of the substrate.

To explain the net stereochemical bias in these systems, Baldwin et. al.207 postulated a stepwise enzymatic mechanism of cyclopropane ring opening in which stereochemical equilibration is faster than the subsequent bond breaking process. This mechanism is illustrated with methyl-substituted ACC in Scheme 5.1.5 (see overleaf). Baldwin et, al?^n suggest that cleavage of the cyclopropane ring can occur at both C(l)-C(2) and C(l)-C(3) and that the C(l)-C(3) cleavage would result in complete scrambling of stereochemistry by rotation around C(2)-C(3), if this process is faster than the subsequent cleavage of the remaining C(l)-C(2) bond. Hence, they suggest that the net stereochemical bias derives only from initial cleavage at C(l)-C(2), where the proportion of cis- and trans-alkene formed would depend upon both the equilibrium of the pair of radicals formed by initial cleavage, as well as the topology of the enzyme.

5.1.1 Theoretical Studies on the Mechanism of ACC to Ethene Conversion

It has been suggested208 that enzyme reactions have more in common with gas phase reactions where solvent interactions are absent, than reactions in solution where sucli interactions dominate. Now, the understanding of an enzyme reaction would involve the as isolation and characterisation of the enzyme as wellAanalysis of the individual steps involved in the overall reaction and the determination of the mechanisms of the latter. Hence, Dewar208 outlines the important contribution that theoretical calculations using semi-empirical methods, in particular AM 1,47 can make to the latter half of this process, by providing information about essentially 'gas-phase' reactions. He208 stresses that such an application of a quantum mechanical method to problems in biochemistry is now feasible with the advent of AM 1.47 This is a 'third generation' quantum mechanical method, where the weaknesses of its highly popular predecessors, MNDO and MINDO/3, in the area of

165 hydrogen bonding have been overcome. Scheme 5.1.5 i) Initial C(l)-C(3) Cleavage -----^racemisation

In accordance with this view, we decided to apply the MNDO and AMI theoretical methods to the study of the mechanism of biosynthesis of ethene from ACC. In particular, we studied Pirrung's mechanism^Ol as shown in Scheme 5.1.4 which involves a sequence of single-electron-transfers and ring opening of a zwitterion radical intermediate, 5.3. In 166 addition, wc studied Baldwin's^? hypothesis which involves ring opening a ' nitrogen based radical species, 5.2.

Scheme 5.1.6

5.2 RESULTS AND DISCUSSION

5.2.1 The Energetics of Pirrung's and Baldwin's Hypotheses

Scheme 5.2.1.1 Pirrung's Mechanism^Ol

Transition .-...... ^ state, 5.7

2 e*

+ NCCO2H NH 5.6 +. Table 5.2.1.1 The Energetics of Pirrung and Baldwin Mechanisms2bl>207 jn |{ca| moi-l

Method AW s j a .5.! AHb5.7.5.3.1 AHc5<4_3>1 AHds.s.5.4 AH °S.6-5.S ^^pr-5.6

MNDO 71.27 22.23k,6.87* 4.91 -64.60 66.00 -30.11

AMI 78.34 22.14^, 4.78* -14.51 -50.70 61.28 - 20.68

Method AHS5#2-5.1 AH^s.s.5.2 AHi5.5.5.2

MNDO 34.04 10.18 -17.53

AMI 35.08 6.60 -21.96 a = AHf(5.3) - AHf(5.1) b A H ^ .s.j.j = AHf(5.7) - AHf(S.3.1) c AHs.4-5.3.1 = AHf(5.4) - AHf(5.3) d AH5.5.5.4 = AHf(5.5) - AHf(5.4) e AH5.6.5.s = AHf(5.6) - AHf(S.5) f AHpr.5.6 = AHf(ethene) + AHf(formic acid)- AHf(5.6) g AH 5.2.5.1 = AHf(5.2) - AHf(5.1) h = AHf(Transition state for ring opening from 5.2) - AHf(5.2) 1 AH5 5.5 2 = AHf(5.5) - AHf(5.2) J Bond length in Angstroms. ^ Transition state with 1 negative eigenvalue and correct form for vibrational eigenvectors. 1 Transition state with 1 negative eigenvalue but not the correct form for vibrational eigenvectors.

168 Table 5.2.1.2 Calculated Heats of Formation and Miscellaneous Properties of Intermediates in Pirrung's Mechanism

Method 5.3.1 5.4 5.5 5.6 5.7

MNDO 0.75 0.76 0.76 1.02 1.35a,0.76b CN bond length .0 1.45 1.32 1.29 1.24 1.41a,1.32b Atom on which 0 C(l) C(1) C(1),C(3) C(l),C(3),Oa the bulk spin resides. C(l)b Total charge on the -0.40 -0.94 -1.16 -0.44 -0.40a,-0.94b two oxygen atoms. AH(f)d -14.86 -9.95 -74.67 -8.56 7.37a, -8.00b

AMI 0.76 0.76 0.76 1.00 1.18a,0.76b CN bond length .0 1.43 1.31 1.29 1.23 1.38a, 1.31b Atom on which 0 C(l) C(l) C(1),C(3) C(l),C(3),Oa the bulk spin resides. C(l)b Total charge on the -0.40 -0.89 -1.12 -0.43 -0.43a, -0.89b two oxygen atoms. AH(f)d -11.25 -25.76 -76.46 -15.18 10.89a, -6.47b a Transition state with 1 negative eigenvalue and correct form for vibrational eigenvectors, h Transition state with 1 negative eigenvalue but not the correct form for vibrational eigenvectors. c Bond length in Angstroms. d AH(f) is the MNDO or AMI calculated heat of formation.

169 Calculations of the heats of formation of the structures shown in Scheme 5.2.1.1 were carried out to assess the feasibility of this mechanism, which was originally proposed by Pirrung.201 Baldwin's mechanising^ differs from that of Pirrung's^Ol in that initial ring opening occurs with the radical anion, 5.2, which opens out to form 5.5. The remaining pathway leading to the formation of ethene is then identical to that shown in Scheme 5.2.1.1. The results of these calculations are shown in Table 5.2.1.1. For the molecules involved in the Pirrung mechanism, values of the CN bond length, the identity of the atom on which the bulk spin resides, and the total charge on the oxygen atoms is included in Table 5.2.1.2, to help characterise the electronic configuration of the molecule. This is necessary because the steps involving the loss of an electron can lead to more than one possible electronic configuration. For example, for loss of one electron from 5.1, can also lead to 5.3.1 as well as 5.3 (see Scheme 5.2.1.1). An UHF calculation based on the geometry of 5.3 resulted in finding an electronic configuration corresponding to 5.3.1, as can be seen by the fact that most of the spin resides on O, in this case (see Table 5.2.1.2). Such a finding indicates that 5.3.1 is the ground state. Hence a calculation of the electronic configuration of 5.3 would involve exciting an electron specifically from a nitrogen lone- pair orbital to an oxygen orbital in a multi-configuration calculation. In the absence of solvation, or stabilisation by an enzyme, 5.3.1 is likely to remain the ground state, and the energy of the excited state, 5.3, is likely to be high, since zwitterions are not stabilised well in the gas phase. Hence, in the present unsolvated system, the energy of 5.3.1 is likely to be a lower bound to that of 5.3. However, in the presence of solvent or enzyme, the energy of 5.3 could well decrease sufficiently so that it then becomes the new ground state. Such a possibility would require further investigation.

In the meantime, factors such as the position of spin density, total charge on the oxygen atoms and the CN bond length indicate that the electronic configurations of 5.4 - 5.6 are indeed as depicted in Scheme 5.2.1.1. For example, the value of CN bond length in 5.3.1 is slightly shorter than that found for a sp3 hybridised single CN bond (1.47A209), whilst for 5.4 and 5.5, the CN bond length falls in the double bond range (1.28A209). For 5.6, CN bond length is shorter than an average double bond length. For the ring opening of 5.3.1, two transition states were located by both the MNDO and AMI methods. Force constant analysis showed that both had one negative eigenvalue, however, only the higher

170 energy of the two transition states had the correct form of vibrational eigenvectors in both the MNDO and AMI case. Figure 5.2.1.1 shows these transition states with the vibrational eigenvectors, at both the MNDO and AMI levels.

Considering first the results for Pirrung's mechanism^ 1, it is interesting to compare the differences in the results between MNDO and AMI calculations. Major differences in the energies of 5.4 and 5.6 occur, with the MNDO energies for these zwitterionic molecules being much higher than the corresponding AMI values. However, both methods agree on the value of the enthalpy of activation of the ring opening of 5.3.1. Comparison of these results with the Baldwin mechanism^O? shows that the latter is certainly a feasible alternative. For the Baldwin mechanism207 the energy of intermediate 5.2 is much lower than that of the intermediate, 5.3.1. Also, the MNDO and AMI enthalpies of activation for ring opening of 5.2 are certainly lower than the corresponding MNDO and AMI enthalpy of activation for the ring opening of 5.3.1. In this respect, the Baldwin mechanism is consistent with the kinetic investigations of Pirrung,204 which suggests that the ring opening of 5.3 is a very fast process and so it is not the rate determining step. Since the energy of the excited state 5.3 is likely to be higher than that of 5.3.1 in the gas phase, the enthalpy of activation would be expected to be much lower with respect to 5.3 than the ground state, 5.3.1.

The ring opening of the intermediates 5.2 and 5.3.1 were studied by two-dimensional contour maps with the following reaction co-ordinate scheme :

Scheme 5.2.1.2

171 o v Figure 5.2.1.1 MNDO' Transition MNDO' States

172 Figures 5.2.1.2, 5.2.1.3, 5.2.1.4 and 5.2.1.5 show the potential energy contour maps for the MNDO and AMI ring openings of intermediates 5.2 and 5.3’,1 respectively. All the contour maps for both MNDO and AMI, and for ring opening of 5.2 and 5.3^are very similar. They all show four transition states corresponding to stepwise ring opening but no transition states for concerted ring opening of both bonds (Rj and R 2). Hence, this process is confirmed to be stepwise as postulated by Baldwin^^ and Pirrung.^Ol The AMI results are important in this respect because it has been found^O that MNDO tends to favour stepwise reactions more than AMI, but in this case both methods are in qualitative agreement about the reaction mechanism. The AMI contour map for the ring opening 5.3.1 shows some discontinuities. This is probably due to changes in electron configuration which can readily take place in 5.3.1 and the zwitterions 5.7 and 5.4. Since such discontinuities occur at the AMI level but not at the MNDO level, this may indicate that at the AMI level, there is more than one electronic configuration lying close to the electronic ground state.

Although the contour maps calculated using the reaction co-ordinate plan in Scheme 5.2.1.2, are chemically very informative about the nature of the reaction, transition states were difficult to locate from these maps. Frequent attempts to locate transition states from these contour maps resulted in convergence to the reactant geometries. Hence, in order to locate the transition states involved in the ring opening process, a new set of reaction co­ ordinates were defined as follows : Scheme 5.2.1.3

Figures 5.2.1.6 and 5.2.1.7 show the contour maps generated by such reaction co-ordinate schemes for the MNDO ring opening of 5.2 and 5.3, respectively. These contour maps also concur with the previously calculated ones in that there are no transition states corresponding to concerted ring opening.

173 Figure 5.2.1.2 Separation between contour levels is 3.7 kcal mol-1 * TS MNDO Results

174 kcal mol-1 2.8 Figure 5.2.1.3 * TS Separation between contour levels is AMI Results

175 Figure 5.2.1.4 * TS Separation between contour levels is 3.9 kcal mol”1 2.8 MNDO Results 1.4

176 2 nh 2 R Figure 5.2.1.5 *TS Separation between contour levels is 4.7 kcal mol-1 AMI Results

177 C02" NH Figure 5.2.1.6 * TS Separation between contour levels is 3.7 kcal mol-1 2.4 m a x MNDO Results R i 1 A

178 Figure 5.2.1.7 * TS Separation between contour levels is 3.9 kcal mol-1 MNDO Results

179 5.2.2 Conclusions

In Pirrung's mechanism, loss of an electron from 5.1 resulted in an electronic configuration as in 5.3.1 and not 5.3 in a UHF calculation. Hence, in the gas phase, 5.3 is an excited state of the 5.3.1 ground state. This situation may change in solution or in the presence of an enzyme, where 5.3 may be stabilised sufficiently to become the new ground state. Hence, a detailed study of the effect of solvation on 5.3 and 5.3.1 may prove enlightening.

Comparison of the mechanism of ring opening to ethene from Baldwin's^? an(j Pirrung's^Ol intermediates, ie. 5.2 and 5.3.1 (in this case 5.3.1 was used as a model for 5.3), shows that Baldwin's mechanism involves relatively lower energy intermediates. The enthalpy of activation of the ring opening process is is much smaller for the Baldwin intermediate, 5.2, than for 5.3.1. Of course, this situation may change if the elctronic configuration 5.3 is calculated. The result of ring opening of 5.2 is in accordance with the isotopic rate studies carried out by Pirrung,204 which indicate that the ring opening step is a fast process. Interestingly, there are major differences in the MNDO and AMI predicted energies of the open-chain radical zwitterionic intermediates, 5.4 and 5.6, in Pirrung's mechanism^Ol (Scheme 5.2.1.1). The MNDO heats of formation for these species are much higher in energy than the corresponding AMI values. This may highlight the weakness of the MNDO method for calculations involving such zwitterionic species, whereas the lower energy AMI results may indicate that any such difficulties seem to have been overcome at the AMI level.

Contour maps for the ring opening of both 5.2 and 5.3.1, in the Baldwin and Pirrung mechanisms, respectively, indicate that the ring opening is a completely stepwise process at both the MNDO and AMI levels of theory. The contour maps reveal that concerted ring opening is high-energy process, there being no transition state ( ie. saddle-point) corresponding to concerted bond breaking. Hence, the stepwise mechanism involving the ring opening of either 5.2 or 5.3, would be in accord with the observed^OO-l scrambling of stereochemistry for deuterium labelled ACC.

