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Representation of Kohn–Sham free atom eigenfunctions by Slater‐type orbitals
Author(s) -
Romanowski Zbigniew,
Jalbout Abraham F.
Publication year - 2008
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.21668
Subject(s) - eigenfunction , kohn–sham equations , mathematics , nonlinear system , atomic orbital , linear combination of atomic orbitals , mathematical analysis , galerkin method , atom (system on chip) , slater type orbital , type (biology) , basis set , mathematical physics , eigenvalues and eigenvectors , density functional theory , physics , quantum mechanics , electron , computer science , ecology , biology , embedded system
Abstract Slater‐type orbitals are applied to represent the numerically obtained Kohn–Sham eigenfunction of free atom. The algorithm evaluating the nonlinear expansion coefficients of this approximation is described. Standard iterative solution of Kohn–Sham equation to obtain the nonlinear expansion coefficients is avoided and replaced by the projection method. First, the eigenfunction is obtained in the B‐spline space based on the Galerkin formulation of the finite element method. Then, based on the density functional theory, the conditions are formulated, which leads to the set of nonlinear equations. The proposed algorithm is general and can be applied for any atomic Kohn–Sham eigenfunction. As an examplary application of the proposed algorithm, the set of nonlinear equations is derived for occupied states of N, Al, Ga, and In atoms. The expansion coefficients, obtained for these atoms, are evaluated numerically by Newton procedure and listed in the tables. © 2008 Wiley Periodicals, Inc. Int J Quantum Chem, 2008