%0 Journal Article
%T Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates
%A De quan Yu
%A He Huang
%A Gunnar Nyman
%A Zhi gang Sun
%J Chinese Journal Of Chemical Physics
%@ 1003-7713
%V 29
%N 1
%D 2016
%P 112-122
%K Discrete variable representation;Hermiticity;Time-dependent wavepacket method;Absorption spectra
%X 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.
%R 10.1063/1674-0068/29/cjcp1507141
%U http://cjcp.ustc.edu.cn/hxwlxb_en/ch/reader/article_export.aspx?file_no=cjcp1507141&flag=1&export_type=EndNote
%1 JIS Version 3.0.0