Short Communication

Origins of non-perfect synchronization in the lowestenergy path of the identity proton transfer reaction of allylanion� propene: a VBSCF study

Nathan Harris,1 Wu Wei,1,2 William H. Saunders, Jr3* and Sason Shaik1

1Department of Organic Chemistry and the Lise Meitner-Minerva Center for Computational Quantum Chemistry, The Hebrew University,Jerusalem 91904, Israel2Department of Chemistry, Xiamen University, Xiamen, Fujian 361005, China3Department of Chemistry, University of Rochester, Rochester, New York 14627, USA

Received 22 October 1998; revised 13 November 1998; accepted 7 December 1998

ABSTRACT: Direct computational evidence is presented that the lag in delocalization at the transition state in protontransfers from carbon acids yielding delocalized anions provides the lowest energy path. It does not, contrary to acommon assumption, deprive the transition structure of all resonance stabilization that could otherwise lower thebarrier. Copyright 1999 John Wiley & Sons, Ltd.

KEYWORDS: non-perfect synchronization; identity proton transfer; resonance stabilization, VBSCF; delocalization

Kresge1 suggested that the lag in delocalization in thedeprotonation of carbon acids such as nitromethane arosebecause only a fraction of the charge transferred frombase to substrate could be delocalized within thedeveloping conjugate base. This argument has beenextended and quantified by Bernasconi and co-workers2

as the principle of non-perfect synchronization (PNS).While the PNS provides a plausible analysis of thephenomenon, it has never been clear why a transitionstructure that makes greater use of the supposedlyenergy-lowering effect of delocalization is avoided.

Paradigms that provide qualitative reasons have beenproposed. Hine3 used the principle of least nuclearmotion to argue that high barriers result from thegeometric changes on going from the reactant to thetransition structure which increase the energy of avalence bond (VB) contributor with a reactant-likeelectron distribution. This effect could be minimized byreducing delocalization and thereby geometric change.Pross and Shaik4 pointed out that an important con-tributor to the resonance hybrid transition structure in thedeprotonation of nitromethane should be a triple ionspecies,1, which would both lower the energy of thetransition structure and favor localization of charge onthe carbon of the developing anion. Both suggestionshave been largely ignored in the subsequent literature.

Recent computational evidence has demonstrated thatthe lag in delocalization is an intrinsic property thatpersists in the gas phase.5,6One of the systems studied bymolecular orbital-based calculations, the identity reactionproton transfer from the methyl group of propene to allylanion,6b shows the key characteristics of a reactionfollowing the PNS. This reaction was chosen for furtheranalysis by the VB method, with the aim of elucidatingquantitatively why proton transfer and charge delocaliza-tion are non-synchronous, and to provide a general modelof the phenomenon in terms of mixing of resonancestructures into the wavefunction of the transition state.

The valence bond program from the Xiamen group isbased on spin free valence bond theory, and its technicaldetails can be found in the original literature.7 Here weuse the VBSCF procedure in which the orbitals andstructure coefficients are optimized simultaneously toprovide the lowest energy wavefunction for a given set ofVB structures. The 6–31�G basis set was used.

The trans-anti transition structure2 was alteredslightly to make the C—C� � �H� � �C—C dihedral angleexactly 180° (we did not study the less symmetricalgauche transition structure6). This modification facili-tates the separation of thep orbitals from thes frame-work, and its energetic effect is negligible [<1 kcalmolÿ1 (1 kcal = 4.184 kJ)]. Six inner-shell s orbitals on

B:ÿ H� ÿ :CH2NO2

1

JOURNAL OF PHYSICAL ORGANIC CHEMISTRYJ. Phys. Org. Chem.12, 259–262 (1999)

Copyright 1999 John Wiley & Sons, Ltd. CCC 0894–3230/99/030259–04 $17.50

*Correspondence to:W. H. Saunders, Jr, Department of Chemistry,University of Rochester, Rochester, New York 14627, USA.Contract/grant sponsor:ISF.Contract/grant sponsor:VW Stiftung.

carbon plus ten C—H and four C—Cs orbitals weretreated as a frozen core. The remaining four C—Cporbitals, including those that form the two carbanion-likecenters and the orbitals associated with the migratingproton, were utilized in the VBSCF procedure.

