TY - JOUR

T1 - Dual transformation for wave packet dynamics

T2 - Application to Coulomb systems

AU - Kawata, Isao

AU - Kono, Hirohiko

PY - 1999/12/1

Y1 - 1999/12/1

N2 - A dual transformation technique that can deal with awkward Coulomb potentials is developed for electronic wave packet dynamics. The technique consists of the variable transformation of the Hamiltonian and the transformation of the wave function with a normalization constraint. The time evolution is carried out by the alternating-direction implicit method. The operation of the transformed Hamiltonian on the wave function is implemented by using three- and five-point finite difference formulas. We apply it to the H atom and a realistic three-dimensional (3D) model of H+2. The cylindrical coordinates ρ and z are transformed as ρ=f(ξ) and z=g(ζ), where ξ and ζ are scaled cylindrical coordinates. Efficient time evolution schemes are provided by imposing the variable transformations on the following requirements: The transformed wave function is zero and analytic at the nuclei; the equal spacings in the scaled coordinates correspond to grid spacings in the cylindrical coordinates that are small near the nuclei (to cope with relatively high momentum components near the nuclei) and are large at larger distances thereafter. No modifications of the Coulomb potentials are introduced. We propose the form f(ξ)=ξ[ξn/(ξn + αn)]ν. The parameter α designates the ρ-range where the Coulomb potentials are steep. The n=1 and ν=1/2 transformation provides most accurate results when the grid spacing Δξ is sufficiently small or the number of grid points, Nξ, is large enough. For small Nξ, the n=1/2 and ν=1 transformation is superior to the n =1 and ν=1/2 one. The two transformations are also applied to the dissociation dynamics in the 3D model of H+2. For the n=1/2 and ν=1 transformation, the main features of the dynamics are well simulated even with moderate numbers of grid points. The validity of the two transformations is also enforced by the fact that the missing volume in phase space decreases with decreasing Δξ

AB - A dual transformation technique that can deal with awkward Coulomb potentials is developed for electronic wave packet dynamics. The technique consists of the variable transformation of the Hamiltonian and the transformation of the wave function with a normalization constraint. The time evolution is carried out by the alternating-direction implicit method. The operation of the transformed Hamiltonian on the wave function is implemented by using three- and five-point finite difference formulas. We apply it to the H atom and a realistic three-dimensional (3D) model of H+2. The cylindrical coordinates ρ and z are transformed as ρ=f(ξ) and z=g(ζ), where ξ and ζ are scaled cylindrical coordinates. Efficient time evolution schemes are provided by imposing the variable transformations on the following requirements: The transformed wave function is zero and analytic at the nuclei; the equal spacings in the scaled coordinates correspond to grid spacings in the cylindrical coordinates that are small near the nuclei (to cope with relatively high momentum components near the nuclei) and are large at larger distances thereafter. No modifications of the Coulomb potentials are introduced. We propose the form f(ξ)=ξ[ξn/(ξn + αn)]ν. The parameter α designates the ρ-range where the Coulomb potentials are steep. The n=1 and ν=1/2 transformation provides most accurate results when the grid spacing Δξ is sufficiently small or the number of grid points, Nξ, is large enough. For small Nξ, the n=1/2 and ν=1 transformation is superior to the n =1 and ν=1/2 one. The two transformations are also applied to the dissociation dynamics in the 3D model of H+2. For the n=1/2 and ν=1 transformation, the main features of the dynamics are well simulated even with moderate numbers of grid points. The validity of the two transformations is also enforced by the fact that the missing volume in phase space decreases with decreasing Δξ

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U2 - 10.1063/1.480281

DO - 10.1063/1.480281

M3 - Article

AN - SCOPUS:0000791515

VL - 111

SP - 9498

EP - 9508

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 21

ER -