Using a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrodinger equation for C2H4
Using a pruned basis, a non-product quadrature grid, and the exact Watson normal-coordinate kinetic energy operator to solve the vibrational Schrodinger equation for C2H4
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DOI：
10.1063/1.3617249
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发表时间：
2011-08-14
影响因子：
4.4
通讯作者：
Carrington, Tucker, Jr.
中科院分区：
文献类型：
--
作者：
Avila, Gustavo;Carrington, Tucker, Jr.
在本文中，我们提出并验证了一种计算六原子分子振动能级的数值方法。我们使用剪枝乘积基、非乘积求积、Lanczos算法和带有pi(T)mupi项的精确法向坐标动能算符(KEO)。Lanczos算法被应用于具有KEO的哈密顿量，对于KEO，在平衡时对其Mu进行评估。计算得到的本征值和本征向量被用作计算最终能级的基础。设计了求积格式，以使位势中最重要的项的积分将是精确的。该程序在C2H4上进行了测试。所有12个坐标都被显式处理。我们只需要类似于1.52x10(8)个正交点。一个可以计算相同能级的乘积高斯网格至少有5.67x10(13)点。(C)2011年美国物理研究所。[DOI：10.1063/1.3617249]
In this paper we propose and test a method for computing numerically exact vibrational energy levels of a molecule with six atoms. We use a pruned product basis, a non-product quadrature, the Lanczos algorithm, and the exact normal-coordinate kinetic energy operator (KEO) with the pi(t)mu pi term. The Lanczos algorithm is applied to a Hamiltonian with a KEO for which mu is evaluated at equilibrium. Eigenvalues and eigenvectors obtained from this calculation are used as a basis to obtain the final energy levels. The quadrature scheme is designed, so that integrals for the most important terms in the potential will be exact. The procedure is tested on C2H4. All 12 coordinates are treated explicitly. We need only similar to 1.52 x 10(8) quadrature points. A product Gauss grid with which one could calculate the same energy levels has at least 5.67 x 10(13) points. (C) 2011 American Institute of Physics. [doi:10.1063/1.3617249]