180 5.3 The Effect of Alkyl Substituents on the Mechanism: Future Theoretical Studies

An interesting future project would be the theoretical investigation of the factors affecting the stereochemical outcome of alkyl-substituted ACCs. For example, Baldwin et have postulated a mechanism for the observed net stereochemical bias in the enzyme transformation of methyl-substituted mono-deuterated ACC (5.8) into cis- and trans- alkenes, see Scheme 5.1.5. They postulate that the observed net stereochemical outcome is due to significant initial cleavage at the C(l)-C(2). A pre-liminary MNDO study of the ring opening of this substituted ACC (5.8) as in Scheme 5.1.5, is shown in the form of a potential energy contour map in Figure 5.3.1. The following reaction co-ordinate scheme was used:

5.8

The contour map (Figure 5.3.1) is again qualitatively similar to the others calculated for the ring opening of 5.2 ie. the reaction is stepwise, there being no transition states for concerted ring opening. However, in this case the contour map no longer has diagonal symmetry. In this case, the transition state for cleavage of C(l) - C(2) is now three contour levels (ca. 3 kcal mol“l) lower in energy than the corresponding transition state for C(l) - C(3) cleavage. Although such a result is well within the limits of error for the MNDO method, this does tend to lend support to Baldwin’s^^ hypothesis. A thorough investigation of this subject would involve the location of the transition states for ring opening from the contour map, and investigating the barrier to inversion of configuration at C(2) or C(3) in the intermediates formed by cleavage of one C-C bond. Comparison of such inversion barriers with the energy of the transition state for cleavage of the remaining

181 Figure 5.3.1 Me" Separation between contour levels is 2.9 kcal mol 1 MNDO Results 1.4

182 C-C bond would allow assessment of Baldwin's^? hypothesis for the enzyme-free system. Of course, determining the mechanism of ACC to ethene conversion in the absence of enzyme, ie. in the gas phase as mimicked in theoretical calculations, leads to indirect information about the role that the enzyme must play in such reactions.

183 Computational Procedure

184 6.1 THE BENZILIC ACID REARRANGEMENT

6.1.1 Geometry Optimisation and Location of Transition States at the MNDO or AM.1 levels

Calculations were carried out using the MNDO SCF-MO method^ with a standard s i p valence basis set and the closed shell single determinantal restricted Hartree-Fock approach. In studying the migration of group R from from the sp 3 to the sp 2 carbon atom, two reaction co-ordinates were defined; Rj, the projected horizontal distance of the group R along the C-C bond, and R 2 corresponding to the vertical height of group R from the C-C bond: Scheme 6.1.1.1

(X)(0)C ----1----C(0H)(0-) ------

R i Such a co-ordinate system was employed previously in studying migrations in carbon radicals.82 Within such a definition, Rj corresponds to direct [1,2] migration of the group R, and R 2 to dissociation / recombination of R_. Enthalpies of formation were calculated at fixed values of R^ and R 2, and the central CC bond length was fixed to prevent dissociation for all but the hydrogen migration systems, full optimisation of the remaining 3N-9 variables was used to construct a contour map. Approximate transition states were located as saddle points on these contour maps. These approximate geometries were then located exactly with full optimisation of all geometric parameters, by minimising the sum of the squared scalar gradients.73 Such structures were characterised as transition states by calculating the cartesian force constant matrix55,211 an(j showing that this had only one negative eigenvalue with the correct form of the eigenvectors. Where transition states differed only in the nature of the group R or X, previously optimised structures could be used as a starting point in the refinement of the saddle-point. Similarly, all ground states ie. reactants, products and intermediates, whether closed-shell or open-shell were located exactly by full optimisation of all the 3N-6 geometric variables. Again the cartesian force constant matrix was calculated^ >2 H and the ground states were characterised by the 185 absence of any negative eigenvalues.

For the mechanism where a single electron transfer occurs before migration of group R to give either 2.5 (Scheme 2.1.3.1, path b) or 2.10, the excited state wavefunction was modelled using a triplet state, calculated using the spin unrestricted HF method.^ Whilst clearly an approximation, such a procedure should give a quali tative indication of the characteristics of such species and the expected substituent effects. The UHF procedure however cannot be used to model quantitatively the conversion of biradicals such as 2.5 to 2.3, since a conversion from the triplet to singlet manifold occurs. The contamination of the triplet calculation by mixing with other states in a UHF calculation, was monitored by use of the spin expectation factor, S2.212 The expectation value for is S(S+1), where S is the total spin. Hence, for a triplet should 2.0. For all but the aromatic systems studied, < 2.2, for the aromatic systems > 2.2 ie. spin contamination is only important in the case of the aromatic systems.

The second single electron transfer route, pathway c (Scheme 2.1.3.1), involves intramolecular proton transfer in 2.5 resulting in the formation of singlet biradical 2.6, followed by migration to form 2.4. Since such a process occurs entirely on the singlet manifold, it could be quantitatively studied within the UHF formalism. For a biradical, should be 1.0, in practice values of <1.1 for non-aromatic systems, and > 1.1 for aromatic systems. Again contamination of the biradical state by mixing with higher spin states is only significant for the aromatic systems. Apart from the case of glyoxal and phenylglyoxal, calculations of the biradical species, 2.6, were fraught with difficulties in achieving self-consistence.

For the migration of group R in the mechanism involving epoxide intermediates, approximate transition states were located by means of reaction path calculations. An appropriate reaction co-ordinate, Rj, was incremented and the total molecular energy determined with optimisation of the remaining 3N-7 geometric variables :

186 Scheme 6.1.1.2

The reaction co-ordinate, is the distance of the migrating group, R, from a reference point and it corresponds to the direct [1,2] migration of the group R from C(2) to C(l). Such a scheme was employed since the MNDO package used (ie. Ampac^l^) does not allow the use of negative bond lengths or angles. Hence, the use of a reference point [to the right of C(2)] allows the migration of group R from C(2) to C(l), by increasing the distance of group R from the reference point. Again the approximate structures were further refined with full optimisation of all geometric parameters, minimising the sum of the squared scalar gradients^ and characterised as transition states by calculating the cartesian force constant matrix, 55,21 1 ancj showing that this had only one negative eigenvalue whose vectors corresponded to the correct transformation of reactant to product.

For monosubstituted glyoxals, the various enol intermediates derived from proton abstraction fromA5a* (see Scheme 2.1.1.3), were located by full optimisation of all 3N-6 geometric variables, initially at the MNDO SCF-MO level of theory. Characterisation as ground states was again carried out by force constant calculation as for all ground states calculated. For this system, full optimisation was also carried out at the ab initio level of theory, with the initial starting guess as the MNDO optimised geometries.

6.1.2 Geometry Optimisation and Transition State Location at the Ab initio Level

Ab initio calculations were carried out for the benzilic acid rearrangement of glyoxal, the Cannizzaro rearrangement of formaldehyde, and for the enolate intermediates derived by proton abstraction from 5 (see scheme 2.1.1.3). The MNDO optimised stationary points were reoptimised at the 3-21G level using the method reported by SchlegelJ^ and were characterised by inspection of the calculated Hessian matrix, within the GAUSSIAN 82 program system.61 Additional optimisations of these stationary points were made with a 187 larger basis set, 6-31G, and also with the diffuse p functions augmented 6-31+G basis set. Further calculations including electron correlation corrections up to the RMP4 level^ were made at the 6-31G and 6-31+G optimised geometries.

6.1.3 Calculation of Thermodynamic Properties from Molecular Vibrational Frequencies

The calculation of the harmonic Cartesian force constant (Hessian) matrix of a chemical system is of vital importance for several reasons. Firstly, such information is useful in characterising stationary points, both transition states and ground states. Furthermore, vibrational frequencies can be calculated from the mass-weighted Hessian matrix.214 From the vibrational frequencies, a wealth of thermodynamic information can be derived eg. heat capacities, entropies and isotope effects. Although, such a procedure has its drawbacks in terms of limited accuracy compared to experimentally determined vibrational frequencies, nevertheless, there are important situations where theoretical estimates of vibration frequencies could be very useful. Entropies of activation, equilibria involving transient species at high temperatures, and the thermodynamic properties of large molecules are examples of such cases.

From the MNDO, and where appropriate ab initio, fully optimised geometries, the force constant matrix^, 211 an(j the vibrational frequencies^^ Were calculated for all ground and transition states studied.

6.1.4 Calculation of Kinetic and Equilibrium Isotope Effects

The deuterium kinetic and equilibrium isotope effects were calculated for the hydride transfer reactions of glyoxal and formaldehyde by first calculating the vibrational frequencies for both the normal and isotopically substituted molecules from the force constant matrix.214

To calculate kinetic isotope effects, the gas phase, rigid rotor, harmonic oscillator approximation was employed. In other words, a gas phase molecule at temperatures high enough so that non-classical rotations could be ignored, was used as a model.

188 Furthermore, it was assumed that the 3 external translational and 3 external rotational (2 in the case of linear molecules, 0 in the case of atoms) modes could be factored out from each other and from the 3N-6 (3N-5 for linear molecules, zero for atoms) remaining internal degrees of freedom. In addition, it is assumed that these internal vibrations can be described with harmonic oscillator partition functions. The kinetic isotope effects based on this model and in the absence of tunnelling {ie. HRRs), were calculated from a program operating on the following theory53 :

For a reaction A + B ------> C5* h S2K s2B s 1C = HRR = V*1 (VP)(EXC)(ZPE) ...6.1

*2*1A j 1B S2C V*2 v p = 3n-6 A.n (u2i / )3n‘6 (v2i / «u) / 3n'7 c,n o>2i/ ou ) ...6.2

EXC =3n'6 AIT(1- e-'Jli/ l-e-')2i)3n‘6B;n (l - e-^li/1- e-«2i)^-3n'7^FKl - e-"li/ 1- e-«2i)

...6.3 ZPE = exp [ 3n‘6 A. 2 (du - i)2i) / 2] exp [ 3n'6B. 2 (u,i - v 2i) / 2] ... 6.4 exp [ 3n’7 Cj 2 (Vii -v2j) / 2]

Superscripts A and B refer to the reactants, whilst C refers to the transition state. The subscripts 1 and 2 refer to the light and heavy isotopes, respectively, s are symmetry numbers, refers to the frequency of the imaginary mode of the transition state, and Uj = hv[ / kT. VP refers to the vibrational product contribution the kinetic isotope effect; EXC is the excitation factor term which includes the product over that part of the harmonic oscillator partition functions which account for the population statistics of the upper levels; and ZPE is the zero point energy term which accounts for the difference in vibrational zero point energy between the reactants and the transition state. A correction for quantum mechanical tunnelling (£>t) was also included based on a simple

189 approximation by Bell ^7 for tunnelling through a parabolic barrier (Equation 6.5) :

2t = /W 2 sin (AM/2) where ]Ut = hv*/kT

h = Plank'sA constant T = absolute temperature

Similarly, equilibrium isotope effects were calculated from a program based on the following procedure^ 15 : For an isotopic exchange equilibrium : A + B* A* + B The equilibrium constant, Keq = VP x EXC x ZPE ... 6.6 VP = in {[a>i (A*) Di (B)] /[Vi (A ) Di (B*)]} ...6.7 EXC = in{[(l-exp(--ui(A))(l-exp(-'Oi(B*»] / [(l-expC-vKA^Xl-expC-UiCB))]} ...6.8 ZPE = exp {£[- dXA) - t>i(A*)] /2) ______...6.9 exp (S[--0i(B)--0i(B*)]/2)

A* and B* refer to the isotopically substituted species and the other symbols have the same meaning as in the case of kinetic isotope effects.

6.1.5 Calculation of Entropies

Entropies of activation were calculated for the migration of group R in the benzilic acid rearrangement for monosubstituted glyoxals, by calculating first the absolute entropies of the reactant and transition state from the vibrational frequencies. This was achieved by means of a computer program based on a procedure^l^ employing the rigid rotor, harmonic oscillator approximation. Neglecting the effects of rotation-vibration coupling, anharmonicity and centrifugal distortion, the absolute entropy (S®) of an arbitrary molecule without any internal rotations are given by the standard formulas of statistical mechanics as 190 the sum of the translational (Str®), rotational (Srot®) and vibrational (Svjb®) contributions :

so = s„o + srote + Svib9 ... 6.10 Su-0 = (5/2)/? Ill T + (3/2)/? In m + R In [(2tt /AO1-5 (k / A3)2-5] + (5/2)/? - R In p ...6.11

Sro[0 =/?/2 {3 In 7"- In ABC - 2 In 0 + In [ it (k/hc)3 ] + 3) ...6.12 For non-linear molecules. Srot0 = R [ In T + In (k l he) - In B - In a + 1] ...6.13 For linear molecules. Svibe = R iX g[ In [1- exp (-co [he / kT)] + (Rhc / kT) iZtCgpvj exp ( -w[hc / kT)) / (1- exp (-w\hc / kT))] ...6.14 A, B and C are rotational constants and are calculated from the corresponding moments of inertia. The terms w[ and gi are the vibrational frequencies (in cm-1) and their degeneracies, respectively.

6.2 A MNDO SCF-MO Study of Proton, Hydride and Radical Hydrogen Transfer Reactions

Calculations were carried^using the MNDO-SCF MO method^ with a standard sip valence basis set and the single determinantal restricted Hartree-Fock approach for closed shell systems, and with the unrestricted Hartree-Fock (UHF)69 method for open shell systems. Ground states, ie. reactants and intermediates,. were calculated by optimisation^all of* geometric variables with respect to the energy. They were characterised by the calculation of the force constant matrix, showing that this had no negative eigenvalues. Ground state energies of the reactants for the intermolecular reactions were calculated not as supermolecules but separately instead. In general, the lowest energy ground states were used, except where there was extra stabilisation from intramolecular hydrogen bond formation, as in the cases of R = (CH 2)2 and (CT^ since such interactions are likely to be disrupted in solution, so that all the systems should behave similarly in solution. Since all the transfers studied were symmetrical, transition states were located by imposing symmetry conditions ie. a plane of symmetry or C 2 axis. The lowest energy transition states located by such means were used. All the transition states were 191 characterised by calculation of the force constant matrix and showing that this had only one negative eigenvalue whose vectors corresponded to the correct transformation of reactant to product.

