Exact exchange potential evaluated from occupied Kohn-Sham and Hartree-Fock solutions
- Institute of Physical Chemistry of the Polish Academy of Sciences, 44/52 Kasprzaka, 01-224 Warsaw (Poland)
The reported algorithm determines the exact exchange potential v{sub x} in an iterative way using energy shifts (ESs) and orbital shifts (OSs) obtained with finite-difference formulas from the solutions (occupied orbitals and their energies) of the Hartree-Fock-like equation and the Kohn-Sham-like equation, the former used for the initial approximation to v{sub x} and the latter for increments of ES and OS due to subsequent changes of v{sub x}. Thus, the need for solution of the differential equations for OSs, used by Kuemmel and Perdew [Phys. Rev. Lett. 90, 043004 (2003)], is bypassed. The iterated exchange potential, expressed in terms of ESs and OSs, is improved by modifying ESs at odd iteration steps and OSs at even steps. The modification formulas are related to the optimized-effective-potential equation (satisfied at convergence) written as the condition of vanishing density shift (DS). They are obtained, respectively, by enforcing its satisfaction through corrections to approximate OSs and by determining the optimal ESs that minimize the DS norm. The proposed method, successfully tested for several closed-(sub)shell atoms, from Be to Kr, within the density functional theory exchange-only approximation, proves highly efficient. The calculations using the pseudospectral method for representing orbitals give iterative sequences of approximate exchange potentials (starting with the Krieger-Li-Iafrate approximation) that rapidly approach the exact v{sub x} so that, for Ne, Ar, and Zn, the corresponding DS norm becomes less than 10{sup -6} after 13, 13, and 9 iteration steps for a given electron density. In self-consistent density calculations, orbital energies of 10{sup -4} hartree accuracy are obtained for these atoms after, respectively, 9, 12, and 12 density iteration steps, each involving just two steps of v{sub x} iteration, while the accuracy limit of 10{sup -6} to 10{sup -7} hartree is reached after 20 density iterations.
- OSTI ID:
- 21550104
- Journal Information:
- Physical Review. A, Vol. 83, Issue 6; Other Information: DOI: 10.1103/PhysRevA.83.062515; (c) 2011 American Institute of Physics; ISSN 1050-2947
- Country of Publication:
- United States
- Language:
- English
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Related Subjects
ACCURACY
ALGORITHMS
ARGON
ATOMS
BERYLLIUM
CONVERGENCE
DENSITY FUNCTIONAL METHOD
DIFFERENTIAL EQUATIONS
ELECTRON DENSITY
EXCHANGE INTERACTIONS
HARTREE-FOCK METHOD
ITERATIVE METHODS
KRYPTON
MATHEMATICAL SOLUTIONS
MODIFICATIONS
NEON
POTENTIALS
ZINC
ALKALINE EARTH METALS
APPROXIMATIONS
CALCULATION METHODS
ELEMENTS
EQUATIONS
FLUIDS
GASES
INTERACTIONS
MATHEMATICAL LOGIC
METALS
NONMETALS
RARE GASES
VARIATIONAL METHODS