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Mapped Finite Element discrete variable representation

Chinese Journal of Chemical Physics 2013年第6期26卷 755-764,I0005页

作者： De-quan Yu Shu-lin Cong Dong H. Zhang Zhi-gang Sun School of Physics and Optoelectronic TechnoloEy Dalian University of Technology Dalian 116024China State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical and ComputationalChemistry Dalian Institute of Chemical Physics Chinese Academy of Science Dalian 116023 China

Efficient numerical solver for the SchrSdinger equation is very important in physics and chemistry. The finite element discrete variable representation （FE-DVR） was first proposed by Rescigno and Mc-Curdy [Phys. Rev. A 62, 032706 （2000）] for solving quantum-mechanical scattering problems. In this work, an FE-DVR method in a mapped coordinate was proposed to improve the efficiency of the original FE-DVR method. For numerical demonstration, the proposed approach is applied for solving the electronic eigenfunctions and eigenvalues of the hydrogen atom and vibrational states of the electronic state 3E＋ of the Cs2 molecule which has long-range interaction potential. The numerical results indicate that the numerical efficiency of the original FE-DVR has been improved much using our proposed mapped coordinate scheme.

关键词： discrete variable representation Mapped Fourier method Ultra-cold atomic photoassociation Schrodinger equation solver Singularity of Coulomb potential

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Numerical Convergence of the Sinc discrete variable representation for Solving Molecular Vibrational States with a Conical Intersection in Adiabatic representation

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Chinese Journal of Chemical Physics 2019年第3期32卷 333-342,I0001-I0002页

作者： Hai-mei Shi Guang-hai Guo Zhi-gang Sun School of Mathematics and Physics Qingdao University of Science and TechnologyQingdao 266061China State Key Laboratory of Molecular Reaction Dynamics and Center for Theoretical Computational Chemistry Dalian Institute of Chemical PhysicsChinese Academy of SciencesDalian 116023China

Within the Born-Oppenheimer(BO)approximation,nuclear motions of a molecule are often envisioned to occur on an adiabatic potential energy surface(PES).However,this single PES picture should be reconsidered if a conical intersection(CI)is present,although the energy is well below the *** presence of the CI results in two additional terms in the nuclear Hamiltonian in the adiabatic presentation,i.e.,the diagonal BO correction(DBOC)and the geometric phase(GP),which are divergent at the *** the same time,there are cusps in the adiabatic *** usually it is regarded that there is numerical difficulty in a quantum dynamics calculation for treating CI in the adiabatic representation.A popular numerical method in nuclear quantum dynamics calculations is the Sinc discrete variable representation(DVR)*** examine the numerical accuracy of the Sinc DVR method for solving the Schrodinger equation of a two dimensional model of two electronic states with a CI in both the adiabatic and diabatic *** results suggest that the Sinc DVR method is capable of giving reliable results in the adiabatic representation with usual density of the grid points,without special treatment of the divergence of the DBOC and the *** numerical uncertainty is not worse than that after the introduction of an arbitrary vector potential for accounting the GP,whose accurate form usually is not easy to obtain.

关键词： discrete variable representation Conical intersection Adiabatic and diabatic representaton Geometric phase

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

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Chinese Journal of Chemical Physics 2016年第1期29卷 112-122,I0002页

作者：于德权黄鹤 Gunnar Nyman 孙志刚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

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.

关键词： discrete variable representation Hermiticity Time-dependent wavepacket method Absorption spectra

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