In studying the anti-periplanar interactions in the six-membered ring transition states, two reaction co-ordinates corresponding to the dihedral angles of the two OH groups were defined: Scheme 6.2.1 H

Enthalpies of formation were calculated at fixed values of Rj and R 2, for both equatorial and axial OH positions with optimisation of the other geometries variables placed under the constraints of preserving a plane of symmetry.

Thermodynamic quantities, and kinetic and equilibrium isotope effects were calculated from the normal vibrational frequencies as previously described in Sections 6.1.4 and 6.1.5.

6.3 An SCF-MO Study of the Relative Barriers to Inversion and Ring Opening in Three- membered Ring Carbanions

Initial calculations for the study of inversion barriers in three-membered ring systems as in in Scheme 4.1.1 were carried out using the MNDO SCF-MO method^ using a standard sip valence basis set with full optimisation of all geometric variables, using the spin- restricted (RHF) SCF procedure for the closed-shell systems involved. Two types of .reaction co-ordinate were defined; R^, the bond corresponding to the cleavage of the ring to give either the enol anion and R 2, corresponding to the dihedral angle giving the degree of co-planarity of the XH component with the three-membered ring:

192 Scheme 6.3.1 Y

H

Enthalpies of formation were calculated at fixed values of Rj and R 2, with full optimisation of the remaining 3N - 8 geometrical variables and used to construct a contour map. Approximate transition states were located either as saddle points on these contour maps, or from one-dimensional plots in which only Rj was varied. These approximate geometries were then located exactly by minimising the sum of squared scalar gradients^ and characterised as transition states by calculating the cartesian force constant matrix^ and showing that this had only one negative eigenvalue with the correct form for the eigenvectors. Initial estimates of the ab initio energies were obtained using a 3-21G* basis set at these MNDO geometries, employing the GAUSSIAN 82 program system.61 For the carbanion systems, major differences in the calculated MNDO and 3-21G* enthalpies of activation energy for inversion and ring opening were obtained by this procedure. In the case of the cyclopropyl carbanion, the MNDO ground-state geometry appeared qualitatively incorrect. Accordingly, the stationary points were re-optimised at the 3-21G* level using the method reported by SchlegelJS and again characterised by inspection of the calculated Hessian matrix. Further corrections to the ab initio energies were made at these geometries by either including a zero-point energy correction (see Section 6.1.4), obtained from the normal vibrational frequencies, calculated from the Hessian matrix, or by including electron-correlation corrections up to the RMP4 level. 19 Since C" species have been shown^l to require the addition of diffuse p functions to reproduce inversion barriers correctly, a further set of calculations using the 6-31+G augmented basis set were carried out, again with re-optimisation of the geometries and inclusion of RMP4 correlation corrections.

193 6.4 A MNDO and AMI SCF-MO Study of the Mechanism of the Biosynthesis of Ethene

The calculations were carried out using the standard MND0^4 and AM1^7 procedures, with full optimisation of all geometric variables, using the spin-restricted (RHF) SCF procedure for closed-shell systems and the spin-unrestricted (UHF) SCF procedure for open-shell systems. 69 All ground states were characterised by force constant calculation,^ showing that this had no negative eigenvalues. Transition states for the ring opening of 5.2 and 5.3.1 were initially located by calculating the energy of these systems as a function of the two reaction co-ordinates, Rj and R 2, and locating an approximate saddle point from a contour map: Scheme 6.4.1 1

u O

N ^CO i \

v n h 2 UK X• NH 5.2 5.3.1

co"2 co^ rX/ i a X I^ R i x n h 2 ^ N• H 5.2 5.3.1 Two sets of contour maps were calculated, ie. one set with two CC bond lengths as the reaction co-ordinates, whilst another set employed one CC bond length and a CCC bond angle as the reaction co-ordinates. Although the former set of contour maps were chemically more informative, the latter were better for the purposes of locating transition states. The approximate transition states so located were then refined by minimising the sum of the squared scalar gradients^ and characterised as transition states by calculating the force constant matrix^ and showing that this had only one negative eigenvalue, whose vectors corresponded to the correct transformation of the reactant to product.

6.5 Computers Employed in the Calculations

MNDO calculations were carried out on a CDC Cyber 855 running NOS2. Also, a VAX J 194 FPS running VMS was used, which included the AMPAC packagc^^ incorporating the MNDO and AMI methods. The supercomputers, CRAY1S and CRAY2S, were used for running ab initio calculations with the G82 packaged Tektronix 4010 / 4014 compatible terminals were used for graphic displays.

6.6 Plotting of Contour Maps and Molecular Orbitals

All the contour maps were plotted with the graphics package STEK^l? and displayed on a Tektronix compatible 4010 or 4014 monochrome terminal. Prior to plotting, the data for energy contour maps, was smoothed by 2-5 interpolations using a cubic spline fitting. Hardcopy was obtained on a Kingmatic flatbed plotter, and more recently on a Benson 1645 drum plotter. Molecular orbitals were plotted using a locally modified version of PSI / 77.218

6.7 Examples of Reaction Path Calcluations

Some examples of reaction path calculations, carried out in order to locate transition states are shown overleaf.

195 Reaction Path for Hydride Migration

vo O s o

AHf

R l Reaction Path for Phenyl Migration

VO AHf

R i Reaction Path for Phenyl Migration

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208 Commun., 1983, 290. 201 M. C. Piming, J. Am. Chem. Soc., 1983, 105. 7207. 202 G. D. Peiser, T.-T. Wang, N. E. Hoffman, S. F. Yang, H.-W. Liu and C. T. Walsh, Proc. Natl. Acad. Sci. U. S. A., 1984, 81, 3059; M. C. Piming, Bioorg. Chem., 1985, J5, 219. 203 R. Legge and J. Thomson, J. Plant Cell Physiol., 1982, 23,171. 204 M. C. Piming and G. M. McGeehan, J. Am. Chem. Soc., 1986, 108, 5647. 205 N. E. Hoffman, S. F. Yang, A. Ichihara, S. Sakamura, Plant Physiol., 1982, 70, 195. 206 M. C. Piming and G. M. McGeehan, J. Org. Chem., 1986, 51, 2106. 207 J. E. Baldwin, R. M. Adlington, G. A. Lajoie and B. J. Rawlings, J. Chem. Soc., Chem. Commun., 1985, 1496. 208 M. J. S. Dewar, Enzyme, 1986,26, 8. 209 G. March, Advanced Organic Chemistry,Wiley-Interscience, 1985. 210 D. Agrafiotis and H. S. Rzepa, unpublished work. 211 cf. J. N. Murrell and K. J. Laidler, Trans. Faraday Soc., 1968, £4, 1431. 212 M. J. S. Dewar and S. Olivella, /. Chem. Soc., Faraday Trans. II, 1979, 829. 213 A QCPE program written by J. P. Stewart. 214 E. B. Wilson, J. C. Decius and P. C. Cross, Molecular Vibrations, McGraw-Hill, New York, 1955. 215 S. Gabbay and H. S. Rzepa, J. Chem. Soc., Faraday Trans 2, 1982, 78, 671. 216 M. J. S. Dewar and G. P. Ford, J. Am. Chem. Soc., 1977, 99, 7622. 217 Written by H. S. Rzepa. 218 Written by J. P. Stewart.

209 LIST OF ABBREVIATIONS

A Angstrom units ACC 1-aminocyclopropane-l-carboxylic acid BSSE Basis Set Superposition Error EEE Equilibrium Isotope Effect EXC Excitation ; The contribution to the harmonic rate ratio due to thermal excitation into the upper levels of the oscillators. GTO Gaussian Type Orbital HOMO Highest Occupied Molecular Orbital HRR Harmonic Rate Ratio KIE Kinetic Isotope Effect LUMO Lowest Unoccupied Molecular Orbital MBS Minimal Basis Set MINDO Modified Intermediate Neglect of Differential Overlap MNDO Modified Neglect of Diatomic Differential Overlap NAD+/NADH Coenzyme Nicotinamide Adenine Dinucleotide NMR Nuclear Magnetic Resonance SET Single Electron Transfer SOMO Singly Occupied Molecular Orbital STO Slater Type Orbital TS Transition State VP Vibrational Product contribution to HRR ZDO Zero-Differential Overlap ZPE Zero-Point Energy m/rv Minimum ma>c M ax ifnum

210 PUBLICATIONS

1 1. Rajyaguru and H. S. Rzepa, /. Chem. Soc., Perkin Trans. 2, 1987, 359.

2 I. H. Rajyaguru and H. S. Rzepa, J. Chem. Soc., Perkin Trans. 2, 1987, in press.

3 I. H. Rajyaguru and H. S. Rzepa, /. Chem. Soc., Chem. Commun., 1987, in press.

Copies of reprints and submitted papers can be found in the pocket in the back page.

211 Rajyaguru and Rzcpa, page 1

Correspondence and Proofs to; Dr H. S. Rzcpa, Department of Chemistry, Imperial College, London, SW7 2AY.

A MNDO SCF-MO Study of the Mechanism of the Benzilic Acid and Related Rearrangements.

Indira Rajyaguru and Henry S. Rzepa*

Department of Chemistry, Imperial College, London, SW7 2 AY.

Abstract.— Mechanisms for the benzilic acid and related rearrangements have been studied using the MNDO SCF-MO method. The barriers to concerted closed shell [1,2] migration of a substituent R in the initially formed intermediate 2 were found to display a much smaller range of values than is commonly found in rearrangements involving cations or radicals. Both the formation of 2 and its subsequent rearrangement are predicted to be enhanced if either R or the non-migrating group X bears electron withdrawing substituents. The calculated N hydrogen isotope effect and Bell tunnelling correction for the rearrangement of glyoxal are both significantly larger than for the analogous hydride transfer in the Cannizzaro reaction of formaldehyde. Alternative open shell pathways involving intramolecular single electron transfers (SET) to the carbonyl group are relatively high in energy if the non-migrating substituent X is not capable of stabilising an adjacent radical centre {ie X=H), but are much more favourable for eg the case of X =Phenyl. When R bears an electron withdrawing substituent, electron transfer to this group is favoured. We suggest on this basis that an SET mechanism may explain the migration of hydrogen rather phenyl in the reaction of phenylglyoxal. Electron transfer is also favoured for the rearrangement of benzoin to benzilic acid itself, and is predicted to result in the formation of low energy cyclic intermediates. Intervention of a counter ion was modelled with Li(H20)2 coordinating to two oxygen atoms during migration. The migratory barriers were actually increased as a result, and it is suggested that the role of the counter ion in non-polar solvents is to alter the pre-equilibrium in favour of the intermediate 2. Rajyaguru and Rzcpa, page 2

The bcnzilic acid rearrangement is one of a general class of molecular rearrangements which involves the hydroxyl anion catalysed conversion of a 1,2 diketone (1) to an a hydroxy carboxylic acid (4). Such reactions arc thought to proceed by reversible addition of a nucleophile such as OH~ to a carbonyl group to give the intermediate 2, followed by a rate limiting intramolecular [1,2] migration of a formally nucleophilic R“ group to the second carbonyl group (Scheme 1, path a).1'2 The kinetics of such a reaction can be expressed by equation 1.

Under steady state conditions, the observed second order rate constant is given by the expression; fcobs = fci/O + k ^ / k 2) ...... 2

If k2 » 1, this reduces to;

&obs ?= K.&2 ....3 where K represents the equilibrium constant for the formation of 2. The composite nature of the observable rate constant means that it is difficult to interpret substituent effects in this reaction in terms of a single constant. Nevertheless, a wide variety of substituent effects on the overall rate of reaction have been established, and also the identity of the migrating group R for pairs of substituents R and X by means of isotopic labelling. One of the most unusual features of this reaction is the wide variety of formally nucelophilic groups that have been observed to migrate, including R=H, alkyl, K f ' aryl, acyl, aroyl, ester, amide and acid. In addition, a wide range of structural variation is tolerated.1’8 It is also interesting to contrast these results with the migratory properties of the corresponding electrophilic R+ groups, as known from the molecular rearrangements of carbocations and related species, and with a third category of migratory group formally intermediate to R~ and R+, the neutral radical species R-. We have previously studied the mechanism of such [1,2] migrations in radicals using the MNDO SCF-MO procedure, finding9 surprisingly different mechanisms according to the nature of the migrating radical R-. This led us to speculate whether similar diversity might be found in the migration of formal R“ groups. It has also been recently reported that the mechanism of the closely Rajyaguru and Rzcpa, page 3 related Cannizzaro reaction may involve an intermolecular single electron transfer (SET)10 followed by hydrogen atom migration, as an alternative to the transfer of a formal H“ group. Mechanisms involving a SET process have hitherto not been suggested for the benzilic acid type rearrangement. We report in this paper a theoretical study of this type of rearrangement, using the MNDO SCF-MO procedure.11 This method was previously used in our theoretical study of the Cannizzaro reaction12 and has been recently shown13 to predict transition state structures for a wide variety of molecular systems in reasonable accord with results obtained from more time consuming ab initio calculations. Computational Procedure. Calculations were carried out using the MNDO SCF-MO method11 with a standard s/p valence basis set and the closed shell single determinantal restricted Hartree-Fock approach. In studying the migration of a group R from the sp3 to the sp2 carbon atom, two reaction coordinates were defined; Rh the projected horizontal distance of the group R along the C-C bond, and R2 corresponding to the vertical height of group R from the C-C bond (Figure 1). Such a coordinate system has been previously employed by us in studying migrations in carbon radicals.9 Within such a definition, Ri corresponds to direct [1,2] migration of the group R, and R2 to dissociation/recombination of R“. Enthalpies of formation were calculated at fixed values of R! and R2, with full optimisation of the remaining 3N-8 geometrical variables, and used to construct a contour map. Approximate transition states were located as saddle points on these contour maps. These approximate geometries were then located exactly by minimising the sum of the squared scalar gradients14 and characterised as transition states by calculating the cartesian force constant matrix15 and showing that this had only one negative eigenvalue with the correct form for the eigenvectors. Where transition states differed only in the nature of the group R or X, previously optimised structures could be used as a starting point in the refinement of the saddle point. For the mechanism where a single electron transfer occurs before migration of group R to give either 5 (Scheme 1, path b) or 10, the excited state wavefunction was modelled using a triplet state, calculated using the spin unrestricted HF method.16 Whilst clearly an approximation, such a procedure should give a qualitative indication of the characteristics of such species and the expected substituent effects. The UHF procedure however cannot be used to model quantitatively the conversion of biradicals such as 5 to 3, since a conversion from the triplet to singlet manifolds occurs. Pathway c (scheme 1) involves intramolecular proton transfer in 5 resulting in the Rajyaguru and Rzcpa, page 4 formation of a singlet biradical 6, followed by migration to form 4. Such a process can be studied within the UIIF formalism, since it occurs entirely on the singlet manifold. Thermodynamic quantities and kinetic and equilibrium isotope effects were calculated from the normal vibrational frequencies as previously described17.

