HYPERCONJUGATION THEORY O F CARBONIUM ION REACTIONS
March 5 , 1964 [CONTRIBUTION FROM
THE
847
CHEMISTRY DEPARTMEXT, BROOKHAVEN KATIONAL LABORATORY, LPTON, S . Y.]
Hyperconjugation Theory of Carbonium Ion Reactions' BY S . EHRENSOX RECEIVED JULY 31, 1963 The notion t h a t hyperconjugation may be t h e major driving force in some reactions where carbonium ion products or transition states are formed is supported by results of semiempirical LCAO-MO theory reported here. In the particular cases of aromatic and olefin protonations, good internal consistency is found among several organic chemical rules, parameters in the Taft linear free energy equation, and the theoretical energies computed for these reactions. The Baker-Nathan effect, Markownikoff, and Saytzeff-ll'agner rules are rationalizable in terms of hyperconjugative models of various refinements. Analogous effects noted in the ultraviolet spectral shifts for the alkylbenzenes are discussed The effects of inductive electron donation in these systems and the possibilities of ion stabilization by nonclassical structures are also examined
1.
Introduction
I t is a matter of continuing controversy whether ascription t o hyperconjugation ( H CJ) of several clearly demonstrable effects accompanying alkyl substitution in organic molecules is justified.2 The observables provoking disagreement in interpretation cover a broad range, e.g., bond length variations, ultraviolet frequency and n.m.r. proton shifts, e.s.r. splittings, and reactivities in the vapor and solution phases. As a result of such widespread and often less than discriminate use, the concept has drawn many criticisms. These seem a t times capable of impairing b y generalization whatever utility HCJ might have upon careful application. Perhaps the most detailed, useful, and, at the same time, most widely criticized application of the HCJ concept has been in explanation of the enhanced effects noted for p - v s . m-position alkyl substitution on various aromatic molecule reactivities. The criticisms naturally are directed in terms of alternative explanations3; although many are provocative, none a t present seem any more satisfactory in the general sense than hyperconjugation. The latter seems quantitatively most compelling when viewed in the context of the dual substituent linear free energy equation. Taft and Lewis' have shown that the inductive-resonance effect separations made for the alkyl groups as substituents are normal with respect to similar separations for groups where conjugative ability is generally accepted. Further, the Baker-Xathan effects may be rationalized in terms of a larger C-H than C-C bond contribution to UR. Additivity per bond, C-H and C-C, to the total effect of the particular alkyl group is also found, in agreement with empirical rules previously noted. 2 b , 5 I n this paper, a semiempirical LCAO-&IO investigation is described for electrophilic substitution reactions which, as a group. are well represented in the Taft correlations. Specifically considered are protonation reactions of olefinic and aromatic molecules which result in carbonium ions in the product or transition states. These ions, very different from their precursors, are expected by virtue of the isovalent HCJ interactions possible to be most favorable subjects for articulation of resonance effects on reactivities. Comparisons are sought with the applicable T a f t correlation parameters. Special attention is paid to the relative C-H to C-C bond H CJ effects and their variations between aromatic (1) Work performed under t h e auspices of t h e U S Atomic Energy C o m mission. ( 2 ) (a) M J S D e w a r , "Hyperconjugation," Ronald Press C o . , N e w Y o r k . Pi Y . , 1962, a n d (b) J W . Baker, "Hyperconjugation," Oxford Uni versity Press, S e w Y u r k . N Y ,19.52, discuss this question i n great detail f r o m widely divergent points of view C C Price a n d I) C 1,incoln J . A m C h r m Soc , 7 3 , 5836 ( 1 9 5 1 ) . eeny a n d W hl S h u b e r t , ibid , 76, 4622 ( l 9 . 5 4 ) , V J Shiner. i b i d , 7 6 , 1608 ( ] P a r ) ; A . B u r a w a y a n d E. Spinner, J C ' h r m Soc , :3752 (1954). I. S Bartell. J Chum P h y s , 32, 827 (1960). (4) I t . W T a f t . J r , a n d I . C. Lewis, Teluahedron, 6, 210 (1959) (.5) J. W. Baker a n d W . S P i a t h a n , J . C h e m Soc , 1844 (193A)
and olefinic reactivities. Coincidental questions such as the theoretical implications of the Markownikoff6 and Saytzeff-Wagner rules' are also examined, again in the attempt to find the common ground for theory, empirical correlations, and chemical intuition. 2.
