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Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates
De-quan Yu,He Huang,Gunnar Nyman,Zhi-gang Sun
Author NameAffiliationE-mail
De-quan Yu State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computa-tional Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, China  
He Huang State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computa-tional Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, China;School of Physics and Electronic Technology, Liaoning Normal University, Dalian 116029, China  
Gunnar Nyman Department of Chemistry, Physical Chemistry,;teborg University, SE-412 96 Gö;teborg, Sweden  
Zhi-gang Sun State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and Computa-tional Chemistry, Dalian Institute of Chemical Physics, Chinese Academy of Science, Dalian 116023, China;Center for Advanced Chemical Physics and 2011 Frontier Center for Quantum Science and Technol-ogy, University of Science and Technology of China, Hefei 230026, China zsun@dicp.ac.cn 
Abstract:
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 correctly 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 OClO 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.
Key words:  Discrete variable representation  Hermiticity  Time-dependent wavepacket method  Absorption spectra
FundProject:
键长-键角和Radau坐标下哈密顿算符在傅里叶基组表象下的厄米性
于德权,黄鹤,GunnarNyman,孙志刚
摘要:
在量子动力学计算中,有时候为了规避奇点问题或者节省计算量,我们经常需要对哈密顿量进行变换. 然而,在使用傅里叶基矢计算时,哈密顿量的变换形式容易导致哈密顿矩阵失去厄米性,进而有些情况下使数值计算变得不稳定. 本文主要讨论构建具有厄米性的哈密顿算符的方法. 以三原子分子为例,构建了键长—键角和Radau坐标下描述分子运动的各种形式的哈密顿量. 基于这些哈密顿量,采用含时波包方法计算了OClO分子的吸收光谱,讨论了非厄米性矩阵对计算结果的影响. 本文所得到的结论对基于基函数展开的量子动力学计算都是适用的.
关键词:  哈密顿量  快速傅里叶变换  傅里叶基组  含时波包方法  吸收光谱
DOI:10.1063/1674-0068/29/cjcp1507141
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