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The Alkyl Inductive Effect, II Theoretical Calculation of Inductive Parameters

Harry F. Widing and Leonard S. Levitt Department of , College of Science, The University of Texas at El Paso, El Paso, Texas 79968

Z. Naturforsch. 34b, 321-326 (1979); received August 29, 1978

Alkyl Inductive Effect, Inductive Constants of Alkyl Groups

Three models of alkyl groups, "derealization", "through-the-bond", and "electric field" models, are presented, all of which enable the calculation of <7I(R) from first prin- ciples, and excellent agreement is demonstrated for the calculated and experimental values of <7i(R). For the "derealization" model it is found that —

C-chain R group, CRI(R00) is —0.0687, identical to the value found by a different method in Part I of this series. The "through-the-bond" model gives —FFI(R) = —0.0559 + ii 0.1015 2 Ci/(2i—l)2, where Ci is the number of C-atoms in the ith position from X in RX; 1 n and for the "electric field" model, we obtain —CT^R) = 0.0463 + 0.0102 Z Cidr2, where di 2 is the calculated distance from Ci to Cn in the most probable conformation of the R-group. It is concluded that Taft's (TI(R) values have a real significance whether or not the physical and chemical effects of alkyl substitution reside ultimately in an internal induction mechanism, or in alkyl group polarization by charged centers in the , or a com- bination of the two.

Introduction been used very successfully in the correlation of This paper deals with the theoretical, rather than vapor-phase proton affinities of primary amines [6]. the experimental, basis of Taft's alkyl inductive Since the G parameters arising from LFER ana- substituent constants [1, 2] CTI(R). In the previous lyses are ultimately a function of the interactions paper [3] we have found that the widely used within , it is reasonable to predict that equation [2] they will be related to spectroscopic data [7], dipole moments [2], bond energies [2], ionization poten-

where a(X) and a(R) are ai(X) and cri(R) when R0 more polarized as the electron charge density at X

is H, and a*(X) and cr*(R) when Ro is CH3. Here increases while decreasing in R. Consequently, the the inductive or polar effect under consideration minimum energy needed to remove an electron (77* or Iii) is the difference in ionization potentials, from RX is reduced and therefore Ei(RX) is i.e., the change in Ei upon substitution of R for H decreased relative to Ei(RoX). Thus, from the in HX. forms of the Ei(RX) vs. CTI(R) plots, it can be argued Recently, the most extensive work along these that R is the electron-releaser, and X the electron- lines has been done by Levitt, Levitt, Widing, and withdrawer and the ionization site of molecule RX. Parkanyi who have linearly correlated the first gas- It can also be argued [18-23] that it is only the phase ionization potentials of seventeen series of electronegative X group which exerts a polarizing aliphatic organic molecules with alkyl cr*(R) and effect on the alkyl group, which is thereby forced to CTI(R) values [9]. We have also found good results for yield electron density to X; and the larger and aldehydes [5], Cu and Cr acetylacetonates [10, 13], bulkier (more branched) is the R group, the greater and benzene Cr tricarbonyls [13], as well as for will be its polarizability. This view is, of course, also benzene [14], and thiophene derivatives correct, but which is cause and which is effect is [15]. It is interesting to note that quantum mechani- merely a matter of semantics. Analogous is an H+ cal calculations using simple Hiickel molecular transfer reaction, and the question "does the orbital theory for obtaining values of highest donate H+ or does the base take it ?" occupied molecular orbitals (HOMO) have resulted, It is interesting to note further that the greater for alkenes [1G], disulfides [17], alkylbenzenes [14] the polarization of electron charge toward X and for pyridine and thiophene derivatives [15] in (whether X pulls electrons or R pushes them), the very accurate estimations of the ionization poten- greater will be the basicity and gas-pliase proton [19] tials, comparing very favorably with both the and nitronium ion [23] affinity of X [24], It has been experimental values and those computed from the found that the gas-phase acidities of the alcohols G\ correlations. Therefore it is possible, in general, to follow a trend opposite to that observed for the use the relation solution acidities, but the same trend as the solution basicities [19, 24], Recent quantum mechanical EI(RX) = EI(HX) + ai(X) CTI(R). (4) calculations [20] have been used to estimate total Ionization energies are values which are relatively energies of the neutral, protonated, and depro- free of molecular interaction effects, unlike measure- tonated molecules, with the result that they have ments of rate and equilibrium constants, which been able to reproduce the known orderings of gas- involve solvent-solvent and solvent-solute dipolar phase proton affinities. It appears that alkyl sub- and polarization interactions. Thus the Ei(M) values stitution makes possible the stabilization of both are essentially an intrinsic measure of the intra- negative and positive ions relative to a neutral molecular properties of M. Of prime importance to molecule (MeOH > HoO in both gas-pliase acidity this paper is the information about the intra- and basicity) by providing an extended structure molecular processes of alkyl induction and electron- which can be more effectively polarized by both withdrawal which analysis of the Ei data affords, cationic and anionic centers [21, 22]. and it has been shown that detailed statistical analysis of such data can lead to the calculation of The General Nature of Polar Effects

very accurate and reliable values for the cri(R) For a molecule RX, the polar inductive effect of constants [5]. the group R comprises all those processes whereby Equation (3) quantitatively states that the vari- it can modify the electrostatic forces operating at able group R exerts some variable polar or inductive the reaction center X relative to the reference group H. F. Widing-L. S. Levitt • The Alkyl Inductive Effect 323

