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

Justin Z Gong; Devin A Matthews; P Bryan Changala; John F Stanton

doi:10.1063/1.5040360

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

J Chem Phys. 2018 Sep 21;149(11):114102. doi: 10.1063/1.5040360.

Authors

Justin Z Gong¹, Devin A Matthews², P Bryan Changala³, John F Stanton⁴

Affiliations

¹ Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA.
² Institute for Computational Engineering and Sciences, The University of Texas, Austin, Texas 78712, USA.
³ JILA, National Institute of Standards and Technology, University of Colorado, Boulder, Colorado 80309, USA and Department of Physics, University of Colorado, Boulder, Colorado 80309, USA.
⁴ Quantum Theory Project, University of Florida, Gainesville, Florida 32611, USA.

PMID: 30243279
DOI: 10.1063/1.5040360

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_k + $\frac{1}{2}$ ), with n_k 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.