Ab initiocomputation of semiempirical π-electron methods. III. The benzene molecule, the zero-differential-overlap approximation, and the transferability of parameters

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Abstract
The correlated, size-extensive ab initio effective valence shell Hamiltonian (ℋν) method is used to compute the true π-electron Hamiltonian of benzene and to use it for testing various assumptions of the Pariser–Parr–Pople (PPP) semiempirical electronic structure method. On one hand, the ab initio ℋν method enables computing the low lying valencelike vertical excitation energies and ionization potentials. For example, the calculated ℋν excitation energies deviate from experiment on average by only 0.28 eV, which compares well with similar correlated ab initio calculations. More remarkably, however, the ℋν method can reproduce the vertical excitation energies on average to 0.35 eV simply by employing valence orbitals constructed from symmetry adapted linear combinations of carbon atom pπ orbitals. Thus the ℋν calculations demonstrate that accurate benzene excitation energies can be obtained using a common set of valence orbitals for every valencelike state and, in fact, for every conjugated hydrocarbon! In addition, the true, correlated benzene π-electron effective integrals are ab initio counterparts of semiempirical parameters and transfer extremely well to other small molecules such as ethylene and cyclo-butadiene. The degree of transferability is improved when increasing the size of the primitive ab initio basis set. An analysis of the ℋν effective integrals demonstrates that the true PPP model can indeed neglect a portion of one- and two-electron parameters which are assumed to be small by the zero differential overlap (ZDO) approximation, since the correlation contributions render some effective integrals negligible. On the other hand, some typically neglected parameters, such as two-electron, three-center interactions, are computed as too large to just neglect. Likewise, the exact π-electron ℋν contains three-electron many-body interactions which are large (greater than 0.1 eV) and thus cannot be explicitly neglected in PPP models.