After several attempts, we ascertained that the VBSCFenergy converges with respect to the basis set of VBstructures, and is lower than the corresponding HF energyThe weights in Scheme 1 and the energies presentedbelow are based on calculations in which the eight VBorbitals are constrained to be localized atomic functionson the six carbons and the migrating proton. VBSCFcalculations off1–f5 or f1–f8 allowing the VB orbitalsto optimize freely give orbitals which are slightlydelocalized and give a lower energy than HF. Suchorbital optimization results in delocalization tails of theatomic functions and optimization is equivalent toinclusion of more VB structures in the set.8 Energies inthe two calculations are the same to within 0.1 mhartree(0.06 kcal molÿ1), and the weights of the structures usingthese unconstrained basis functions are in completeagreement with the weights in Scheme 1.

We now present the key features of the calculations.Scheme 1 shows the eight resonance structures thatcontribute to the description of the transition structurealong with their weights in parentheses. (The coefficients

for the seven non-orthogonal structuresf1–f7 areÿ0.29,ÿ0.14,ÿ0.29,ÿ0.14, 0.47, 0.16 and 0.16.)

The members of the three ‘left–right’ resonance pairsin Scheme 1, (f1, f3), (f2, f4), (f6, f7), are related bysymmetry and possess identical energies (i.e.E1 = E3,E2 = E4, E6 = E7). Mixing these pairs leads to the hybridstructuresf1,3, f2,4, f6,7.

It is striking that for each configuration type theweights are in favor of localization of the negative chargeon the two allylica-carbons and against delocalization ofcharge to the twog-carbons. Thus the contributions of(f1,3) are far more important than those of (f2,4) and thatof f5 is much larger than those of (f6,7).

Clearly, our analysis of weights of contributing struc-tures shows that the charge is not yet half delocalized,although the proton is half transferred. Thus, a variationalVB calculation shows that these two different indicatorsof reaction progress do not vary synchronously.

Let us consider now the energetic cost of attaining atransition structure for which the proton transfer andcharge delocalization are fully concerted. VB theoryenables us to calculate such a putative transition structureby taking appropriately constrained linear combinationswhere the coefficients of the VB structures in Scheme 1maintain the relationsc1 = c2, c3 = c4 andc6 = c7 = 1/2c5.As shown in Scheme 2, the energy of the fully

CH2=CH—CH2—Hÿ:CH2—CH=CH2 CH2=CH—CH2:ÿH—CH2—CH=CH2

f1 (0.187) f3 (0.187)

CH2=CH—CH2—H CH2=CH—CH2:ÿ ÿ:CH2—CH=CH2 H—CH2—CH=CH2

f2 (0.049) f4 (0.0497)

CH2=CH—CH2:ÿ H� ÿ:CH2—CH=CH2

f5 (0.402)

CH2=CH—CH2:ÿ H� CH2=CH—CH2:

ÿ ÿ:CH2—CH=CH2 H� ÿ:CH2—CH=CH2

f6 (0.059) f7 (0.059)ÿCH2—CH=CH2 H� CH2=CH—CH2:

ÿ

f8 (0.006)

Scheme 1

Scheme 2

Copyright 1999 John Wiley & Sons, Ltd. J. Phys. Org. Chem.12, 259–262 (1999)

260 N. HARRISET AL.

delocalized hypothetical wavefunction is 8.2 kcal molÿ1

higher than the optimum (non-synchronous) wavefunc-tion. This gives a measure of the energy preference infavor of non-synchronicity. Another putative transitionstructure is the one with a fully localized wavefunctiongiven by a linear combination off1–f3, local =(af5� bf1,3

�). As seen in Scheme 2, the fully localizedstructure is 26.6 kcal molÿ1 higher than the optimumstructure formed from the full VB structure setf1–f8. Itis apparent that a fully delocalized wavefunction has anenergy in between those of a fully localized wavefunctionand the non-synchronous wavefunction. It follows oncemore that non-synchronicity is a feature that optimizesthe energy of the transition structure.

