1,3,5-Cyclohexatriene captured in computro; the importance of resonance

Abstract

The geometry and energy of 1,3,5-cyclohexatriene, the reference molecule for the determination of the extra stabilization of benzene, have been calculated using an Ab Initio Valence Bond method. The theoretical resonance energy, according to Dewar, calculated as the energy difference between two-structure benzene and single-structure 1,3,5-cyclohexatriene, both with completely optimized geometries and orbitals, is only )12.05 kcal/mol. Resonance energies of )25.37 (local orbitals), )19.82 (delocal orbitals) and )44.13 (breathing orbitals) kcal/mol are found using the Pauling definition. The concept of the vertical resonance energy, however, is proven to be not tenable beyond a minimal basis. Ó

A comparison of approaches to estimate the resonance energy

“…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.…”

“…It is also possible to mimic the thermochemical approach computationally, by calculating the parts of a molecule (non-aromatic counterpart) and the whole (real molecule). That has been defined in valence bond as a theoretical resonance energy (TRE) [7]-the energy difference between the resonating, multi-structure VB wave function used for the description of benzene (real molecule) and the single structure VB wave function that describes its non-aromatic counterpart 1,3,5-cyclohexatriene in a relaxed D 3h symmetry. In contrast, in the block-localised wave function (BLW) [11][12][13] approach, the resonance energy is defined as the energy that is gained by the delocalisation of the localised constituent parts (blocks), computed using a BLW wave function (non-aromatic counterpart), to the delocalised molecule, calculated using the Hartree-Fock wave function (real molecule).…”

“…Benzene is the archetype of aromatic molecules, and its aromatic stabilisation is still a matter of dispute [7,11,13]. To illustrate our considerations, we compare the resonance energies, obtained using the BLW approach and the VB approach, using different orbital models i.e.…”

“…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.…”