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 SO2, and H2O molecules including anharmonic effects has been calculated. © 2013 Wiley Periodicals, Inc.
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