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Fully numerical solutions of the hartree‐fock equation in momentum space: A numerical study of the He atom and H + 2 ion
Author(s) -
Rodríguez Wilfredo,
Ishikawa Yasuyuki
Publication year - 1988
Publication title -
international journal of quantum chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.484
H-Index - 105
eISSN - 1097-461X
pISSN - 0020-7608
DOI - 10.1002/qua.560340848
Subject(s) - position and momentum space , momentum (technical analysis) , truncation (statistics) , diatomic molecule , hartree–fock method , truncation error , kinetic energy , space (punctuation) , coordinate space , physics , ion , atomic physics , chemistry , quantum mechanics , mathematics , mathematical analysis , molecule , geometry , linguistics , statistics , philosophy , finance , economics
A major impediment to achieving accurate solutions of the momentum‐space Hartree‐Fock equation in fully numerical form lies in the error caused by the truncation of momentum space. We use a coordinate transformation, which is characterized by P = tan(α/2), thus avoiding this truncation to achieve accurate solutions of the Hartree‐Fock equation. Using this approach, we have re‐examined the He model problem previously analyzed by Delhalle and Defranceschi [Intern. J. Quantum Chem. Symp. 21 425 (1987)]: The kinetic, nuclear attraction and Coulomb repulsion energies of the He atom have been evaluated using both conventional spherical polar momentum coordinates, ( p , θ, φ) and the transformed coordinates, (α,θ,φ) in order to compare their accuracies. We have performed a number of fully numerical calculations on the H + 2ion in order to examine the influence of the number of points in the mesh on the accuracy of the computed total electronic energy of the diatomic molecule.