| 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 |
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| 引用本文： | 于德权,黄鹤,GunnarNyman,孙志刚.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[J].化学物理学报,2016,29(1):112-122. |
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| 作者姓名： | 于德权 黄鹤 GunnarNyman 孙志刚 |
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| 作者单位： | 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,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;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 |
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| 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.
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| 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 |
| 收稿时间： | 7/4/2015 12:00:00 AM |
| 修稿时间： | 2015/7/13 0:00:00 |
Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates |
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| De-quan Yu,He Huang,Gunnar Nyman and Zhi-gang Sun.Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates[J].Chinese Journal of Chemical Physics,2016,29(1):112-122. |
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| Authors: | De-quan Yu He Huang Gunnar Nyman and Zhi-gang Sun |
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| Institution: | 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,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,Department of Chemistry, Physical Chemistry, Göteborg University, SE-412 96 Göteborg, Sweden and 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 |
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| 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. |
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| Keywords: | Discrete variable representation Hermiticity Time-dependent wavepacket method Absorption spectra |
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