Results and Discussion.

7. The Rearrangement of Glyoxal to Glycolic Acid (R = X = H).— The simplest rearrangement involves the conversion of glyoxal (1, R=X=H) to glycolic acid (4, R=X = H) via a [1,2] intramolecular hydride shift.1 Phenylglyoxal (1, R=H, X=Ph)1 is also known to rearrange via a hydride shift rather than migration of the phenyl group. We chose to study the reaction of glyoxal for our initial studies in order to establish the general features of the MNDO potential surface for this type of reaction.

By analogy with the closely related Cannizzaro reaction12 a mechanistic scheme can be postulated in which not only a classical hydride transfer route can be envisaged (Scheme 1, path a) but also alternative routes involving a single electron transfer to the carbonyl oxygen atom, either before (path b) or after (path c) a proton transfer between the oxygen atoms. A potential energy contour map for path a reveals (Figure 2) that the rearrangement of (2, X=R=H) to (3, X=R=H) is a concerted process occuring via transition state 7, with a calculated barrier (Table 1) rather higher than that found for the Cannizzaro reaction itself12. This is to be expected for what is a highly non-linear hydride transfer, although the magnitude of the barrier is not inconsistent with the known rearrangement of glyoxal.1 The contour map reveals no dissociative pathway corresponding to formation of isolated H~ ion, in contrast to the results obtained previously for the rearrangement of ethyl radical,9 where two pathways corresponding to dissociative and concerted migration were apparent. Since single-electron-transfers (SET) have been implicated18 in a number of electron rich reactions, we also investigated several routes for the glyoxal reaction which include such a process. The first of these (Scheme 1, path b) corresponds to intramolecular electron transfer to the carbonyl group to give an excited singlet electronic state 5, followed by migration of R and then proton transfer. We modelled Rajyaguru and Rzepa, page 5 this route by calculating (5, X = R = H) as a triplet state using the spin unrestricted UIIF approximation,16 finding this species to be 39.4 kcal mol'1 higher in energy than 2. Since MNDO is known to predict excitation energies to be too low,19 this is likely to be a lower bound on the energy of the SET process, suggesting that a SET is improbable for the reaction of glyoxal itself. It is interesting to compare the triplet potential surface (Figure 3) for the conversion of 5 to 3 with the singlet surface previously calculated (Figure 2). A purely dissociative mechanism operates, with no corresponding concerted pathway available for rearrangement of 5. A second route (Scheme 1, path c) corresponds to initial proton transfer to give the biradicaloid species 6, followed by migration of group R=H. Species 6 was higher in energy than 5 by 22.3 kcal mol'1 and the potential surface for rearrangement to 4 is predicted to involve a concerted migration with an extremely early transition state (Figure 4) and a low barrier of 8.0 kcal mol'1. A third possibility, of electron transfer to the migrating group R itself, is excluded for the specific case of R = H. We conclude that the glyoxal involves an intramolecular hydride transfer and occurs on the ground state singlet surface, with a low probability of eg any single electron transfer process occuring.

2. Kinetic Isotope Effects for the Hydride Transfer in (1, R = X = H).— There has been much recent speculation on the degree of linearity of hydride transfers and whether tunnelling is important in such reactions.20 The rearrangement of glyoxal is of some interest since it can be considered as an almost unique example of a highly non-linear hydride transfer. In order to be able to compare the reaction of glyoxal with other types of hydride transfers, we have focused on the intramolecular conversion of 2 to 3 via transition state 7. The calculated primary hydrogen isotope effect for this step and the tunnelling correction factors derived from the formula given by Bell21 are shown in Table 2, together with the results previously obtained for the Cannizzaro reaction.12 Both the hydrogen isotope effect, and the tunnelling correction are significantly larger than was previously predicted for the relatively linear intermolecular hydride transfer in the Cannizzaro reaction.12 We have also calculated the equilibrium isotope effect on the pre-equilibrium step (cf eqn. 3).17 A small inverse isotope effect was obtained (Table 2), which is probably due to the weakening of the C-H(D)bond in 2 as a result of the ’oxy-anion’ effect.22 Overall, the observable isotope effect via the classical hydride transfer tvs- mechanism is predicted to Aquite large by the MNDO procedure.23 3. Migration of Group R via Transition State 7 and with X = H. — There has been considerable Rajyaguru and Rzcpa, page 6 discussion concerning the electronic factors which control the rate of the rearrangement 1 to 4.1 The equilibrium between 1 and 2 is clearly controlled by the ability of R to enhance the electrophilic nature of the a carbonyl group. On the other hand, the rearrangement of 2 to 3 entails the migration of a nucleophile towards an electrophilic centre, which it has been assumed will be enhanced if R is a good nucleophile. The observed enhancement by electron withdrawing substituents on the migrating group R has been rationalised1 by proposing an early transition state, such that the equilibrium constant K rather than the rate constant ki is the dominant term. However, such a simple Hammond type model may be over simplified, particularly if other mechanistic pathways involving eg electron transfer are possible, or if the transition state is a very ’tight’ one in which the nucleophilic characteristics of the migrating group are less important. The specific substituent effect on the rate constant /:2 can be studied theoretically by the expedient of calculating the barriers for the conversion of 2 to 3 and maintaining the second substituent constant (X=H, Table 1). We initially chose to study the route following path a in scheme 1 via transition state 7. One general feature that emerges (Table 1) is that the migration is generally concerted and does not involve the type of cyclic intermediates that were found previously for the corresponding migrations of eg vinyl or phenyl groups at the radical or cation oxidation level. The other notable feature is that the range of activation energies is much smaller than was found for eg the migration of R- or R+ groups (Table l).9 The calculated entropies of activation for the migration step (Table 1) tend to be similar in value and generally negative (with the exception of the COSH group), suggesting a relatively tight and symmetrical transition state (Figure 5). This symmetry is also reflected in the similar values of the calculated bond lengths to the migrating group R. (Table 1). The calculated overall charges on R range from -0.38 for R = H to -0.85 for R = COSH, with R=Ph having an intermediate value of ca -0.6. In general the larger negative charge is found on the better electron withdrawing groups. Unactivated alkyl groups such as methyl are predicted to have relatively high barriers to migration, although if the alkyl group is contained within eg a four membered ring the barrier is significantly reduced. It is indeed known that cyclobutane 1,2 dione rearranges in water without any added OH- catalyst.6 Cyclohexane 1,2 dione is also reported1 to undergo ring contraction slowly, but in general methyl groups are not observed to readily migrate.3,5,7 We note that such migration is predicted to Rajyaguru and Rzcpa, page 7 occur with retention of configuration at the carbon centre (Figure 5). The other substituent where MNDO predicts a large barrier to migration is OH. In this case, the method may be partly in error, since the calculated energy of an isolated OH~ is too high23 by2 - * 36 f kcal mol'1. Experimentally of course, it would be difficult to prove if OH migration ever occurs, since the product would be indistinguishable from the species formed in the reversible pre-equilibrium. Groups such as ester, acid and amide are predicted to have relatively small barriers. The best such group is thiolacid (or ester) (Table 1), for which experimental results appear not to have been reported. We note that such groups were also predicted to migrate readily in radical reactions9. Other groups such as vinyl or phenyl are predicted to migrate less readily in the benzilic acid type rearrangements with respect to eg ester than they are in radical rearrangements.

The most revealing trend is to be found for the three para substituted aryl groups (Tables 1 and 3). It is known experimentally1,4 that electron withdrawing substituents (modelled here with p CN) on the migrating group R significantly enhance the observed rate of rearrangement, although the assumption has been that this is due largely to the effect on the equilibrium constant K rather than on the rate constant k2. The MNDO results indicate that, for phenylglyoxal at least ( X = H), both K and k2 are favoured by such substitution. For example a p cyano substituent on the group R = Ph is predicted to promote the equilibrium in favour of 2 (by AH = 7 kcal mol'1, Table 3), to decrease the barrier to migration (by 2.7 kcal mol'1), and to increase the calculated overall negative charge on R, the entropy of activation, the bond lengths in the transition state and the formal resemblance of the migrating group to R- (Table 1). The change in entropy in particular is in such a direction as to favour AG for the electron withdrawing group (Table 1). The calculated effect of an electron donating substituent on R such as p OH is more complex, increasing the barrier to migration and the bond lengths in the transition state. The above results illustrate the dangers of simplifying assumptions regarding the nature of the transition state in such reactions, ie the migrating group appears not to behave as a formal nucleophile in terms of the substituent effects. Certainly there is no theoretical evidence here to support the accepted interpretation of an early transition state.1

4. The Effect of Substituent X on the Migration of R. — Comparison of substituent effects on K or k2 directly is experimentally complex because of the composite nature of the observed rate constant (eqn. 3). Nevertheless, it can be readily established for a pair of substituents R and X from isotopic labelling Rajyaguru and Rzcpa, page 8 experiments which one will migrate in preference to the other. It also follows from eqn. 3 that the relative rates of the two isomeric reactions are related to the difference in free energy between 1 and 7, and not directly to the barrier for the rearrangement step 2 to 3. Since 1 and OH- are common to both reactions, only the relative free energies of the two isomeric transition states 7 need be compared. Under these circumstances, it becomes apparent that the group X may have a significant role to play in determining the relative stability of transition state 7. We discuss initially calculations (Table 3) for two specific pairs of substituents (R/X = H or Ph1 and cyclopropyl or C02H8), for which migratory preferences have been experimentally established by isotopic labelling.

4.1 The Rearrangement of Phenylglyoxal via Transition state 7 (R/X — H/Ph). — The hydroxyl ion catalysed rearrangement of phenylglyoxal to phenylglycolic acid has been established1 as proceeding via hydrogen migration in preference to phenyl migration. The results in Table 1 with X = H indicate little difference between R = H and R = Ph in enthalpic contribution to the rate constant k2. The classical explanation for the observed specificity would be that an aldehyde (ie 2, R=H, X=Ph) is more susceptible to nucleophilic attack than a ketone (ie 2, R=Ph, X = H), and that therefore the migration is determined by the value of the equilibrium constant K and not the rate constant k2. The MNDO calculations indeed predict the isomer R = Ph, X = H to be 7.5 kcal mol'1 less stable than R = H, X = Ph. However, the barrier for [1,2] migration (ie AH7. 2) for R = H, X=Ph is 14.0 kcal mol'1 higher in energy than for R = Ph, X=H, a difference that arises largely from the substituent effect of the group X! Overall therefore, the absolute energy of (7, R=Ph, X = H) corresponding to migration of the phenyl group via route a in scheme 1 is 6.5 kcal mol'1 lower than that for hydride transfer (7, R=H, X=Ph, Table 3), in apparent contradiction with experiment. We note at this point that a similar result was obtained for the pair of substituents R/X = H and p-cyanophenyl. Although such results are within the limits of accuracy of the MNDO method, this does suggest that alternative explanations such as those involving single electron transfers should be considered.

4.2 The Rearrangement of Phenylglyoxal involving Single Electron transfer. — If the migrating group R = H, only one mode of SET is possible, giving 5. However, if R = Ph, an SET can occur to give either the biradical 5, or the species 10 via electron transfer to the aryl group itself. We were indeed able to locate two triplet states corresponding to 5 or 10 with X = H, R = Ph, and one state corresponding to 5 with X = Ph, R = H (Table 3). Rajyaguru and Rzcpa, page 9

Discussing firstly the specific ease of X = H, we note that the intermediate biradicals 5 or 6 arc not significantly stabilised compared with glyoxal, irrespective of the nature of the migrating group R. Thus triplet 5 is 39.4 kcal mol'1 higher than 2 when R = H, and 35.9 kcal mol'1 higher when R = Ph, values that effectively exclude the possibility of such electron transfer. The triplet state of 10 (R = Ph) also high in energy ( 31.50 kcal mol'1 relative to 2). The corresponding transition state 7 is 8.9 and 4.5 kcal mol'1 lower than 5 and 10 respectively, indicating that neither SET pathway involving the migration of the phenyl group is favoured. The situation is different when X=Ph, since the phenyl group can stabilise the adjacent radical centres in 5 or 6. In this case (5,X=Ph, R=H) is now only 23.5 kcal mol'1 higher than 2, a stabilisation of 15.9 kcal mol'1 relative to (X = R = H). The energy of (5, X=Ph, R=H) is now calculated to be lower than that of the transition state (7, X=Ph, R=H) by as much as 17.5 kcal mol' 1 (Table 3). The subsequent fate of a biradical such as (5, X=Ph, R=H) is also of some interest, since the process resembles quite closely a [1,2] hydrogen atom migration. We had previously shown that such a process in a simple radical system has a prohibitively high energy.9 It was not possible to directly study the [1,2] hydrogen atom migration of 5 to 3 on the singlet surface as discussed above. However, the related conversion of singlet (6, R = X = H) to 4 has a relatively low barrier (8 kcal mol'1), as noted above. This latter process is probably facilitated by the ’oxy-anion’ effect22, and therefore the barrier for [1,2] hydrogen atom migration in 5 is probably somewhat higher, but not so large as in a conventional radical.9 If this is true also for the singlet conversion of (5, X = Ph, R = H) to 3, then paths b or c may indeed constitute viable routes for the migration of hydrogen rather than phenyl. We suggest therefore that the observed migratory preference in phenylglyoxal might be rationalised by a mechanism involving an intramolecular SET from the oxy-anion substituent to the carbonyl group followed by a [1,2] hydrogen transfer. We are unaware of any such previous proposal in the literature for this reaction. How can this hypothesis be tested experimentally? One approach might be to investigate the effect of a para substituent attached to group X = Aryl (Table 3) on the rate of migration of the group R = H, via the effect on the two constants K and ki- The entries in Table 3 include the enthalpy of reaction of Rajyaguru and Rzcpa, page 10

(1 + OH- ) giving 2. Changes in this quantity should reflect the substituent effect in X on the equilibrium constant K (assuming no entropic differences). The /?-CN substituent on X has a surprisingly large effect on the stability of 2, promoting its formation by 7.4 kcal mol'1 relative to X = Ph (with R = H) and by 6.2 kcal mol'1 (with R = Ph). Such /? activation of a dicarbonyl compound should be verifiable experimentally. The /?-CN group on X is also predicted to act on k2 by reducing the barrier to [1,2] hydride migration by 2.9 kcal mol'1. However, such a group also promotes the SET process via 5 by 5.6 kcal mol'1, which would also favour k2. We predict therefore that electron withdrawing groups on the non-migrating substituent X should enhance the rearrangement of arylglyoxals, but that this effect would not differentiate between paths a, b or c in Scheme 1. In contrast to these results, an electron donating substituent on X such as /7-hydroxy appears to have only very small effects on K, the barrier to migration, and the SET process leading to 5.

