Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates

作     者：于德权 黄鹤 Gunnar Nyman 孙志刚 

作者机构：中国科学院大连化学物理研究所分子反应动力学国家重点实验室大连116023 辽宁师范大学物理与电子技术学院大连116029 瑞典哥德堡大学化学学院哥德堡 中国科学与技术大学量子信息与量子科技前沿协同创新中心合肥230026 

出 版 物：《Chinese Journal of Chemical Physics》 (化学物理学报（英文）)

年 卷 期：2016年第29卷第1期

页      面：112-122,I0002页

核心收录：

学科分类：07[理学] 0702[理学-物理学] 

基　　金：This work was supported by the National Basic Research Program of China (No.2013CB922200)  the National Natural Science Foundation of China (No.21222308  No.21103187  and No.21133006)  the Chinese Academy of Sciences  and the Key Research Program of the Chinese Academy of Sciences 

主　　题：Discrete variable representation Hermiticity Time-dependent wavepacket method Absorption spectra 

摘      要：In quantum calculations a transformed Hamiltonian is often used to avoid singularities in a certain basis set or to reduce computation time. We demonstrate for the Fourier basis set that the Hamiltonian can not be arbitrarily transformed. Otherwise, the Hamiltonian matrix becomes non-hermitian, which may lead to numerical problems. Methods for cor- rectly constructing the Hamiltonian operators are discussed. Specific examples involving the Fourier basis functions for a triatomic molecular Hamiltonian （J=0） in bond-bond angle and Radau coordinates are presented. For illustration, absorption spectra are calculated for the OC10 molecule using the time-dependent wavepacket method. Numerical results indicate that the non-hermiticity of the Hamiltonian matrix may also result from integration errors. The conclusion drawn here is generally useful for quantum calculation using basis expansion method using quadrature scheme.