Department of Chemistry, The University of Texas at Austin, Austin, Texas 78712, USA.
Institute for Computational Engineering and Sciences, The University of Texas, Austin, Texas 78712, USA.
J Chem Phys. 2018 Sep 21;149(11):114102. doi: 10.1063/1.5040360.
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 ( + ), with 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 HO, SiC, and cyclic-CH molecules.
本文提出了一种基于无量纲直线正则坐标下的 Watson 哈密顿量的四阶振动微扰理论（VPT4）。其中，项是线性和立方的，其中 是零阶谐振子量子数，在第四阶出现，并扩展了更为简单的二阶振动微扰理论模型。通过瑞利-薛定谔微扰理论推导出了四阶项的相当复杂的表达式，描述了验证其正确性的过程，并提供了一个从势能面导数生成 VPT4 常数的计算机代码。本文最后给出了 HO、SiC 和环状-CH 分子的数值示例。
