TY - JOUR
ID - 10.1063/1674-0068/29/cjcp1507141
TI - Hermiticity of Hamiltonian Matrix using the Fourier Basis Sets in Bond-Bond-Angle and Radau Coordinates
AU - De-quan Yu
AU - He Huang
AU - Gunnar Nyman and Zhi-gang Sun
VL - 29
IS - 1
PB -
SP - 112
EP - 122
PY -
JF - Chinese Journal Of Chemical Physics
JA -
UR - http://cjcp.ustc.edu.cn/hxwlxb_en/ch/reader/view_abstract.aspx?file_no=cjcp1507141&flag=1
KW - 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
KW - Discrete variable representation;Hermiticity;Time-dependent wavepacket method;Absorption spectra
AB - 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.
ER -