Finite element calculations for systems with multiple Coulomb centers

JOURNAL OF COMPUTATIONAL AND APPLIED MATHEMATICS

卷:236

Article

Braun, Moritz

关键词: Cusp condition;    Effective;    Schrodinger equation;    Method of finite elements;    Python;    Coulomb center;   

DOI  :  10.1016/j.cam.2012.02.005

来源: Elsevier

【 摘 要 】

The presence of multiple Coulomb centers in molecules or solids poses a challenge when solving the effective Schrodinger equation, required as a crucial ingredient in density functional or Hartree-Fock calculations. This is primarily because Kato's cusp condition needs to be satisfied close to each nucleus and the matrix elements of the Coulomb potential at the nuclei are rather difficult to evaluate when using global basis functions. A novel method for dealing with these challenges is introduced, rewriting the wavefunction as a product of a function satisfying the nuclear cusp conditions and a smooth function, resulting in a transformed variational principle and a regularized potential. Results of three-dimensional finite element calculations based on this ansatz for the ground state of the molecule H-2(+) in the Born-Oppenheimer approximation are presented, which were obtained using custom written Python/Fortran code. (C) 2012 Elsevier B.V. All rights reserved.

【 授权许可】

Free