VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory
VPT2+K spectroscopic constants and matrix elements of the transformed vibrational Hamiltonian of a polyatomic molecule with resonances using Van Vleck perturbation theory
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DOI：
10.1080/00268976.2013.808386
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发表时间：
2014-01
影响因子：
1.7
通讯作者：
A. Rosnik;W. F. Polik
中科院分区：
文献类型：
--
作者：
A. Rosnik;W. F. Polik
用货车-Vleck微扰理论分析了多原子分子的振动能级，将实验能级与计算的分子势能面联系起来。振动矩阵元计算从一个四次势函数通过二阶货车Vleck微扰理论，一个程序，处理弱和强的相互作用之间的振动状态，通过近似块对角化的振动哈密顿量。一个清晰和完整的推导出的非谐和共振常数，以及一般表达式的对角和非对角矩阵元素的变换哈密顿量。方程被写在部分分数的形式，并作为一个常数乘以谐振子矩阵元素，以便于消除强相互作用的共振态的影响，无论是在分析公式和计算机代码。推导出的方程进行了数值验证，并包括甲醛（H2 CO，HDCO，D2CO）的同位素异构体的结果。零点能计算和实验拟合方程的影响进行了讨论。VPT 2 +K方法由这些结果定义，用于拟合和计算振动能级。
Vibrational levels of polyatomic molecules are analysed with Van Vleck perturbation theory to connect experimental energy levels to computed molecular potential energy surfaces. Vibrational matrix elements are calculated from a quartic potential function via second-order Van Vleck perturbation theory, a procedure that treats both weak and strong interactions among vibrational states by approximately block-diagonalising the vibrational Hamiltonian. A clear and complete derivation of anharmonic and resonance constants as well as general expressions for both on- and off-diagonal matrix elements of the transformed Hamiltonian is presented. The equations are written in partial fraction form and as a constant multiplied by a harmonic oscillator matrix element to facilitate removing the effect of strongly interacting resonant states both in analytical formulae and in computer code. The derived equations are validated numerically, and results for the isotopomers of formaldehyde (H2CO, HDCO, D2CO) are included. The implications of the equations on zero-point energy calculations and experimental fits are discussed. The VPT2+K method is defined by these results for use in fitting and calculating vibrational energy levels.