While non-synchronicity is clearly demonstrated in theforegoing discussion, it is still interesting to elucidate theunderlying rules which determine the non-synchronicity.Let us analyze the mixing pattern of the differentstructures (f1–f8) in the VB wavefunction by appeal toFig. 1.

In Fig. 1(a), the resonating pair of structuresf1–f3

mixes to form hybrid symmetrized structuresf1,3� [and

f1,3ÿ, not shown in Fig. 1(a)]. The mixing is strong, in

line with the large overlap between the two structures(S13 = 0.18), and results in a large stabilization of95.6 kcal molÿ1 [Fig. 1(a)]. On the other hand, the mix-

ing betweenf2 andf4 is weak because of poor overlap(S24 = 0.003), and gives only a small stabilization of4.2 kcal molÿ1 for the hybrid. A similar weak mixingcharacterizesf6–f7 (S67 = 0.03). Hence the resonatinghybridsf2,4

� andf6,7� are barely stabilized because of

poor overlap of the constituent structures, whereasf1,3�

is greatly stabilized for the opposite reason. Qualitatively,these overlaps are inversely proportional to the distanceover which the electron is shifted to interconvert theconstituent structures of each symmetrized hybrid.9 Thus,a large overlapS13 is related to the small distancebetween the allylica-carbons, while the small overlapS24

is related to the large distance between the allylicg-carbons, etc.

Let us turn to the mixing patterns of the symmetrizedhybrids with the triple ion structure,f5, in Fig. 1(b). Thestrongest interaction shown in Fig. 1(b) is betweenf1,3

�

andf5. Two factors contribute to this. The first is theirmatrix element, which is large since their interconversioninvolves shifting electrons across the short C1—Hdistances of the transition structure. The second factoris thef1,3

�–f5 energy gap, which is small owing to theself-stabilization off1,3

� [Fig. 1(a)]. Thus, thef5–f1,3�

interaction leads to an energy lowering of 44.1 kcalmolÿ1 and is the main interaction which sustains thedelocalized C—H—C bonding of the transition state.

Figure 1. VB interaction diagrams with relative energies in kcal mol.ÿ1 (a) Mixing of the degenerate structures f1 and f3 givesresonating structure f1,3

�. Similar mixing of f2 and f4 gives hybrid f2,4�. Strength of mixing is related to the overlaps S13 and

S24. (b) Mixing of stabilized hybrid f1,3�with triple ion f5 gives localized structure local. Weak mixing of local with high-energy

structures f2,4�, f6,7

� and f8 gives the non-synchronous structure nonsync

Copyright 1999 John Wiley & Sons, Ltd. J. Phys. Org. Chem.12, 259–262 (1999)

NON-PERFECT SYNCHRONIZATION IN LOWEST ENERGY PATH OF IDENTITY PROTON TRANSFER 261

The resulting wavefunction, local, still has purelylocalized allylic moieties. It can achieve partial allylicdelocalization by mixing withf2,4

�, f6,7� andf8, but

these structures are high lying and possess poor matrixelements with local. Consequently, their mixings arerather weak, giving a total stabilization of 26.6 kcalmolÿ1 [Fig. 1(b)] in increments of 13.2, 12.6 and0.8 kcal molÿ1.

It follows, therefore, that non-perfect synchronicity isan outcome of a selective mixing of the VB structureswhich constitute the electronic structure of the transitionstate. This selective VB mixing determines the optimumbalance between maximizing the strength of the C1—H—C2 bond in the transition structure, and theconservation of delocalization in the allylic moieties.The result of this optimization is the non-synchronouswavefunction, nonsync [Fig. 1(b)], which follows therules of variational VB mixing and has the optimumelectronic structure for the transition state.

Acknowledgements

The research at the Hebrew University is supported inpart by a grant from the ISF, established by the Israel

Academy of Sciences, and in part by the VW Stiftung.The research at the University of Rochester is supportedby NSF Grant CHE-9706242. W.H.S. thanks ProfessorAddy Pross for stimulating suggestions.

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262 N. HARRISET AL.