Theory
Previous work where HCJ effects on the basicities of the methylbenzenes were examineds provided the basis for the present study. The model employed is a refinement of the one developed in that work, to the extent where two-dimensional HCJ (ie., quasi-rx and r Y ) with Coulomb, exchange, and overlap integral coupling between dimensions is considered. A further extension allowing generation of self-consistent eigenvalues and vectors for excited states was also made. The latter was used in calculations on the ultraviolet frequency shifts accompanying the alkylation of benzene. The Wheland model,g modified to relate the free energies for reaction or activation to the resonance energy differences between reactants and products or transition state carbonium ions, is again adopted. Theref ore A F a E , (ion) - E , ( 9 . M . ) - E H + = J E T
- El11
(1)
and - R T In K / K ,
= AF -
SF, = A A F = pJAE,
(2)
EH+is the energy of the proton or protonating species, assumed independent of the reaction within a particular series; K is now either an equilibrium or rate constant, and S denotes the standard reaction, generally for the nonalkylated substrate. E n (N.XI.) is the *-electron energy of the neutral molecule and I-( is the proportionality constant relating the double difference in a-electron energies to the corresponding free energies. The assumptions concerning the disposition of A S and A E , within the A F and A E e l e c t r o n i c terms have been carried over directly from ref. 8. The p-position protonation reactions of the monoalkylbenzenes, toluene, ethyl-, isopropyl-, and t-butylbenzene, assumed representative of strong electrophilic reactions on aromatic substrates, may be pictured as
where X and 1' are hydrogen or methyl. The A - , quasi-a-framework extends over S( 10) sites in the parent aromatic and 9( 11) sites in the ion in the one (two) dimensional model. Both species have S( 10) *-plus quasi-a-electrons. The x y dimension. orthogonal to ( 6 ) W Markownikoff. A n t i , 163, 2.76 (1870) (7) C'j P K a r r e r , "Organic C h e m i s t r y , ' ' Elsevier Co , Xew Y o r k , S Y 1950. p . . i 4 (8) S Ibhrenson, J A m C h r m . S o c , 8 8 , 1493 (1961) (9) G. W . U'heland, i b i d , 64, 900 (1942)
S.EHRENSON
848
ax,it should be noted, contains only the two orbitals of the alkyl group and two electrons. Albeit as unstable intermediates, the existence of such ions as above is readily demonstrable (e.g., from ultraviolet and n.m.r. spectral0; Olah and Kuhn have isolated a variety of salts which are stable a t low temperatures"). Protonation reactions of the alkyl substituted olefins are, however, less amenable to precise definition as regards the structures of their transition states. At present, informed opinion is directed to the view that in acid-catalyzed solvolyses and halogen acid additions, in particular, which shall serve as prototype reactions herein, the transition states are a-protonated carbonium ions. l 2 A representative electrophilic addition to an olefin is, then, the formation of an isopropyl-type carbonium ion from a vicinal dialkyl substituted ethylene 1
1
2
2
Vol. 86
exercised by a mechanism of charge leakage from the ay to the formally charge deficient axdimension.I4 3. Computations The computational approach is the same as that described in section 3 of ref. S with the following major modifications : i.-Inclusion of the second a-dimension may be viewed as expanding the secular determinant to give two orthogonal minors. Direct interactions between dimensions is therefore impossible ; however, in the cycling procedure such interactions are permitted through the a , S (and p) parameters. The process of coupling of such elements recognizes the response to differential electron deficiencies or excesses between the x and y dimensions of a given site or sites, and, in fact, may be viewed in terms of self-polarizability of the atom or quasi-atom in the a-framework. Specifically a I(coupled) =
7ilai
a , (coupled) = ( 1 -
m
and ( B i ~ / p " ) s "fSI,(coupled)
m
These structures show the principal one-dimensional HCJ model for the reaction. Six and four delocalizable a-electrons are contained, respectively, in the olefin and ion. The orthogonal ry dimension, which contains only quasi-r sites, is somewhat more difficultly pictured. Fixing attention on the ion, it is apparent t h a t not only will the methyl hydrogen quasi-groups and the carbons to which they are attached constitute ay sites, but that the central, formally sp2 hybridized carbon is capable of participation as well. This would follow conceptually upon incorporation of the central hydrogen and one C(XzU) group into a quasi-group, VZZ.