4.3 The Rearrangement of R/X = Cyclopropyl/C02H.— It has been noted experimentally for this system that the ester (or acid ) group migrates in preference to the cyclopropyl group, and also that the cyclopropyl substituent slows down the rate of rearrangement compared with a simple alkyl substituent (egX = CH3, R = CO2H).8 Our calculations are consistent with both these observations. We find the barrier for the conversion of 2 to 3 with R = CO 2H, X= cyclopropyl is 6.8 kcal higher than the corresponding barrier with R = CO 2H, X = H. The intermediate 2 is also more stable by 6.0 kcal mol'1 for the combination (R=C02H, X=cyclopropyl) than for the alternative (R=cyclopropyl, X = C02H), due to enhancement of the electrophilic characteristics of the a carbonyl group by the ester substituent. Overall, the transition state 7 is 22.8 kcal mol'1 higher in energy for the combination X jk X & R = C02H, a = cyclopropyl than for the isomeric R = cyclopropyl, X = C02H and clearly indicates that only the ester or acid group should migrate. The energy difference between R = C02H or cyclopropyl for the migration step (ie AH7. 2) is actually much smaller (JUS. kcal mol'1) when X = H in both cases, again clearly illustrating that both substituents have a very important joint role to play in controlling the rate of this rearrangement. There is no reported experimental evidence that this specific reaction occurs with any opening of the cyclopropyl ring.8 It is therefore unlikely that an SET mechanism is occuring with this combination of substituents, since the formation of a biradical such as (5, X= cyclopropyl, R = CO 2H) should result in the formation of products corresponding to opening of the ring. Our calculations (Table 3) also show that the SET process is not favoured in this case. Rajyaguru and Rzcpa, page 11

Nevertheless, observation of ring opening in a cyclopropyl group may indeed provide a convenient method of obtaining experimental evidence for the operation of an SET process in the benzilic acid type rearrangements.

5. The Benzilic Acid Rearrangement Proper (R =X=Ph). —

The proceeding results for phenylglyoxal suggest that an SET mechanism involving the formation of a species such as 5 or 10 may be particularly favourable for the rearrangement of benzoin itself (1, R = X=Phenyl). There are however several important differences to be expected between the migration of the group R = H and that of R = Aryl. Previous results9 indicated that in simple radicals, [1,2] hydrogen migration was a relatively high energy concerted process, whereas migration of a group such as phenyl was predicted to be comparatively facile stepwise reaction, proceeding via a cyclic intermediate. The analogues of these intermediates for the benzilic acid reaction would be species such as 8 or 9. For phenyl migration in phenylglyoxal, MNDO does indeed predict such intermediates to occur on the pathway for conversion of triplet (5, R=Ph, X=H) to 3 and for singlet (6, R=Ph, X = H)to 4 via 8 and 9 respectively (Table 4). Thus (8, R=Ph,X —H) was found to be 15.0 kcal mol'1 less stable than 2, and the barrier to its formation from 5 was quite high (35 kcal mol'1). We also note at this point that the charge and spin distribution clearly indicated that the negative charge was located on the oxygen atom shown for 8 (as opposed to other representations involving location of the negative charge on the phenyl ring or the other oxygen) and that therefore 8 should be susceptible to significant stabilisation by the substituent X. This is indeed found to be true for benzoin itself, where (8, R=X=Ph) is now 1.0 kcal mol'1 more stable than 2 and 26.5 kcal mol'1 more stable than triplet 5. The latter itself is now 15.1 kcal mol'1 lower in energy than the transition state 7 (Table 3). The isomer 9, differing only in the position of the proton, is similar in energy to 8, but as expected shows a smaller substituent effect due to X (Table 4). These results do raise the possibility that species such as 8 or 9 might be capable of being trapped under suitable circumstances. Since a great deal of information regarding substituent effects is available where R = X — aryl, we chose to study two such systems as models (Table 3). These results will be discussed with reference to the effect on K, on &2 and on the SET and the species resulting from this. The effect of replacing phenyl by p-cyanophenyl is to favour the formation of 2 by 7.8 kcal mol'1 when on the group R and only by slightly less when on group X (6.2 kcal mol'1), as was noted above for the arylglyoxal system. Rajyaguru and Rzcpa, page 12

In contrast, little elTect is predicted on k2 (AH7.2, Table 3) when the substitution is on R, whilst an increase in the barrier is calculated when such substitution is on X. This is in contrast to the previous calculations (Table 1) for the case of X = H rather than phenyl, which indicated that substituents on the R group had a rather greater effect on the barrier to [1,2] migration.

Two triplet states of (2, X = Ph, R = p- cyanophenyl) were characterised, corresponding to single electron transfers to give 5 and 10, the latter being the more stable species (by 4.8 kcal mol'1). For the isomeric combination (X = p-cyanophenyl, R = Ph), only 5 could be characterised and not 10, presumably due to the relative stabilisation of 5 by group X. These results mean that if an SET to give 5 occurs, electron withdrawing substituents are favoured on X and not R, contrary to experiment. On the other hand, an SET to form 10 shows little discrimination between R and X in terms of the para substitution (Table 3). An electron donating group such as p-OH has a much smaller effect on K, k2 and the energy of the SET process. In summary, these results imply that electron withdrawing substituents in the rearrangement of substituted benzoins act principally by influencing the equilibrium constant K, with a much smaller effect on the rate constant k2. These results are to be contrasted with those previously discussed for arylglyoxals, where it was predicted that both K and k2 are subject to substituent effects. Clearly, the group X does not play a passive role in such reactions! We also predict that there may be two types of SET process possible, with differing substituent effects. Electron transfer to give 10 is the most consistent with experimental observation. The energetics of the electron transfer appear to indicate that such mechanisms have to be seriously considered as an alternative or complementary process to the classical reaction mechanism.

6. The Role of the Positive Counter-Ion.— In solvents such as water, the role of the counter-ion to the hydroxyl ion appears not to be important. However, when the reaction is carried out in less polar solvents, it has been suggested25 that the positively charged ion does indeed play an active role by coordination to the two carbonyl oxygens, prior to nucleophilic attack by OH" and concomitant R“ migration. We chose to model this by calculating the barriers to migration of two groups R= H and C02H with X = H in both cases and with Li(H20)2 coordinating to the two oxygen atoms of the erstwhile carbonyl groups as in 12. (Figure 6). The calculations show that the intrinsic barrier to migration is actually increased, by 4 kcal mol'1 in the case of R = H and by 15 kcal mol'1 in the case Rajyaguru and Rzepa, page 13 of R = C02H. The reason for this can be seen in the calculated overall charge on the whole of the migrating group (Table 1). A group with little opportunity to delocalise negative charge such as methyl typically has a charge of ca -0.41 at the transition state, compared with a C02H group with a value of -0.69. The addition of a positive counter ion such as Li(H20)2 reduces the negative charge on the migrating group quite significantly, the acid group for example now having the value -0.47 and with a corresponding barrier to reaction quite similar to a methyl group. If the counter ion appears to play no role in promoting the intrinsic ability of a group to migrate, its effect must be to displace the equilibrium away from 1 and towards the coordinated system 7. This hypothesis was investigated by calculating the enthalpy of reaction for the two equilibria (reactions 4 and 5). I + OH" = 2 ...4 II + H20 = 12 ...5 We note initially that the heat of formation of OH- is predicted by MNDO to be too high by 36 kcal mol'1, whereas the corresponding values for alkoxide anions are correctly reproduced.24 If this correction is applied, it is found that AH for reaction (5) ( - 34.5) is 3.5 kcal mol'1 more exothermic than for reaction (4) ( -31.0). Such a calculation does not take into account any entropic factors or solvation effects, but it does provide a possible indication that coordination to a counter-ion might affect the value of the equilibrium constant K and hence the observed kinetics of benzilic acid type rearrangements.

Acknowledgements. We are grateful to the SERC for the award of a studentship (to IR) and to the University of London for access to the FPS-164 service.

References.

1 S. Selman and J. F. Eastham, Quart. Reviews, 1960,14, 221.

2 H. Dahn and A. Donzel, Helv. Chim. Acta., 1967, 50(7), 1911.

3 H. Dahn and S. Karoui, ibid., 1969, 52(8), 2491. Rajyaguru and Rzepa, page 14

4 A. Novelli and J. R. Barrio, Tetrahedron 1969, 41, 3671.

5 II. Dahn, II. Gowal and H. P. Schlunkc, Ilelv. Chim. Acta., 1970, 53(7), 1598.

6 J. M. Conia and J. M. Denis, Tetrahedron Lett., 1971, 30, 2845.

7 H. Rode-Gowal and H. Dahn, ILelv. Chim. Acta., 1973, 56(6), 2070.

8 H. Dahn, Le H. Das and R. Hunma, ibid., 1982, 65, 2458.

9 J. J. Russell, H. S. Rzepa and D. A. Widdowson, J. Chem. Soc., Chem. Comm., 1983, 625.

10 S. K. Chung, J. Chem. Soc, Chem. Comm., 1982, 480; E. C. Ashby, D. T. Coleman and M. P. Gamasa, Tetrahedron Lett., 1983, 24, 851.

11 M. J. S. Dewar and W. Thiel, J. Am. Chem. Soc., 1977, 99, 4899, 4908; M. J. S. Dewar and M. L. McKee, ibid, p. 5841; M. J. S. Dewar and H. S. Rzepa, ibid, 1978, 100, 58, 777; M. J. S. Dewar, M. L. McKee and H. S. Rzepa, ibid, p. 3607. For an extensive index to MNDO calculations, see T. Clark, “A Handbook of Computational Chemistry”, John Wiley, New York, 1985.

12 H. S. Rzepa and J. Miller, J. Chem. Soc, Perkin Trans. 2, 1985, 717.

13 S. Schroder and W. Thiel, J. Mol. Struct. (Theochem), 1986,138, 248. 14 P. K. Weiner, Ph. D. Dissertation, University of Texas (Austin), 1974.

15 cf J. N. Murrell and K. J. Laidler, Trans. Faraday Soc., 1968, 64, 1431; M. J. S. Dewar, G. P. Ford, M. L. McKee, H. S. Rzepa, W. Thiel and Y. Yamaguchi, J. Mol. Struct., 1978, 43, 135.

16 M. J. S. Dewar, S. Olivella and H. S. Rzepa, Chem. Phys. Lett., 1977, 47, 80.

17 (a) S. Bruce Brown, M. J. S. Dewar, G. P. Ford, D. J. Nelson and H. S. Rzepa, J. Am. Chem. Soc., 1978, 100, 7832 and references quoted therein, (b) For a discussion of equilibrium isotope effects see S. Gabbay and H. S. Rzepa, J. Chem. Soc., Faraday Trans 2, 1982, 78, 671.

18 E. C. Ashby, A. B. Goel and W. S. Park, Tetrahedron Lett., 1981, 22(42), 4209; E. C. Ashby, A. B. Goel and R. N. DePriest, ibid., 1981, 22, 4355; idem., J. Org. Chem., 1981, 46, 2429; E. C. Ashby, A. Rajyaguru and Rzcpa, page 15

B. Gocl and J. N. Argyropoulos, Tetrahedron Lett., 1982, 22, 2273; E. C. Ashby and W. S. Park, ibid., 1983, 24(16), 1667; E. C. Ashby, D. Bac, W. S. Park, R. N. DePriest and W. Y. Su, ibid., 1984, 25(45), 5107. 19 M. J. S. Dewar, M. A. Fox, K. A. Campbell, C. -C. Chen, J. E. Friedheim, M.K. Holloway, S. C. Kim, P. B. Liescheski, A. M. Pakiari, T. -P. Tien and E. G. Zoebrisch, J. Comput. Chem., 1984, 5, 480.

20 (a) B. G. Hutley, A. E. Mountain, I. H. Williams, G. M. Maggiora and R. L. Showen, J. Chem. Soc., Chem. Comm, 1986, 267. ( b)S . M. Van der Kerk, W. Van Gerresheim, Reel. Trav. Chim. Pays- Bas., 1984, 103, 143. (c) M. C. A. Donkersloot and H. M. Buck, J. Am. Chem. Soc., 1981, 103, 6549. (d) O. Tapia, J. Andrea, J. M. Aullo and C. -I. Branden, J. Chem. Phys., 1985, 83, 4673. 21 R. P. Beil, ’The Tunnel Effect in Chemistry’, Chapman and Hall, London, 1980.

