DOI: 10.1063/1.1381013. Can optimized effective potentials be determined uniquely?

Can optimized effective potentials be determined uniquely?

10.1063/1.1381013

Crossref journal-article

AIP Publishing

The Journal of Chemical Physics (317)

Abstract

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.

Bibliography

Hirata, S., Ivanov, S., Grabowski, I., Bartlett, R. J., Burke, K., & Talman, J. D. (2001). Can optimized effective potentials be determined uniquely? The Journal of Chemical Physics, 115(4), 1635â1649.

Authors 6

So Hirata (first)
Stanislav Ivanov (additional)
Ireneusz Grabowski (additional)
Rodney J. Bartlett (additional)
Kieron Burke (additional)
James D. Talman (additional)

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Dates

Type	When
Created	23 years, 1 month ago (July 26, 2002, 8:44 a.m.)
Deposited	1 year, 6 months ago (Feb. 11, 2024, 1:45 a.m.)
Indexed	3 weeks, 1 day ago (Aug. 6, 2025, 9:05 a.m.)
Issued	24 years, 1 month ago (July 22, 2001)
Published	24 years, 1 month ago (July 22, 2001)
Published Print	24 years, 1 month ago (July 22, 2001)

Funders 0

None

BibTeX

@article{Hirata_2001, title={Can optimized effective potentials be determined uniquely?}, volume={115}, ISSN={1089-7690}, url={http://dx.doi.org/10.1063/1.1381013}, DOI={10.1063/1.1381013}, number={4}, journal={The Journal of Chemical Physics}, publisher={AIP Publishing}, author={Hirata, So and Ivanov, Stanislav and Grabowski, Ireneusz and Bartlett, Rodney J. and Burke, Kieron and Talman, James D.}, year={2001}, month=jul, pages={1635–1649} }

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