P
PI
Two such representations, essentially identical, are seen to be possible for these ions, contrasted to one for the ethyl- and three for the t-butyl-type ions. The __ other possible ay structures, e . g . , H-C-[CXzY,C(Hz, XZY)], for the isopropyl ion are assumed unimportant and ignored in the present calculations.13 The multiple a y structures in the isopropyl- and tbutyl-type ions are incorporated into the computations by (a) assuming mutual orthogonality to each other, in addition to the formally imposed orthogonality to the ax structure ; (b) filling each n'heland-Mulliken MO: (c) cycling to self-consistency in charge densities and bond orders: and finally (d) distributing the four available quasi-a, electrons equally among the selfconsistent a,-MO's. Interactions between these structures is accomplished by a direct coupling technique for Coulomb and overlap integrals, discussed in detail in the next section. The over-all result of this procedure is to recognize computationally the stabilization effects afforded by the second HCJ dimension, essentially (10) C . Reid. J A m Chrm S o c , 76, 3261 (1954). C M a c L e a n , J H v a n der Waals. a n d E I, M a c k o r , M o l P h y s . , 1, 247 (1938) ( 1 1 ) C i G A Olah a n d S J K u h n . J An7 Chem Soc , 80, 653.5 (19538) 112) J Manassen a n d F S Klein. J C h r m . S O L , 4 2 0 3 ( l Q 6 0 ) : Y Pocker, ibid 1292 (1960). J S C o e a n d V Gold, rbrif , 4771 (1960), M J S Dewar a n d I< C F a h e y , Chpm Eirg V r u ' s , 4 1 (IO!, R8 (IU6:3), J A m C ' h e m . S i x , 86, 221.5. 9 2 4 8 (1963) ( I R ) T h e s e s t r u c t u r e s a r e easily seen t o resemble t h e s u b s t i t u e n t alkyl groups themselves with ilnly small Coulomb integral differences a t site 3 Crrnseriuently. the contributions of such s t r u c t u r e s t o t h e resonance energies *hr,uld he negligible within t h e approximation employed
(@kl/bo)So
skl
+ (1 - ~ ~ j ) a , + aJ
(3)
f (1 -
(4)
7,j)ai
= 7ljklSlr
(coupled)
(1 -
~ i ,
7iJkl)SiJ
7;Jkl)Skl
+
7,lklSkl
The coupling is carried out after the self-consistency adjustments and prior to re-solution of the secular determinant. The coupling factors, 7, generally taken as 0.5, were restricted to parameters associated with the same site. =Ipplication of this technique may be illustrated by returning to the isopropyl-type ion (structures IV-VI). Sites 1 and 13; 2 and 12; 3 , 7 , and 11; 4 and 8 ; 5 and 9 are a-coupled. Bonds 1,2 and 12,13; 3,4 and 7,X; 4 , 5 and S,9 are S (and p) coupled. 3-The inability to estimate a priori, parameters for the methyl-bearing quasi-a-groups with even the most modest expectations of theoretical justification has been the principal reason why C-C bond HCJ has been ignored in quantitative discussions. l5 This problem is especially acute for Coulomb integral terms and seems likely to remain so for some time. Rather than guess a t parameter sets, the following procedures were adopted. (a) A grid of Coulomb integrals centered roughly about the value a = a o - 0.3po was considered, the central value representing the most reliable estimate for the (Ha) and (H2) quasi-groups.16 Further, one may show that a smooth variation of a is to be expected in passing from methyl, through ethyl and isopropyl, to t-butyl, if free rotation of these groups is allowed. The difference in the values for these parameters, per C-C for C-H bond substitution, is, to a good approximation, equal to v I 2 A E q , where v = w" - w H C H i - WCHIH - WCH,'" and A E q is the energy difference between the antibonding orbitals in the (Hz, CH3) quasi-group. (The w-values follow Mulliken's notation.I7) The question of magnitude, or, indeed, even the sign of the quantity, v 'IzAE,, cannot be answered by presently available methods, mainly because of V : t h a t a regular change in the quasi-group a ' s is to be expected over the alkyl series is, however, usefully recognized. (b) Employing the quasi-group wave functions and again assuming free rotation, the order SCH,>
+
+
(14) T h i s procedure should be compared t o t h a t of N. Muller a n d Iroxirnation2' is employed under which t h e transitions rrf interest for benzene are. (Xoj2iX*lih ( X ? ) ~ ( X * I ) ~ ( X a*n~d) correspondingly f o r t h e alkylhenzenes f x n ) ( x A , ) 2 ( x ) 2 ( x 2 ) 2 ( x1) 2 ( X") I! x A , ) 2 ( xI 1 2 f x2 ) 2 ( x8 ) ! x $1 (23) C.f C C J R o o t h a a n a n d K S Mulliken J hem P h y s , 16, 118
-
(1948)
,
-
HYPERCONJUGATION THEORY O F CARBONIUM I O N RE.4CTIONS
March 3, 1964
14
FIRST
85 1
(X,Y)C-Ar - H TRANSITION
7-77 0 - 0
12
9 W
a a " -0
ALOPE
10 0
?
I 7.6
20
I
W
a
8
N2
I
0 6
SLOPE
4
a(H2,=-.567,0~,~,~~=-.3 I
0
I
I
I
0.30
I
I
=-.3
0.75
- a x21 1p.O Fig. 2.-Computed transition energies for the alkyl-substituted benzenes, referenced t o benzene, as a function of quasi-rgroup Coulomb integral.
accordance with intuition, a-electronic charge is seen to be released from the alkyl group to the ring (>0.01 electron), thereby stabilizing the excited state and lowering the 0-0 transition energy relative to t h a t of benzene. Of further interest, and beyond qualitative expectations, the release is predicted t o occur most strongly to the ring atom bearing the alkyl group and somewhat more weakly to the o-positions. The small transition dipole predicted is in agreement with the relatively small extinction coefficients noted for these transitions; from ref. 21, emax