22 M. L. Steigerwald, W. A. Goddard and D. A. Evans, J. Am. Chem. Soc., 1979, 101, 1994. For MNDO Calculations on this subject, see I. A. El Karim and H. S. Rzepa, J. Chem. Soc., Chem. Commun., 1986, in press.

23 Calculations at the ab initio level for this and related reactions will be reported in a separate paper, I. Rajyaguru and H. S. Rzepa, to be published.

24 M. J. S. Dewar and H. S. Rzepa, J. Am. Chem. Soc., 1978,100, 784.

25 N. S. Poonia, P. K. Porwal and S. Sen, Bull. Soc. Chim. Belg., 1981, 90(3), 247. Rajyaguru and Rzcpa, page 16

Caption to Figures.

Figure 1. Reaction coordinate system for studying the migration of R.

Fi gure 2. Energy contour map as a function of the two reaction coordinates R! and R 2 for the conversion of 2 to 3 (R = X = H). The separation between contour levels is 3.6 kcal/mol. Figure 3. Energy contour map as a function of the two reaction coordinates R! and R2 for the conversion of 5 to 3 (R = X = H)on the triplet UHF surface. The separation between contour levels is 2.4 kcal/mol.

Figure 4. Energy contour map as a function of the two reaction coordinates Ri and R2 for the conversion of 6 to 4 (R=X = H)on the singlet UHF surface. The separation between contour levels is 4.0 kcal/mol.

Figure 5. Transition states on the reaction pathway between 2 and 3 for (a) R = H, ( b) R= cyclopropyl (c) R=C02H and ( d) R=Phenyl. Arrows indicate the calculated MNDO displacement coordinates for the imaginary frequency.

Figure 6. Transition states on the reaction pathway between 2 and 3 for (a) R=H, (b ) R=C02H with the inclusion of a coordinated Li(H20)2 counter-ion. Arrows indicate the calculated MNDO displacement coordinates for the imaginary frequency. (t) _ 0 H

0 OH

I X

OH (9)

» 3 s ' X \

/

X N3as \ ^0" \ r r X \ » H* O /'*as vo / \ o U i 0 1 Table 1. Calculated MNDO Transition State Properties for the Benzilic acid Re-arrangement

AH3-2° Bond6

i . j c d A6 AH, Length Angle R AHJ ASb ► - 2 q

H 28.,81 -5..96 30,.55 -9.,45 -0..38 1 .,55 58,.8 (-20..11) (1 ,.50) CH_ 36.. 17 -1 .. 13 36.. 50 -10.,27 -0..41 2..08 42.,3 3 (-24..23) (2..05) CH=CH_ 30.,34 -4 . 22 31 .,58 -12.,09 -0..45 2..00 44..7 2 (-23..69) (1 ..94) CO H 20..94 -0,.81 21 ..18 -7.,00 -0., 69 2..26 39..7 Z (-14..64) (2,.18) Z\ 31 ..84 -2,.51 32..58 -14.,99 -0,.59 2..19 39 ,. 9 (-28..95) (2..20) -CH CH - 26,.26 4 . 11 25..06 1 1 ..47 2..41 36..4 Z Z (2,.69) (2,.51 ) CN 26..34 -2..74 27..14 -13.. 15 -0,.65 1 .,98 45..4 (-21..01 ) (1 ,.94) CHO 28..46 -3..55 29 ., 50 -12..39 -0..50 2.,09 42..7 (-25..07) (2..03) CONH 21 ..55 -1 ,,73 22.,06 -8..45 -0..68 2..26 39..9 Z (-20.. 02) (2..16) OH9 48..57 -7..58 -0,.63 2..03 44 ,.7 (-15..49) (1..91 ) COSH 17..10 5..77 15..41 -9..56 -0..85 2..66 34 ..4 (-15..46) (2..41 ) CO CH 9 18.. U5 -13..10 -0..79 2..39 37,.7 2 3 (-24..94 ) (2,.29) Ph 27..02 -2..71 27 .,81 -12,.82 -0,.57 2,. 1 1 42..3 (-22,.82) (2..06) p-PhCN 24 ,.28 -1 ..46 24 ..71 -12..13 -0,.63 2,.16 41 ,.5 - - (-24,.30) (2..10) p-PhOH 27,.14 -1 ..79 27 ..66 -11 ..78 - 0 ,.58 2,. 12 42,.2 (-26.19) (2.06) a : In kcal mol . b : In Xcal moj,"1 K_1fat 293K. c : AH^ 2 = ^H (3)-AH (2). Values in parenthesis correspond to

AHf(4)-AHf(2). d : Charge on the migrating group in the transition state. e : Bond length Cj-R and (CR ) in the transition state, in Angstroms. f : Angle C^-R-C in the transition state, g : Transition states for OH and CO^CH^ trans^er were not characterised by force constant calculation due to problems with hydroxy and methyl group rotations leading to the presence of extra negative eigenvalues.

3 Table 2. Calculated Hydrogen Isotope Effects for the Re-arrangement of (1 , R = X = H).

HRR3 TUN C0Rb K C KIE, u * Reaction TEMP/K eq

„ 12 Cannizzaro 300.0000 3.868304 2.350 0.90 8.2

373.0000 2.980047 1.450 0.94 4.1

400.0000 2.770632 1.354 0.98 3.7

1-*4,(R=X=H) 300.0000 4.700285 - 0.84

373.0000 3.452827 1.998 0.90 6.2

400.0000 3.168900 1 .696 0.91 4.9

: HRR = Harmonic Rate Ratio as defined in Ref. 17.

i : TUN COR = Tunnelling correction as defined in Ref. 21.

: : K = K /K D for the equilibrium 1I = 2 as defined in Ref. 17 . eq H (HRR)*(TUN COR)i * (K ) 1 : KIE,(obs) u , = eq

1 Table 3. Calculated MNDO Energies For Different £ and X Substituents

in kcal mol

2 AH 7 X R 1 2- Rea &H7-2b 5 iH5-2C (toi

H H -62.64 -135.45 -31.04 -106.63 28.81 -96.06 39.39

H Ph -38.94 -104.45 -23.74 -77.43 27.02 -68.52 35.93 (-72.95) (31 50)

Ph H -38.94 -112.02 -31.31 -70.96 41.06 -88.54 23.48

H p-CN-Ph -6.28 -78.83 -30.78 -54.56 24.28 -45.02 33.81 (-57.91) (20.92) p-CN-Ph H -6.28 -85.79 -38.76 -47.63 38.16 -67.87 17.92

H p-OH-Ph -87.19 -152.57 -23.61 -125.43 27.14 -121.31 31.26 (-123.55) (29.01) p-OH-Ph H -87.19 -160.59 -31.63 -120.84 39.74 -138.35 22.24

Ph Ph -13.18 -78.80 -23.85 -38.21 40.59 -53.31 26.16 p-CN-Ph Ph 19.20 -52.57 -30.00 -9.24 43.33 -31.78 20.80

Ph p-CN-Ph 19.20 -54.23 -31.66 -13.84 40.39 -26.11 28.12 (-30.90) (23.33) p-OH-Ph Ph -60.65 -127.34 -24.92 -85.80 41.54 -102.60 24.74

Ph p-OH-Ph -60.65 -127.44 -25.02 -85.97 41.47 -101.91 25.53 p-OH-Ph p-CN-Ph -29.34 -102.78 -31.67 -63.07 39.71 -75.90 26.88 p-CN-Ph p-OH-Ph -29.34 -101.12 -30.01 -59.59 41.54 -81.33 19.79

A C02H -128.71 -215.29 -44.81 -187.58 27.71 -178.84 36.45

co 2h -128.71 -209.32 -38.84 -164.75 44.57 -172.66 36.66

a : AH2 D = AHf(2)-AHf(1)-AHf (OH") -Rea b : AH?_2 = AHf[7)-AHf(2) c : = AH (5)-AH (2), similarly values in parenthesis correspond to

AH 1 q_ 2 = AHf(10)-AHf(2)

1 Table 4. Calculated Energies of Intermediate Species For R=Ar

in paths b and c, in kcal mol

X R 8 9 AH. _a AH ,b 8-2 9-2

H Ph -89.43 15.02

H p-CN-Ph -64.76 -75.99 14.07 2.84

H p-OH-Ph -139.10 -150.70 13.47 1.87

Ph Ph -79.78 -78.48 -0.98 0.32 p-CN-Ph Ph -60.66 -51 .79 -8.09 0.75

Ph p-CN-Ph -54.04 -51.76 0.19 2.47 p-OH-Ph Ph -129.82 -127.86 -2.84 -0.52

Ph p-OH-Ph -130.41 -128.89 -2.97 -1.45 p-OH-Ph p-CN-Ph -103.82 -102.99 -1.04 -0.21 p-CN-Ph p-OH-Ph -110.83 -102.09 -9.71 -0.97

= AHf(8)-AHf(2) a : AHe-2 b : AH9_2 = AHf(9l-AHf(2)

1 va/ v>

< p vt r! s*~~ I—!- bi |u.

■ f \ q C v V ~£rJ- u\ v-e

Figure 5

(c) H

\

l

0

* * *

' & \ S' \ \

V Rajyaguru and Rzcpa, page I

Correspondence and Proofs to; Dr H. S. Rzcpa, Department of Chemistry, Imperial College, London, SVV7 2AY.

Hydrogen Isotope effects in Hydride Transfer Reactions of Formaldehyde and Glyoxal. AnAb initio and MNDO SCF-MO Study.

Indira H. Rajyaguru and Henry S. Rzepa*

Department of Chemistry, Imperial College, London, SW7 2AY.

Summary.— Ab initio and MNDO calculations predict the hydroxyl anion catalysed intramolecular hydride

transfer reaction of glyoxal to exhibit a larger kinetic hydrogen isotope effect than the intermolecular Cannizzaro

reaction of formaldehyde.

In contrast to proton transfer reactions between carbon atoms, the properties of simple hydride transfers are less

well established, particularly with regard to the importance of tunnelling and the relationship between the

transition state structure and the magnitude of the primary kinetic isotope effect.1 Two apparently simple

reactions which are thought to involve a hydride transfer as the rate limiting step are the hydroxyl ion catalysed

Cannizzaro reaction of formaldehyde2 (reaction 1) and the benzilic acid type rearrangement of glyoxal to

glycolic acid3 (reaction 2) The former involves an intermolecular hydride transfer, whereas the latter is thought

to involve an intramolecular4 [1,2] hydride shift via a highly bent transition state. Neither reaction has been the

subject of published theoretical studies at the ab initio SCF-MO level.5 We report such calculations6 which

suggest that both reactions will exhibit significant primary isotope effects, with the intramolecular transfer

having the larger values.

Keq —2 H2CO + O H --^£h2C(OH)0- _1^hco 2h + ch3oh 1

1

OHC-CHO + OH- —^ 0HC-CH(0H)0_ CH2(0H)C02H 2 2 Rajyaguru and Rzepa, page 2

ODC-13CHO + O H " ____> CHD(OH)13C02H + ,3CHD(OH)C02H 3

O D 13C -C IIO + O H " ------^ CHD(0H)13C02H + 13CHD(0H)C02H 4

Each mechanism involves the reversible addition of hydroxyl anion to one carbonyl group to form a tetrahedral intermediate 1 or 2, followed by rate limiting hydride transfer to a second carbonyl group to give the products.

We have shown previously that alternative mechanisms involving eg single electron transfers are unlikely for the reaction of formaldehyde53, or glyoxal.5b The observed rate for these reactions (kobs) is the product of the rate constant for the second step (k2) and the equilibrium constant for the pre-equilibrium step (Keq). It follows that the observed isotope effect (k^bs//c^bs) is the product of the two ratios Ke^/Ke^ and These are both readily calculated from the normal vibrational frequencies, of reactant and intermediate for the equilibrium isotope effect7 and of the reactant and the transition state for the kinetic isotope effect8.

The calculated transition state for reaction 1 (Figure 1) shows pronounced asymmetry in the C-H bond lengths at the 3-21G basis level, but not at the higher 6-31+G level, or indeed with MNDO. Houk and Wu have reported a similarly asymmetric geometry for hydride transfer between methoxide anion and formaldehyde at the ab initio

3-21G level.9 We also find that the linearity of the transition state for reaction 1 shows a large basis set dependence (176.8°//M NDO, 136.5°//3-21G, 148.2°//6-31G, 162.2°//6-31 +G , Figure l).10 Houk and Wu in their study9 reported a similar basis set effect, with angles very similar to ours {e.g. 159°//6-31 + G). In contrast, Williams and coworkers11 report that hydride transfer from methylamine to methyleneammonium has an essentially linear C-H-C linkage at the 3-21G basis set level.10 It has been previously noted that hydride transfers are more easily bent than the equivalent proton transfer.12

The calculated barriers for the hydride transfer step in each reaction are shown in Table 1. For reaction 1, both the MNDO and the ab initio method give barriers similar to those reported for other hydride transfer reactions9'

13. The barriers we obtained for reaction 2 are uniformly higher than for reaction 1, with a structure for the transition state which formally at least, involves a highly bent hydride transfer (Figure lb).

Calculated isotope effects based on the uncorrected normal vibrational frequencies obtained at the MNDO, 3-

21G and 6-31+G levels are shown in Table 2. The calculated harmonic rate ratios (HRR) are for and are all typical of quite large primary effects. The 6-31+G values tend to be intermediate between the MNDO and the 3-21G values, with much less variation observed for the isotope effects than for the Bell tunnelling Rajyaguru and Rzepa, page 3

correction14. This is not unexpected since the latter are very sensitive to the magnitude of the calculated imaginary frequency, which is in turn highly basis set dependent.9,11 The ratio Kc^/Kc^ for the pre- equilibrium step is predicted to show an interesting inverse effect by all three methods, due we think to the ’oxy- anion’ effect15 weakening the C-FI bond adjacent to the alkoxide substituent in the intermediate, relative to the same bond in the starting material. The observable isotope effect ((&obs/&obs)) is therefore somewhat attenuated, but the values obtained are still substantial, and very similar to experimental hydride transfer isotope effects recently reported by Watt and co-workers13. Particularly noteworthy is that the semi-classical isotope effects are predicted at all three levels to be larger for reaction 2 than for reaction 1. It has long been accepted for example that non-linearity decreases the expected magnitude of a simple proton transfer16, and the present result may indicate that hydride transfers differ radically in this respect from proton transfers. The calculated tunnelling corrections show an opposite trend, being larger for reaction 1 at both the 3-21G and 6-31+G levels.

