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An investigation of the kohn‐sham and slater approximations to the hartree‐fock exchange potential
Author(s) -
Mcnaughton David J.,
Smith Vedene H.
Publication year - 2009
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.560040740
Subject(s) - kohn–sham equations , virial theorem , hartree–fock method , atomic orbital , slater type orbital , binding energy , quantum mechanics , chemistry , atom (system on chip) , atomic physics , hartree , linear combination of atomic orbitals , physics , electron , density functional theory , galaxy , computer science , embedded system
The self‐consistent‐field equations for the ground state of the argon atom have been solved for a range of values of the parameter C in the local approximation:\documentclass{article}\pagestyle{empty}\begin{document}$$ V_{{\rm Exch}}^C ({\bf r}) = ‐ 6C[3/8\pi \rho \left( {\bf r} \right)]^{1/3} $$\end{document}to the Hartree‐Fock exchange potential. The orbital solutions with and without the Latter tail modification are used to investigate the relative merits of the Slater ( C = 1) and Kohn‐Sham ( C = 2/3) local exchange potentials. To do this various expectation values are calculated. Total and one‐electron binding energies are calculated as the expectation value of the Slater determinant built up from the orbitals and by using the statistical approximation to that expression. It is this statistical approximation for the total energy which Kohn‐Sham varied to obtain their local exchange potential. When computing one‐electron binding energies for frozen orbitals in the statistical approximation, it is only in the Slater case ( C = 1) that the eigen‐values of the self‐consistent‐field equations may be so interpreted. The role of the virial theorem and the improvements yielded by scaling are discussed. The Kohn‐Sham model compares better with Hartree‐Fock than the Slater model with regard to total energy, one‐electron binding energies and the virial theorem. Other choices for C , according to various criteria, are discussed with the view towards a better statistical approximation to the Hartree‐Fock exchange potential.