THE DELOCALIZATION ENERGY OF BENZENE AND THE NONEMPIRICAL MO THEORY

Algebraic expressions for the vertical Delocalisation Energy (DE) of b enzene are derived from non-empirical MO theory. For comparison with e arly work in the pi-electron approximation, and ultimately with Huckel theory, the results are formulated in terms of a core resonance integ ral, beta, and pi-electronic repulsion integrals. All integral values are inferred from the results of ab initio SCF calculations. Two expre ssions are derived, which refer to two ways of forming the localised p i MOs: one where three pairs of adjacent atomic orbitals are selected from a set of six orthogonalised orbitals; and another where a non-ort hogonal set of atomic orbitals is used. The first expression is formal ly similar to an expression originally derived by Pople from a differe nt point of view and with many approximations. This expression gives t oo large a magnitude for DE when used with an ab initio value of beta. The second expression gives a result much closer to an empirical valu e of DE and shows that the main reason for DE being about 50% of 2 bet a rather than 2 beta is the stabilising effect of overlap in the local ised structure, and that the less important factor is the inclusion of electronic repulsion.