The correlated pi-Hamiltonian of trans-butadiene as calculated by the ab initio effective valence shell Hamiltonian method: Comparison with semiempirical models

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Abstract
The pi-electron Hamiltonian ℋπ of trans-butadiene is calculated using the effective Hamiltonian quasidegenerate many-body perturbation theory formalism to include ‘‘correlation’’ contributions. When four tight, valencelike orbitals are employed, the calculated ℋπ reproduces experimental and calculated (by configuration interaction) valence state excitation energies, but fails to obtain the diffuse Rydberg-like pi-electron states which interleave the valence spectrum. The addition of a pair of Rydberg molecular orbitals to the valence shell leads to an effective Hamiltonian ℋv which accurately describes both valence and Rydberg states simultaneously. These results provide an explanation as to why semiempirical pi-electron theories have required the use of different parameters, particularly resonance integrals, to calculate different properties. Our calculated ℋπ contains hybrid, exchange, and multicenter two-electron integrals which are customarily ignored to varying degrees in zero differential overlap (ZDO) approximation based methods. The ℋπ integrals often differ considerably from their ‘‘theoretical,’’ uncorrelated counterparts, and our ℋπ calculation provides further insight into these ZDO approximations. A more direct comparison is made with the traditional Pariser–Parr–Pople ℋPPP by averaging our ℋπ to generate a form ℋ̄π similar to ℋPPP. Certain aspects of ℋ̄π are very close quantitatively to ℋPPP, but there are other strong differences which are easily understood physically. The full ℋπ with all repulsion integrals and even effective three-electron interactions can now be used as a testing ground against which new types of semiempirical approximations may be tested.