A further striking difference between reactions 1 and 2 is the different predicted temperature behaviour of the isotope effects (Table 2), the Cannizzaro reaction showing a much lower effect than the intramolecular hydride shift.

Also included in Table 2 are results for reactions 3 and 4, which involve the use of isotopically labelled glyoxal, and provide one potential means of measuring these effects. Competing reactions such as hydrogen exchange via a proton abstraction are known3,4 not to occur in either the reactant or the product glycolic acid.* The calculated secondary isotope effects tend to increase the predicted magnitude of HRR, but to decrease the isotope effect on the pre-equilibrium! The overall effect of the use of 13C labels is to slightly increase the observable isotope effect for the hydride transfer.

We thank the University of London for generous allocations of computer time on the two CRAY systems at

ULCC and Dr J. K. M. Sanders for helpful discussions.

t Abstraction by base of the proton a to the carbonyl group in the intermediate 2 would result in formation of the enolate anion H(OH)C = C (O H )0- (or a tautomer), which could then reprotonate to give glycolic acid. The energy of the most stable enol tautomer relative to 2 is predicted to be -16.0 (M NDO) or -9.7 kcal mol- (3-21G).

Since such proton abstraction appears not to occur experimentally, this implies that either the barrier to reaction is a high one (due to electrostatic repulsion between the negatively charged 2 and eg OH- ) or that 2 is more effectively solvated than any of the enol tautomers. Rajyaguru and Rzepa, page 4

References.

I L. Mclandcr and W. H. Saunders, ’Reaction Rates of Isotopic Molecules’, John Wiley and Sons, New York,

1980; R. Stewart and T. W. Toonc, J. Chcm. Soc., Perkin Trans. 2, 1978, 1243.

2. C. G. Swain, A. L. Powell, W. A. Sheppard, and C. R. Morgan, J. Am. Chem. Soc., 1979, 101, 3576.

3 H. Frcdenhagen and K. F. Bonhoeffer, Z. phys. Chem., 1938, A, 181, 379.

4 Experiments using phenyl glyoxal have excluded a proton removal/ reprotonation intermolecular mechanism,

W. v. E. Doering, T. I. Taylor, E. F. Schoenewaldt, J. Am. Chem. Soc, 1948, 70, 455.

5 a H. S. Rzepa and J. Miller, J. Chem. Soc, Perkin Trans. 2, 1985, 717; b, I. Rajyaguru and H. S. Rzepa, J.

Chem. Soc., Perkin Trans. 2, submitted.

6 The Gaussian 82 program package was used throughout; J. Binkley, M. Frisch, K. Raghavachari, W. J. Hehre,

E. Fluder, R. Seeger and J. A. Pople, Carnegie-Mellon University, 1982.

7 See for example S. Gabbay and H. S. Rzepa, J. Chem. Soc, Faraday Trans 2, 1982, 78, 671.

8 See for example S. B. Browm, M. J. S. Dewar, G. P. Ford, D. J. Nelson, and H. S. Rzepa, J. Am. Chem. Soc,

1978,100, 7832.

9 Y. D. Wu and K. N. Houk, J. Am. Chem. Soc., 1987, 109, 906. The same authors report structures for this reaction with two fold symmetry at higher basis set levels, but these were not characterised as true transition states.

10 Such bent geometries are reminiscent of the agostic interactions found in organometallic species; R. H.

C rabtree, Chem. Rev., 1985, 85, 245. Alternatively, the non-linearity may be due to significant interactions between the incipient alkoxide oxygen atom and the carbon atom of the hydride donor.

II B. G. Huntley, A. E. Mountain, I. H. Williams, G. M. Maggiora and R. L. Showen, J. Chem. Soc, Chem.

Commun, 1986, 267.

12 a M. L. McKee, P. B. Shevlin and H. S. Rzepa, J. Am. Chem. Soc., 1986,108, 5793. See also E. S. Lewis and

M. C. R. Symons, Quart. Rev. Chem. Soc., 1958, 12, 230. Rajyaguru and Rzcpa, page 5

13 M. J. Field, I. H. Hillier, S. Smith, M. A. Vincent, S. C. Mason, S. N. Whittleton, C. I. F. Watt and M ,

G uest, J. Chem. Soc, Client. Commun, 1987, 84.

14 R. P. Bell, ’The Tunnel Effect in Chemistry’, Chapman and Hall, London, 1980.

15 M. L. Steigervvald, W. A. Goddard and D. A. Evans, J. Am. Chem. Soc., 1979, 101, 1994. For MNDO

Calculations on this subject, see I. A. El Karim and H. S. Rzepa, J. Chem. Soc., Chem. Commun., 1987, in press.

16 F. H. Westheimer,C/fem. Rev., 1961, 61, 265; R. A. More O’Ferrall, J. Chem. Soc., (B), 1970, 785.

Caption to Figure.

Calculated transition state structures for (a) the hydride transfer step in reaction 1 and ( b ) for reaction 2. Bond lengths are in A at the 6-31+G basis set level and in parentheses at the 3-21G level. Table 1 Barriers to Hydride Transfer for glvoxal and formaldehyde in kcalmol

System MNDO Aja, 3-21G 6-31G RMP4//6-31G 6-31+G RMP4//6-31+G

AHa 28.81 27.36 34. 98 28.78 38.61 34.92

AHb 17.58 I2-4S 7.24 1 3 . 78 4.10 17.01 7.86

a - Barrier to hydride migration for glyoxal b - Barrier to hydride migration for formaldehyde

1 Table 2. Kinetic Isotope Effectsat 373K

H Reaction Method HRR TUN COR KH k kH L x TUN COR eq obs obs 6 K° k k° h eq obs obs 1 MNDO 2.900 1 .450 0.940 2.801 4.062 3-21 G 2.652 1 .494 0.967 2.5653 3.832 6-31+G 2.480 1.940 0.892 2.2 1 2 3 4.292

2 MNDO 3.453 1.998 0.896 3.095^ 6.183 3-2 1 G 4.737 1.172 0.885 4.913 ; - 192b K. 6-31+G 4.771 1.534 0.844 4.026 6.176

3 MNDO 3.871 1 .894 0.867 3.356C 6.357 3-21 G 5.786 1.154 0.797 4.612° 5.322 6-31+G 5.410 1.476 0.810 4.380° 6.464

4 MNDO 3.808 1.917 0.858 3.268^ 6.264 3-21 G 5.615 1.162 0.018 4.593** 5.338 v f 6-31+G 5.222 1 .489 4.343d V 0.832 6.466

For T = 373-7 00K : a , H 317.64/T k . /kD h ■ 1.1011xe (3-21G) . ,.,334xe25,-70/T (6-31+G). obs obs 399.32/T /kD h ■ 1.0654xe (MNDO), 0.9412xe55G'98/T (3-21G), b *H obs„ obs 532.07/T 0.9651xe (6-31+G). 447.23/T , k\ - 1.0139xe (MNDO), 0.8782xe6,9' ,2/T(3-21G), C x"obs „ obs 0.9072xe587‘82/T (6-31+G)

d kH /k° h = 1 .0324xe43°*68/T (MNDO), 0.8939xe611 *18/T (3-21G), obs obs

0.9196xe579' 77/T (6-31+G).

1

J. CHEM. SOC. PERKIN TRANS. II 1987 359

An SCF-MO Study of the Relative Barriers to Inversion and to Ring Opening in Three-membered Ring Carbanions

Indira Rajyaguru and Henry S. Rzepa * Department of Chemistry, Imperial College, London SW 7 2AY

The barriers to inversion of configuration at the centre X and to ring opening in a series of isoelectronic three-membered ring systems (1)— (4) have been investigated at the single determinantal MNDO and a6 initio SCF-MO levels of theory. The MNDO-method-predicted barriers to inversion at carbanionic centres are too low compared with experiment and with theab initio calculations. In the specific case of cyclopropyl carbanion, the MNDO method incorrectly predicts the C“ centre to be planar. The two theoretical methods give more comparable results for inversion at nitrogen and oxygen centres. At the highest level of theory employed (RHF-M P4||6-31+G ), loss of configuration in (1a)— (3a) is predicted to occurvia ring opening to give an enolate anion, rather thanvia direct inversion at C “ . The reverse is true in cyclopropyl anion (4), where direct inversion at the carbon centre has the lower barrier. These results lead to the prediction that oxirane and aziridine anions should be configurationally stable species, whereas thiirane carbanions are predicted to ring-open rapidly to give a thioenol.

It is well established1 that inversion barriers at nitrogen are Although a number of quantitative SCF-MO calculations substantially increased if the nitrogen atom is part of a three- have been carried out for oxaziridines, aziridines, and cyclo­ membered ring. Such barriers are further augmented if an propyl systems, no study of (la) has been reported, and in oxygen atom is also present in the ring, as in oxaziridines (lb), particular no comparative study of the barriers to inversion and indeed the barriers in certain oxaziridine derivatives are and to ring opening has been made. We report here such a sufficiently high to permit resolution of enantiomers.2 In (lb), theoretical study of the systems (1)—(4) using both the this high barrier can be attributed3 to a combination MNDO9 and ab initio 10 SCF-MO procedures. The present study is restricted to unsolvated models for the reactions, no 0 N 0" attempt having been made at this stage to include counter-ions ^-XH 4—XHA A H2C=XH such as Li+. (1) (2) (3) (4) (5) (6) Computational Procedure .—Initial calculations were carried out using the MNDO SCF-MO method9 using a standard sjp a;X = C" a ; X = C valence basis set. Two types of reaction co-ordinate were b;X = N b; X = N+ defined; Ru the bond corresponding to cleavage of the ring to c ; X = 0+ give either the enol anion or the carbene and R2, corresponding to the dihedral angle giving the degree of co-planarity of the XH increased repulsion between the lone-pair electrons on the component with the three-membered ring (Figure 1). Enthalpies adjacent nitrogen and oxygen atoms in the transition state for of formation were calculated at fixed values of Rt and R2, inversion, and the necessarily small C-N-C valance angle in the with full optimisation of the remaining 3N — 8 geometrical three-membered ring favouring sp3 rather than sp2 hybridis­ variables, and used to construct a contour map. Approximate ation at the nitrogen atom. This strain effect can also be used transition states were located either as saddle points on these to rationalise the configurational stability of cyclopropyl carb­ contour maps, or from one-dimensional plots in which only Rt anions, which generally undergo reactions with retention of con­ was varied. These approximate geometries were then located figuration.4 In contrast, cyclopropyl radicals are generally not exactly by minimising the sum of the squared scalar gradients11 configurationally stable,5 and factors other than strain are and characterised as transition states by calculating the clearly important in controlling the barrier to inversion in three- cartesian force constant matrix12 and showing that this had membered rings.1 The configurational stability of other three- only one negative eigenvalue with the correct form for the membered ring systems such as oxirane carbanion (la) has eigenvectors. Initial estimates of the ab initio energies were also been demonstrated.6 Such species are isoelectronic with obtained using a 3-21G* basis set at these MNDO geometries, oxaziridines and should be expected to display similarly high employing the GAUSSIAN 82 program system.10 For the ring barriers to ring inversion. substituent X = C“, major differences in the calculated In the specific case of three-membered ring systems, alter­ MNDO and 3-21G* activation energies for inversion and ring native reactions involving ring opening are possible, and if opening were obtained by this procedure. In the case of (4), reversible would also lead to loss of configuration at the tri- substituted centre. For example, oxaziridines (lb) are known Y to undergo electrocyclic ring-opening under thermal or photo­ chemical conditions to give nitrones (5b) by cleavage of the C-O bond 7 and it has been speculated that under favourable circumstances C-N cleavage may also occur, generating car­ bonyl imines.8 In oxirane carbanion (la), cleavage of the C-O Figure 1. Reaction co-ordinate system for (la)—(4): (a) defining ring bond would result in the formation of an enolate anion (5a). An opening and (b) Newman projection defining the dihedral angle for apparently less likely alternative is C-O bond cleavage giving inversion at the C~ atom. /?t in A, refers to the length of the cleaving the oxyanion carbene (6). C-O bond, R2 in degrees 360 J. CHEM. SOC. PERKIN TRANS. II 1987 u (a) (b)

Figure 2. Energy-contour map as a function of the two reaction co-ordinates Rt and R2 for (a) (la). The separation between the contour levels is 2.8 kcal mol'1, (b) (3a). The separation between the contour levels is 0.8 kcal mol-1, (c) (4a). The separation between the contour levels is 3.5 kcal mol-1. The transition states are indicated with an asterisk the MNDO ground-state geometry appeared qualitatively in­ Results and Discussion correct. Accordingly, the stationary points were reoptimised at Loss of configuration at the C~ centre in (la) could proceed in the 3-21G* level using the method reported by Schlegel,13 and three ways, (i) by direct inversion at this atom, («) by ring again characterised by inspection of the calculated Hessian opening to give (5a), or {Hi) by formation of the carbene (6). The matrix. Further corrections to the ab initio energies were made relative characteristics of (i) and (ii) are shown in an MNDO at these geometries by either including a zero-point energy energy-contour map (Figure 2), which clearly shows two distinct correction, obtained from the normal vibrational frequencies pathways, the lower of which corresponds to inversion (Table calculated from the Hessian matrix, or by including electron- 1). A reaction-path calculation using only Rx as a reaction correlation corrections up to the RMP4 level.6 Since C_ species co-ordinate shows that formation of carbene anion (6) is a have been shown14 to require the addition of diffuse p functions relatively high-energy pathway (A H i 33.7 kcal mol-1) and is to reproduce inversion barriers correctly, a further set of calcul­ significantly endothermic (A H +28.7 kcal mol-1), compared ations using the 6-31 + G augmented basis set were carried out, with the enol anion (5a) which is formed exothermically (A H again with reoptimisation of the geometries and inclusion of — 61.5 kcal mol-1). We do note however that elements such as RMP4 correlation corrections. lithium can stabilise carbenoid systems15 and hence that the J. CHEM. SOC. PERKIN TRANS. II 1987 361

Tabic 1. Calculated barriers to inversion (in kcal mol'1) at the centre X in compounds (1)—(3) + X X O II X = c~ Barrier Barrier II Barrier MNDO (1) 9.17 (1) 31.96 (1) ~ 14“ 3-21G*||MNDO 42.03 28.79 MNDO (2) 1.38* (2) 22.28,“ 28.456 (2) 16.91 * 3-21G*||MNDO 27.46* 17.84,“ 26.99 * 16.35 b MNDO (3) 1.03 (3) 23.32 (3) 9.24 3-21G*||MNDO 19.76 15.65 5.21 * cis. * trans.c 0 -0 Distance not optimised.

