The Resonance Energy of Benzene: A Revisit

Zielinski and van Lenthe recently extended the block-localized wave function (BLW) method by introducing the resonating BLW (RBLW) method and performed test calculations on hexagonal H-6 and benzene [J. Phys. Chem. A 2008, 112, 13197]. However, the Pauling's resonance energies from their RBLW and ab initio valence bond (VB) calculations were greatly underestimated largely due to the imperfect use of either one-electron orbitals (method = delocal) or resonance structures (method = local). Whereas it has been well recognized that electronic resonance within a molecular system plays a stabilizing role, there are many indirect experimental evidences available to evaluate the resonance energy and, thus, to justify computational results. Here we used the BLW method, which can be regarded as the simplest variant of modern ab initio VB theory, to re-evaluate the resonance energy of benzene at the B3LYP level, following the original definition by Pauling and Wheland, who obtained the resonance energy by subtracting the actual energy of the molecule in question from that of the most stable contributing structure. The computed vertical resonance energy (or quantum mechanical resonance energy) in benzene is 88.8, 92.2, or 87.9 kcal/mol with the basis sets of 6-31G(d), 6-311+G(d,p), or cc-pVTZ, respectively, while the adiabatic resonance energy (or theoretical resonance energy) is 61.4, 63.2, or 62.4 kcal/mol, exhibiting insignificant basis set dependency for moderate basis sets. In line with predictions, the geometry optimization of the elusive cyclohexatriene (i.e., the Kekule structure) with the BLW method also resulted in carbon-carbon bond lengths (e.g., 1.322 and 1.523 angstrom with the cc-pVTZ basis set) comparable to those in ethylene or ethane.