The calculation of vibrational energy levels of polyatomic molecules including anharmonic effect using contact transformation perturbation method

摘要

Using contact transformation perturbation method based on the Taylor expansion of the potential energy function in terms of dimensionless normal coordinates up to sixth-order, the vibrational energy levels in terms of force constants are derived. The contact transformation theory has been applied to simplify the calculation of perturbation effects. To calculate the second-order vibrational energy correction, the third and fourth-order terms of potential function have been placed in the first-order perturbation Hamiltonian and the second-order Hamiltonian contains hexatic ones. We present expressions which give relations between the fourth- and sixth-order terms in dimensionless normal coordinates of the potential and the anharmonicity coefficients. For illustration, a set of vibrational energies levels of SO_2, and H _2O molecules including anharmonic effects has been calculated.