Calculation of the vibrational wave function of polyatomic molecules

A modified perturbation approach for the calculation of the vibrational wav e function of polyatomic molecules is discussed. It is demonstrated that if the expansion point of the potential is determined variationally, the lead ing first-order term in the perturbation expansion of the vibrational wave function vanishes. Furthermore, the new expansion point is a very good appr oximation to the vibrationally averaged molecular geometry. The required th ird derivatives of the potential energy with respect to geometrical distort ions have been calculated by numerical differentiation. Two approaches are discussed, one based on the differentiation of the molecular Hessian and th e other on the molecular gradient. Results are presented for the averaged m olecular geometry of a large set of molecules, including studies of electro nically excited states and effects of electron correlation. The largest mol ecule included is butane with a total of 14 atoms. (C) 2000 American Instit ute of Physics. [S0021-9606(00)30905-9].