一种用于计算振动光谱的曲线坐标下的多维斯莫利亚克配置方法。

A multi-dimensional Smolyak collocation method in curvilinear coordinates for computing vibrational spectra.

作者信息

Avila Gustavo, Carrington Tucker

机构信息

Chemistry Department, Queen's University, Kingston, Ontario K7L 3N6, Canada.

出版信息

J Chem Phys. 2015 Dec 7;143(21):214108. doi: 10.1063/1.4936294.

DOI:10.1063/1.4936294

PMID:26646870

Abstract

In this paper, we improve the collocation method for computing vibrational spectra that was presented in Avila and Carrington, Jr. [J. Chem. Phys. 139, 134114 (2013)]. Using an iterative eigensolver, energy levels and wavefunctions are determined from values of the potential on a Smolyak grid. The kinetic energy matrix-vector product is evaluated by transforming a vector labelled with (nondirect product) grid indices to a vector labelled by (nondirect product) basis indices. Both the transformation and application of the kinetic energy operator (KEO) scale favorably. Collocation facilitates dealing with complicated KEOs because it obviates the need to calculate integrals of coordinate dependent coefficients of differential operators. The ideas are tested by computing energy levels of HONO using a KEO in bond coordinates.

摘要

在本文中，我们改进了阿维拉和小卡林顿[《化学物理杂志》139, 134114 (2013)]中提出的用于计算振动光谱的配置方法。使用迭代特征求解器，根据斯莫利亚克网格上的势能值确定能级和波函数。通过将标记为（非直积）网格索引的向量转换为标记为（非直积）基索引的向量来评估动能矩阵 - 向量积。动能算符（KEO）的变换和应用都具有良好的缩放比例。配置便于处理复杂的KEO，因为它无需计算微分算符的坐标相关系数的积分。通过使用键坐标中的KEO计算HONO的能级来检验这些想法。