Kinetic energy operators in linearized internal coordinates

被引:7
作者
Pesonen, Janne [1 ]
机构
[1] Univ Helsinki, Phys Chem Lab, FIN-00014 Helsinki, Finland
基金
芬兰科学院;
关键词
D O I
10.1063/1.2829496
中图分类号
O64 [物理化学(理论化学)、化学物理学];
学科分类号
070304 ; 081704 ;
摘要
It is customary to describe molecular vibrations using as exact kinetic energy operators and as accurate potentials as possible. It has become a standard approach to express Hamiltonians in curvilinear internal displacement coordinates, because they offer a simple and physical picture of vibrational motions, including large amplitude changes in the shape. In the older normal mode model of molecular vibrations, the nuclei are thought to vibrate infinitesimally about the reference configuration, and the shape of the molecule is described using linearized approximations of the true geometrically defined internal displacement coordinates. It is natural to ask how the two approaches are related. In this work, I present a general yet practical way to obtain curvilinear displacement coordinates as closed function of their linearized counterparts, and vice versa. In contrast to the conventional power series approach, the body-frame dependency is explicitly taken into account, and the relations are valid for any value of the coordinates. The present approach also allows one to obtain easily exact kinetic energy operators in linearized shape coordinates.
引用
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页数:8
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