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

Abstract

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.

Comparing the accuracy of perturbative and variational calculations for predicting fundamental vibrational frequencies of dihalomethanes

“…[34,35] However, it is much harder to derive closed-form energy expressions as well as identify and appropriately account for vibrational resonances at fourth order. [36][37][38] The formidable algebraic and computational complexity of RSPT4 has prevented its general implementation to date. In principle, it is possible to find an RSPT solution at very high orders by resummation of divergent series, [39][40][41][42] but such approaches are rather scarce.…”