Theoretical analysis of electronic delocalization

Abstract

A block-localized wave function method is introduced to evaluate the electronic delocalization effect in molecules. The wave function for the hypothetical and strictly localized structure is constructed based on the assumption that all electrons and primitive basis functions can be divided into several subgroups; each localized molecular orbital is expanded in terms of primitive orbitals belonging to only one subgroup. The molecular orbitals belonging to the same subgroup are constrained to be mutually orthogonal, while those belonging to different subgroups are free to overlap. The final block-localized wave function at the Hartree–Fock level is expressed by a Slater determinant. In this manner, the energy difference between the Hartree–Fock wave function and the block-localized wave function can be generally defined as the electronic delocalization energy. The method is applied to two cases. The first concerns the resonance stabilization in the allyl ions. We find that the vertical resonance energies for the planar cation and anion are −45.7 (or −44.7) and −46.7 (or −48.2) kcal/mol at the HF/6-31G* (or 6-31+G*) level, respectively. Their rotational barriers are decomposed in terms of conjugation, hyperconjugation, steric effect, and pyramidalization. The n→σ* negative hyperconjugation in the staggered allyl anion is very strong and stabilizes the system by as much as −13 kcal/mol. The second concerns the hyperconjugation effect in propene. Our calculations suggest that the theoretical hyperconjugation energy in propene is about −5 kcal/mol, which is close to the experimental estimate (−2.7 kcal/mol) derived from the hydrogenation heats of propene and ethylene. Comparisons between the results based on the present block-localized wave function method and those based on the natural bond orbital method are presented and discussed. The examples demonstrate that the block-localized wave function method can be employed as a useful model to analyze chemical bondings and intuitive concepts.

How resonance assists hydrogen bonding interactions: An energy decomposition analysis

“…The BLW method is a further extension and generalization of the idea of localized bond functions with the intention to significantly simplify the computational efforts involved in HLSP wave functions. [33][34][35] The basic assumption in the BLW method is that the overall electrons and primitive basis functions can be partitioned into k subgroups, depending on the targeted resonance structure or in more general, the diabatic state. The ith subspace consists of { i , ¼ 1, 2, .…”

“…Since the present BLW method is established at the HF level, and the HF wave function refers to the real state where all electrons are free to delocalize in the whole system, the energy difference between the HF and BLW wave functions can be generally defined as the electron delocalization energy, which measures intramolecular resonance and hyperconjugation effects or even intermolecular charge-transfer effect. The self-consistent optimization of the block-localized orbitals can be accomplished using successive Jacobi rotation as we initially adopted, 33 or preferably using the algorithm of Gianinetti et al 45 We have implemented the algorithm of Gianinetti et al into our BLW code and ported the code to the GAMESS software, 46 which has the capability of geometrical optimizations. 34 Figure 2.…”

“…6,28 Ab initio VB theory has been rejuvenated in the past two decades, 32 even though its further broad application will require a significant reduction in its computational demands. Alternatively, the recently proposed block-localized wave function (BLW) method, which can be regarded as a variant of the ab initio VB theory, preserves the characteristics and advantages of both the VB and molecular orbital (MO) theory, [33][34][35] and thus provides a practical means to compute the conventional Pauling-Wheland resonance energy. In the BLW method, the wave function of a resonance structure is defined with a Slater determinant and block-localized MOs, which are expanded only in a fraction of the overall basis space.…”

Spin Coupling and Resonance

“…Trying to combine the best of both VB and MO worlds, Mo et al 1 introduced the block localized wave function method (BLW). 1,42 The BLW approach divides all basis functions into subgroups. All MOs then are expanded in terms of the basis functions in only one of the subgroups.…”

“…The fundamental historical interpretation of the resonance energy (PRE) was then defined by Pauling as the difference between the energy of the benzene molecule described with five, resonating Kekulé and Dewar structures and the energy of a single Kekulé structure (Figure 2) E PRE ) E 5res.struc. -E 1Kekule (1) Based on those calculations, he estimated the resonance energy and predicted quite accurately the contributions of the Kekulé and Dewar structures to the overall energy. Since no orbital optimization was performed, all energies were calculated with the same set of orbitals.…”