Generation of Kekulé valence structures and the corresponding valence bond wave function

Abstract

A new scheme, called "list of nonredundant bonds", is presented to record the number of bonds and their positions for the atoms involved in Kekulé valence structures of (poly)cyclic conjugated systems. Based on this scheme, a recursive algorithm for generating Kekulé valence structures has been developed and implemented. The method is general and applicable for all kinds of (poly)cyclic conjugated systems including fullerenes. The application of the algorithm in generating Valence Bond (VB) wave functions, in terms of Kekulé valence structures, is discussed and illustrated in actual VB calculations. Two types of VBSCF calculations, one involving Kekulé valence structures only and the second one involving all covalent VB structures, were performed for benzene, pentalene, benzocyclobutadiene, and naphthalene. Both strictly local and delocalised p-orbitals were used in these calculations. Our results show that, when the orbitals are restricted to their own atoms, other VB structures (Dewar structures) also have a significant contribution in the VB wave function. When removing this restriction, the other VB structures (Dewar and also the ionic structures) are accommodated in the Kekulé valence structures, automatically. Therefore, at VBSCF delocal level, the ground states of these systems can be described almost quantitatively by considering Kekulé valence structures only at a considerable saving of time.

The non-covalent nature of the molecular structure of the benzene molecule

“…Despite the amount of collective time spent on this problem and all published studies concerning the subject, it is still possible to find disagreements in the scientific community regarding the origins of the properties of this class of compounds. [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20] One of the more recent disputes concerns the relative importance of the s and the p electrons to the properties of aromatic molecules. The idea that the benzene molecule owed its preference for the D 6h geometry to the s-frame resistance against distortion along the b 2u ''Kekule ´'' mode was developed and popularized by Shaik et al in a series of papers.…”

Resonance and Aromaticity: An Ab Initio Valence Bond Approach

“…We, therefore, considered only Kekulé valence structures in the wave function to compare it with the VB-delocal approach. The VB-delocal level gives an accurate description of cyclic conjugated hydrocarbons in their ground states with only Kekulé valence structures. , …”

“…The VB-delocal level gives an accurate description of cyclic conjugated hydrocarbons in their ground states with only Kekulévalence structures. 74,75 It has been shown in the past 39 that the VB-delocal resonance energy of benzene ( 1) is practically insensitive to basis set size: both the 6-31G (66 AOs) and the aug-cc-pVQZ (954 AOs) basis set calculations give a resonance energy of 20 ± 0.5 kcal/mol at the VB-delocal level. This insensitivity of VBdelocal resonance energy with respect to basis set is also expected for other related systems.…”

The Nature of the Chemical Bond from a Quantum Mechanical Interference Perspective

“…Benzene is among the most studied systems in chemistry. This emblematic molecule is an annulene composed of 6 carbon atoms displaced on a D 6h symmetric planar ring, and its geometric, electronic and magnetic properties are still reasons for scientific inquiry . From the energetic point of view, the molecule is more stable than their cyclic polyenes analogues.…”