The Alkyl Inductive Effect, II Theoretical Calculation of Inductive Parameters Harry F. Widing and Leonard S. Levitt Department of Chemistry, 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 Substituent 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 —<XI(R) = 0.0455 + 0.0232(1—1/n), where n is the number of C atoms in an w-alkyl group, and for an infinite 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 molecule, 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 molecules, it is reasonable to predict that equation [2] they will be related to spectroscopic data [7], dipole moments [2], bond energies [2], ionization poten- <ri(X) = 0.45 a*(XCH2) (1) tials [8-10], and many other physical properties which directly relates ai to Taft's polar substituent [2, 11, 12]. constants, a*, to be completely invalid for alkyl groups, as is also the relation [4] oi = 0.161 a*. A Molecular Ionization Potentials very simple and accurate relation between these two substituent constants was found to be [3] It has been found that the first gas-phase ioniza- tion energies [8-10] of molecules RX, where R is <7I(R) = ffi(Me) [1-2.04 <R*(R)] ~ an alkyl substituent and X a more electronegative — 0.046(1-2(7*) (2) group, correlate linearly with A*(R) and CN(R) for which was derived using Taft's best defined a values: "ionization series" characterized by constant X and ffi(H) = 0.000, er*(H) = +0.490, cn(Me) = —0.046, varying R. Some relationship is to be expected since and A*(Me) = 0.000. Values of CTI(R) calculated from the CT(R) values are taken as measures of the Taft's CT*(R) using Eq. (2) were found to be in polarizability and electron-releasing ability of the excellent agreement [3, 5] with Taft's original <xi(R) alkyl group R when attached to an electron- values, and <7I(R) values were calculated for 23 withdrawing group X. Hence, an R group which groups for which no previous estimates were avail- more effectively releases electrons to the ionization able [3]. Some of the new ci(R) values have recently site of a molecule will correspondingly cause an increase in electron density there, and this will Requests for reprints should be sent to Prof. Dr. L. S. consequently reduce the minimum energy needed to Levitt, Department of Chemistry, College of Science, remove an electron from it, i.e., decrease the The University of Texas at El Paso, El Paso, Texas ionization potential of the molecule. Using the 79968, USA. LFER method, the difference between the ionization 0340-5087/79/0200-0321/$ 01.0ü/0 322 H. F. Widing-L. S. Levitt • The Alkyl Inductive Effect free-energy change of a molecule RX and some influence over group X, which is measured by the standard RoX should be expressible as the difference dimensionless parameter CTI(R). This influence is due between the ionization energy of RX, Ei(RX), and to electron release from R to X, a more electro- that of RoX, Ei(RoX), so that one has negative group. Thus, as R's ability to release electrons to X increases relative to Ro, i.e., as <TI(R) Ei(RX) — Ei(RoX) = a(X) <r(R), (3) becomes a more negative quantity, RX becomes 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], pyridine 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 acid 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].