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Journal of Chemical Physics / Volume 115 / Issue 4 / ARTICLES / Theoretical Methods and Algorithms

J. Chem. Phys. 115, 1635 (2001); http://dx.doi.org/10.1063/1.1381013 (15 pages)

Can optimized effective potentials be determined uniquely?

So Hirata1, Stanislav Ivanov1, Ireneusz Grabowski1, Rodney J. Bartlett1, Kieron Burke2, and James D. Talman3

1Quantum Theory Project, University of Florida, Gainesville, Florida 32611
2Department of Chemistry, Rutgers University, 610 Taylor Road, Piscataway, New Jersey 08854
3Department of Applied Mathematics and Centre for Chemical Physics, University of Western Ontario, London, Ontario, Canada N6A 5B7

(Received 12 March 2001; accepted 2 May 2001)

Local (multiplicative) effective exchange potentials obtained from the linear-combination- of-atomic-orbital (LCAO) optimized effective potential (OEP) method are frequently unrealistic in that they tend to exhibit wrong asymptotic behavior (although formally they should have the correct asymptotic behavior) and also assume unphysical rapid oscillations around the nuclei. We give an algebraic proof that, with an infinity of orbitals, the kernel of the OEP integral equation has one and only one singularity associated with a constant and hence the OEP method determines a local exchange potential uniquely, provided that we impose some appropriate boundary condition upon the exchange potential. When the number of orbitals is finite, however, the OEP integral equation is ill-posed in that it has an infinite number of solutions. We circumvent this problem by projecting the equation and the exchange potential upon the function space accessible by the kernel and thereby making the exchange potential unique. The observed numerical problems are, therefore, primarily due to the slow convergence of the projected exchange potential with respect to the size of the expansion basis set for orbitals. Nonetheless, by making a judicious choice of the basis sets, we obtain accurate exchange potentials for atoms and molecules from an LCAO OEP procedure, which are significant improvements over local or gradient-corrected exchange functionals or the Slater potential. The Krieger–Li–Iafrate scheme offers better approximations to the OEP method. © 2001 American Institute of Physics.

© 2001 American Institute of Physics

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KEYWORDS and PACS

Keywords

LCAO calculations, potential energy functions, density functional theory, integral equations

PACS

ARTICLE DATA

Digital Object Identifier
http://dx.doi.org/10.1063/1.1381013

PUBLICATION DATA

ISSN

0021-9606 (print)  
1089-7690 (online)

Publisher

$abstract.society.value is a Member of CrossRef American Institute of Physics

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