Fourth-order vibrational perturbation theory with the Watson Hamiltonian: Report of working equations and preliminary results.

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 (nk + 12 ), with nk 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.