Table 2. Calculated barriers for inversion at centre X and for ring opening to (5) for compounds (1)—(4)

(1) (2) (3) (4) > (----- 3 (------r X = c ~ inv* ro“ inv* ro“ inv* ro“ inv* ro“ MNDO 9.17 25.39 1.38 13.79 1.03 3.58 0 18.58 3-21G* 45.00 44.50 37.69 43.57 36.08 16.22 20.78 38.54 RMP4/3-21G* 46.66 26.94 36.54 26.11 34.22 9.31 19.38 26.89 ZPE/3-21G* -1.19 -1.79 -1.47 0.41 -1.21 -0.35 -1.12 -2.15 6-31+G 36.16 34.71 31.46 39.39 34.11 11.80 17.65 35.34 RMP4/6-31+G 35.18 18.23 29.52 23.98 30.15 3.52 16.54 25.36 AS*“/3-21G* -0.68 0.66 -0.14 0.22 -0.36 0.20 -0.88 -0.87 “ A S|98 In cal K.'1 mol'1. 6 Transition-state barrier for inversion at atom X in kcal mol-1. “Transition-state barrier for ring opening to give (5) in kcal mol'1.

Table 3. Reactant energies for X = C~ in compounds (1)— (4) Reactant x = c - (1) (2) (3) (4) MNDO“ 25.538 66.837“ 45.502 56.927 67.757* 3-21G*4 -151.312 97 -131.580 07“ -472.599 06 -115.686 42 -151.630 53 -131.572 38* RMP4/3-21G*" 0.044 28 -131.890 48* -472.923 18 -115.984 94 ZPE/3-21G*J -152.125 34 0.057 71“ 0.042 80 0.069 26 6-31+G*' -152.469 41 -132.293 22“ -474.844 25 -116.317 65 RMP4/6-31 + G 1* -132.626 52“ -475.105 14 -116.635 34 “trans.b cis . “ kcal mol'1. d Atomic units, 1 atomic unit = 627.52 kcal mol'1.

Table 4. Charges on the carbon at the X = C centre in compounds (1)—(4)

(1) (2) (3) (4) A > f \ f X = C" q inv“ q invfl <1 invfl q inv“ MNDO -0.78 9.17 -0.78 1.38 -0.73 1.03 ‘ 0 3-21G* -0.48 45.00 -0.49 37.69 -0.65 36.08 -0.60 20.78 6-31+G -0.91 36.16 -1.05 31.46 -0.73 34.11 -1.08 19.38 q = charge on C at inverting centre. “ Barrier to inversion in kcal mol-1. presence of a Li+ counter-ion may make the formation of gate how the ab initio method reproduces the barriers, energy species such as (6) more favourable. calculations were initially carried out on a range of systems In the related aziridine (2a), the barrier to inversion at carbon (1)—(4), at the fully optimised MNDO geometries, using a 3- was even lower. For the sulphur system (3a), the energy-contour 21G* basis set (Table 1). The results clearly establish that a map shows that the transition states for both inversion and qualitative difference between the two methods is predicted only cleavage to the thioenol are very reactant-like (Figure 2b) and for C” systems. Basis set quality is known to be particularly both barriers are very small. In the case of (4), MNDO predicts important in such negatively charged systems, and it is possible the C" centre to be planar, and the energy-contour map (Figure that the minimal valence basis set employed in MNDO has 2c) is clearly qualitatively different from that for either (la) or serious deficiencies in calculations for such carbanions. Indeed, (2a). This last result is particularly surprising, since numerous it has been previously noted16 that the electron affinities of C~ derivatives of cyclopropane carbanion have been experiment­ systems can be seriously in error if the negative charge is ally demonstrated to be configurationally stable.4 To investi­ localised predominantly on one carbon. 362 J. CHEM. SOC. PERKIN TRANS. II 1987

Figure 4. Transition-state geometries for ring opening in (1)—(4). Bond Figure 3. Transition-state geometries for inversion at atom X in (1)— lengths (in A) optimised at the MNDO (3-21G*) [6-31 -t-G] levels. (4). Bond lengths (in A) optimised at the MNDO (3-21G*) [6-31+G] Arrows indicate the calculated MNDO displacement co-ordinates for levels. Arrows indicate the calculated MNDO displacement co­ the imaginary frequency ordinates for the imaginary frequency the Woodward-Hoffmann rules, and is similar to the result Geometry optimisation at the single determinantal ab initio previously found for the ring opening of oxaziridine to give a level was carried out at the 3-21 G* and (6-31+ G )13 basis set carbonyl imine.4 Although the transition state corresponds to level. The absolute energies so obtained are shown in Table 2, conrotation, it does not have the C2 axis of symmetry associated and the activation energies for inversion at X and for ring with this mode. The strongly pyramidal nature of the C~ atom opening to the enol (5) in Table 3. The two basis sets yield in (la) means that the only element of symmetry common to similar transition-state structures for inversion (Figure 3) and both reactant and product is the plane bisecting this atom. This for ring opening (Figure 4). However, significant differences precludes C2 symmetry, and since the selection rules disfavour between the MNDO and the ab initio structures are found. In Cs symmetry, the transition state can only have Ct symmetry. particular, the carbanionic centre in (4) is correctly predicted to Indeed, when C2 symmetry is imposed, a stationary point with be non-planar at the 3-21G* and 6-31+G levels. The other two negative roots in the force constant matrix is located, the major difference is in the calculated lengths of the cleaving second such root corresponding to out-of-plane motion of the bonds at the transition state for ring opening, for which the central hydrogen atom. MNDO values are consistently shorter than the ab initio ones In contrast to the geometries and energies given by the (Figure 4). We note in this context that the ab initio geometries semiempirical and ab initio procedures, the calculated charge are obtained at the non-correlated RHF SCF level, whereas densities (Table 4) are similar for both methods. For (1), (2a), MNDO in principle includes electron correlation effects at the and (4), the calculated charge at the C“ centre increases for parametric level. It is possible therefore that geometry re­ inversion and decreases for ring opening to an allylic system. In optimisation at the ab initio RMP4 level would give more the former case, the lone pair on carbon becomes orthogonal to comparable results, although the computer resources currently the C-C framework and hence more localised, whereas in the required to do this are prohibitive. It is also known17 that the latter case the charge migrates to the two terminal atoms of the MNDO method overestimates non-bonded nuclear repulsion allylic system. The one exception is the thiirane (3a), for which terms at internuclear distances of ca. 2.0 A. This tends to result both MNDO and the ab initio methods predict an increase in in an overestimation of bond lengths in transition states. This charge on the carbon at the transition state for allylic ring particular failing (apparently corrected at the AMI level,17 a opening. In this aspect, as in several others, the thiirane is reparameterised version of MNDO) does not explain the anomalous. present differences between the two methods. In (3a) Several types of correction to the calculated ab initio energies particularly, the MNDO C-S bond length for ring opening is were also investigated, (i) The calculated correction to the predicted to be much shorter than the ab initio result. The barriers for zero-point energy terms was very similar for both correlated RMP4/6-31+G and MNDO methods do however inversion and ring opening (Table 3). (ii) The entropies of agree in predicting very small barriers to ring opening in (3a). activation for the two types of reaction are both small, There are no significant differences in the calculated geo­ indicating that AH* and AG* will be very similar (Table 3). metries between the 3-21G* basis, which includes polarisation There does appear to be a systematic difference between the functions, and the 6-31G + G basis set, which is augmented entropy of activation for inversion, which is slightly negative, with a set of diffuse p functions. In particular, it is unlikely that and ring opening, which tends to be positive. The only excep­ d-type functions play a major geometric role in the sulphur tion is (4), where both entropies are negative, (iii) Electron- system (3a). The larger 6-31+G basis does however result in correlation corrections carried out to the RMP4 level reduce lower absolute energies, and in lower barriers to inversion and the barriers to inversion significantly less than the barriers to to ring opening. ring opening. This is to be expected, since the former process Both the MNDO and the ab initio methods predict electro- involves no bond breaking, whereas the latter involves signifi­ cyclic ring opening of cyclopropyl carbanion to proceed with cant electronic reorganisation from the a to the n network. conrotation, giving an allyl carbanion. This is consistent with At the highest level of theory (RMP4/6-31 +G||6-31 +G) J. CHEM. SOC. PERKIN TRANS. II 1987 363 the barrier to ring opening of (1; X = C“) is clearly lower in 5 R. W. Fessenden and R. H. Schuler, J. Chem. Phys., 1963, 39, 2147; energy than inversion at carbon. This result applies of course to 1965, 43, 2704; T. Kawamura, M. Tsumura, Y. Yokomichi, and T. Yonezawa, J. Am. Chem. Soc., 1977, 99, 8251; H. M. Walborsky, the gas phase. In solution, it is highly probable that the C” Tetrahedron, 1981, 37, 1625. centre will be associated with the positive counter-ion. This is 6 J. J. Einsh and J. E. Galle, J. Am. Chem. Soc., 1976, 98,4648. Acyclic likely to increase the barrier to inversion, and to decrease the oxy lithiocarbanions have also been demonstrated to be configur­ barrier to ring opening by preferentially stabilising the cnol ationally stable, W. Clark Still and C. Sreckumar, J. Am. Chem. Soc., anion product. Whereas in (la) the barrier to ring opening to 1980, 102, 1201. give (5a) is likely to be sufficiently large for the species to have 7 For a review of the chemistry of oxaziridines and nitrones, sec W. a significant lifetime at low temperatures in solution, the Sliwa, Rocz. Chem., 1976, 50, 667. calculations predict a very low barrier for the sulphur analogue 8 K. Porter and H. S. Rzepa, J. Chem. Res., S, 1983, 262; J. A. Altmann and H. S. Rzepa, J. Mol. Struct., THEOCHEM, 1987, in the press. (3a). If this result is correct, (3a) is most unlikely to have a 9 M. J. S. Dewar and W. Thiel, J. Am. Chem. Soc., 1977,99,4899,4908; significant lifetime in solution. M. J. S. Dewar and M. L. McKee, ibid., p. 5841; M. J. S. Dewar and H. S. Rzepa, ibid., 1978, 100, 58, 777; M. J. S. Dewar, M. L. McKee, and H. S. Rzepa, ibid., p. 3607. For an extensive index to MNDO calculations, see T. Clark, ‘A Handbook of Computational Acknowledgements Chemistry,’ Wiley, New York, 1985. We are very grateful to Dr. A. Pfaltz, ETH, Zurich, for many 10 GAUSSIAN 82, J. S. Binkley, M. Frisch, K. Raghavachari, E. Fluder, helpful comments and for bringing this problem to our atten­ R. Seeger, and J. A. Pople, Carnegie-Mellon University. The 3-21G tion via an exchange studentship supported by ETH and basis set is from J. S. Binkley, J. A. Pople, and W. J. Hehre, J. Am. Imperial College. The calculations were carried out on the Chem. Soc., 1980, 102, 939. The Moeller-Plesset (MP) correlation CRAY-1S and CYBER 855 computers located at the Univer­ treatment is described in J. A. Pople, J. S. Binkley, and R. Seegcr, Ini. sity of London and Imperial College Computer Centres, J. Quantum Chem., Symp., 1976, 10, 1. respectively. 11 P. K. Weiner, Ph.D. Dissertation, University of Texas (Austin), 1974. 12 Cf. J. N. Murrell and K. J. Laidler, Trans. Faraday Soc., 1968, 64, 1431; M. J. S. Dewar, G. P. Ford, M. L. McKee, H. S. Rzepa, W. Thiel, and Y. Yamaguchi, J. Mol. Struct., 1978, 43, 135. References 13 H. B. Schlegel, J. Comput. Chem., 1982, 3, 214. 1 Cf. F. A. L. Anet and J. M. Osyany, J. Am. Chem. Soc., 1967,89, 392; 14 J. Chandrasekhar, J. G. Andrade, and P. von R. Schleyer, J. Am. D. R. Boyd, Tetrahedron Lett., 1968,4561; H. Ono, J. S. Splitter, and Chem. Soc., 1981, 103, 5609. M. Calvin, ibid., 1973, 4107. 15 See for example T. Clark and P. von R. Schleyer, J. Organomet. 2 See for example J. Bjorgo, D. R. Boyd, R. M. Campbell, N. J. Chem., 1980, 191, 347. Thompson, and W. B. Jennings, J. Chem. Soc., Perkin Trans. 2,1976, 16 M. J. S. Dewar and H. S. Rzepa, J. Am. Chem. Soc., 1978, 100, 784. 606. 17 M. J. S. Dewar, E. G. Zoebisch, E. F. Healy, and J. J. P. Stewart, J. 3 J. M. Lehn, B. Munsch, Ph. Millie, and A. Veillard, Theor. Chim. Am. Chem. Soc., 1985, 107, 3902. Acta, 1969,13, 313; B. Levy, Ph. Millie, J. M. Lehn, and B. Munsch, ibid., 1970, 18, 143. 4 L. A. Paquette, T. Uchida, and J. C. Gallucci, J. Am. Chem. Soc., 1984, 106, 335 and references cited therein. Received 28th May 1986; Paper 6/1052