Ab initio Description of Nuclear Motion in Nonrigid M k XY n ( k ≥1) Molecules with Quasirigid XY n Fragments

Abstract

For nonrigid MkXYn (k≥1) molecules, a model is constructed that describes the motion of k M nuclei relative to the quasirigid XYn fragment taking into account 3*k degrees of freedom. The parameters of the potential and kinetic terms of the model Hamiltonian are determined from results of ab initio calculations of the properties of a molecule and its fragments. Solutions of the corresponding Schrodinger equations are obtained by a variational method using bases constructed from products of spherical harmonics and harmonic–oscillator eigenfunctions. The form of model Hamiltonians for nonrigid MXY4 and M2XY4 molecules with quasitetrahedral XY4 fragments are discussed in detail. Group–theoretical analysis of the symmetry of the Hamiltonians is performed. It is shown that the molecular symmetry groups of nonrigid MXY4 and M2XY4 molecules are the G24 and G48 groups, which are isomorphic to the Td and Oh point groups, respectively.