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On the hierarchy of pi-electron models

Stolarczyk L.Z.

Polish Journal of Chemistry

1998

Vol. 72, nr 7S

1691-1736

A systematic derivation of pi-electron models is given, based on a spin-restricted formulation of the molecular-orbital (MO) model for closed- and high-spin open-shell states. A chain of step-by-step approximation leads to the following top-down hierarchy of MO models: ab initio ---> (sigma-pi separation) --->Pariser-Parr-Pople (PPP) --->Hubbard ---> alpha, beta-selfconsistent Huckel Molecular Orbital (HMO) --->beta-selfconsistent HMO---> 'basic' HMO. The PPP semiempirical parameters (alpha' s, beta' s, and gamma' s) are related to exact MO formulas, and the limitations of the PPP MO model are discussed. In general, the parameters of a given pi-electron model are related to those of the preceding one, and limitation of the introduced approximation are indicated. It is shown, for instance, that for the closed-shell alternant hydrocarbons the beta-selfconsistent HMO model, applied for describing the properties of molecular ground-state (equilibrium geometry, thermochemical stability), is equivalent to the more advanced Hubbard model.