Valence bond descriptions of benzene and cyclobutadiene and their counterparts with localized bonds

Abstract

Geometry optimizations have been performed for benzene and cyclobutadiene and for the corresponding moieties with nonresonating double bonds, viz. 1,3,5-cyclohexatriene and 1,3-cyclobutadiene. The calculations were done using the valence bond self-consistent field method including orbital optimization. Both strictly local and delocalized p-like orbitals were used for the system, which influences the strengths of the bonds. The calculations result in geometries and resonance and stabilization energies for benzene and cyclobutadiene, which are compared with theoretical models of aromaticity. The importance of resonance is discussed.

Coupled valence bond theory

“…1). The results obtained for energies, resonance energies, and weights of the various structures of all calculations are in agreement with literature data [16,18,19]. Table 1 presents the polarisability (a) tensors calculated for 1,3,5-cyclohexatriene (1(A)), and benzene (1 (A + B)), and Table 2 those for cyclobutadiene (2(A + B)).…”

A comparison of approaches to estimate the resonance energy

“…To study the basis set dependence of the various resonance energies, we have calculated the resonance energies for hexagonal H 6 . In principle, restrictions on the one-electron basis vanish for a complete basis set, and even a one-centre basis set expansion would suffice to describe a molecule.…”

“…benzene, compared to their non-aromatic counterparts is a subject of considerable interest in chemistry. Many approaches for its calculation have been suggested in the literature, both empirical [1][2][3] and employing Ab Initio quantum chemistry [4][5][6][7][8]. Historically, Pauling and Wheland [9] have defined the resonance energy of an aromatic compound as the difference in energy between the resonating multi-structure valence bond wave function and the lowest contributing structure.…”

“…Historically, Pauling and Wheland [9] have defined the resonance energy of an aromatic compound as the difference in energy between the resonating multi-structure valence bond wave function and the lowest contributing structure. This definition has been widely used by VB calculations [5][6][7][8]. Pauling and Sherman [10] have also published another way to calculate the resonance energy from thermochemical data.…”

“…To illustrate our considerations, we compare the resonance energies, obtained using the BLW approach and the VB approach, using different orbital models i.e. VB-local and VB-delocal [6][7][8]. The interpretation of the obtained results is discussed.…”