Ro acting in the molecule RoX. Polarization former and 0.002 for the latter. It has been shown [3] resulting from differences in group electronega- that a plot of <7I(R) VS. the number of carbon atoms, tivities, consequent dipole formation, and electron n, of the corresponding normal alkyl group gives a derealization may all contribute to these forces. In rectangular hyperbola, and can be represented by principle, polar effects can be separated into field, an equation of the form [3, 26] inductive, and resonance effects [1, 2, 11]. Field effects [25] are transmitted through space and — AI(R„) = —CRI(RC (5a) (b + n) solvent molecules (if present) in contrast to induc- tive effects which are transmitted directly along the where (TI(R00) is the theoretical limiting value for a bonds of the molecular chain. straight chain alkyl group of infinite length; and b in an empirical constant. On evaluation of the The Alkyl Inductive Effect constants in Eq. (10), it was found [3] that ai(Roo) = —0.0686 and b = 1/2, whence Treatment of induction and other transmitted interactions as electron displacement effects may ffI(R) = —0.0686 — = help to elucidate the inductive mechanism. As the electronic theory of atoms and molecules requires, (5 b) intramolecular electron displacements will preserve n nc electron pairing, doublets, octets, and other stable —0.137 = —0.137 electron groups as completely as possible. Assuming 2 n + 1 that all displaced doublets remain bound in their where n and nc are the number of C atoms, and MH original octets, it can be shown that the unequal the number of H atoms in the R-group. sharing of electrons between unlike atoms (due to The magnitude of (XI(R), for a given number of differences) and consequent elec- carbon atoms in a chain, also increases with the trical dissymmetry within a molecule can be amount of branching and closeness of C propagated along a chain of bonded atoms by a packing in R, so that we may write: cri(£-C4H9) > mechanism of electrostatic polarization and dipole o-i(s-C4H9) > (Ti(i-C4H9) > ai(w-C4H9). These rela- induction [1]. This so-called inductive mechanism of tionships of

.C3<- and the greater (more negative) will be CTI(R). where the arrows indicate the direction and magni- Derealization Model of Alkyl Induction tude of electron shift. The attentuation of the Thus, ai(Rra), where Rra is CraH2n+i, is indeed a inductive effect with distance from X is a property good measure of the alkyl inductive effect and which will be of prime importance in the "model" depends on the size and degree of branching in R. derivations below. The size dependence can be thought of as a dereali- zation effect, larger alkyl chains being associated The Attenuation of Alkyl Induction with Alkyl Size with less localized, and therefore more easily A few general remarks about the relation of the polarizable electron clouds. A crude quantitative magnitude of (TI(R) to the structure of R seems measure of this derealization is given by the ratio appropriate here. For the unbranched R groups the of the number of valence electrons in a certain alkyl induction of R increases with increasing carbon R group to the size of the group and is approximated chain length, i.e., a^n-C^Ks) > by (2 + 6 n)/n. This expression, which we will call ai(7i-C3H7) > CTI(C2H5) > CTI(CH3). However, the Dn, can then be taken as a rough measure of the attentuation of the effect with distance results in a amount of electron derealization in a carbon chain much greater difference between CTI(CH3) and with n atoms. Scaling this ratio so that Di is zero

D„ = 1 — 1 In. (6) "branching factor" can be rationalized on the following grounds: the electron releasing ability of For normal (i.e., unbranched) alkyl groups we find R is thought to be affected by branching in the that the <7i(Rn) values are linearly related to Dre and group because of interference effects resulting from given by the equation the bonding of more than one carbon atom to _ (n(Rn) = 0.0455 + 0.0232 Dn ± 0.002. (7) another carbon atom in the group, a structural From equations (6) and (7) we see that in the limit feature not found in the unbranched groups. A crude of very long carbon chains, i. e., as n -> oo, ai(Roo) = analogy to this phenomenon is seen in the case of —0.0687, and this leads to two vector forces of equal magnitude and unequal direction acting on the same point. The resultant

n-Pr 0.058 0.0610 0.0609 0.0603 0.061 where k includes the rc term. This through-the-bond i-Pr 0.064 0.0651 0.0649 0.0649 0.065 expression is found to be linearly related to

The Electric Field Model of Alkyl Induction n-Am d1t. = 2d, = 3)24 d. Another approach to the problem is to consider electric field effects [25]. Here the group X is considered to have a net electron-shielded charge C 1 and to interact through space with the various and 2C// C5 d = d, 15 2 shielded carbon atoms of its associated alkyl sub- \ / stituent group. In this model, the increase in 3C—C4 electron release from R to X, as R increases in size or becomes more branched, is again measured by The appropriate spatial separations given to the

The results for the 3 model calculations of CTI(R) Et d,2 = d2 = 1,54 A (Eqs. (10, 11, 12)) are summarized in Table I and compared with the generally accepted values. n-Pr C C d13 = d3 = 1,62 d2 1 (T The results obtained in this paper, as well as 3 Taft's original determination of the alkyl inductive n-Bu d,4 = 1,5 d3=2,43 d2 substituent constants and the results in refs. [3] / 3 \ X 1 and [5] should put to rest the ideas held in some 4 2 quarters, that the alkyl inductive effect is non-

existent and that CTI(R) = 0 for all alkyl groups [18]; or that the effect does, indeed, exist but is a minor and 2 C d^=d3 -1,62d2 one, and the GI values can be known only to one C C significant figure [4]. 3 4

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