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Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary
Justin Z Gong1, Devin A Matthews2, P Bryan Changala3
1Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA.
Abstract:
A derivation of fourth-order vibrational perturbation theory (VPT4) based on the Watson Hamiltonian in dimensionless rectilinear normal coordinates is presented. Terms that are linear and cubic in the (n + ), with n being the zeroth-order harmonic oscillator quantum numbers, appear in fourth order and extend the much simpler second-order vibrational perturbation theory model. The rather involved expressions for the fourth-order terms are derived with Rayleigh-Schrödinger perturbation theory, the process of verifying their correctness is described, and a computer code to generate the VPT4 constants from the potential energy surface derivatives is provided. The paper concludes with numerical examples featuring the H2O, Si2C, and cyclic-C3H2 molecules.
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