Ensuring proper short-range and asymptotic behavior of the exchange-correlation Kohn-Sham potential by modeling with a statistical average of different orbital model potentials
The long-range asymptotic behavior of the exchange-correlation Kohn-Sham (KS) potential {nu}{sub xc} and its relation to the exchange-correlation energy E{sub xc} are considered using various approaches. The line integral of {nu}{sub xc}([{rho}];r) yielding the exchange-correlation part {Delta}E{sub xc} of a relative energy {Delta}E of a finite system, shows that a uniform constant shift of {nu}{sub xc} never shows up in any physically meaningful energy difference {Delta}E. {nu}{sub xv} may thus be freely chosen to tend asymptotically to zero or to some nonzero constant. Possible choices of the asymptotics of the potential are discussed with reference to the theory of open systems with a fractional number of electrons. The authors adhere to the conventional choice {nu}{sub xc}({infinity}) = 0 for the asymptotics of the potential leading to {epsilon}{sub N} = {minus}I{sub p} for the energy {epsilon}{sub N} of the highest occupied orbital. A statistical average of orbital dependent model potentials is proposed as a way to model {nu}{sub xc}. An approximate potential {nu}{sub xco}{sup SAOP} with exact {minus}1/r asymptotics is developed using the statistical average of, on the one hand, a model potential {nu}{sub xc{sigma}}{sup Ei} for the highest occupied KS orbital {psi}{sub N{sigma}} and, on the other hand, a model potential {nu}{sub xc}{sup GLB} for other occupied orbitals. It is demonstrated for the well-studied case of the Ne atom, that calculations with the new model potential can, in principle, reproduce perfectly all energy characteristics.
- Research Organization:
- Vrije Univ., Amsterdam (NL)
- OSTI ID:
- 20005605
- Journal Information:
- International Journal of Quantum Chemistry, Vol. 76, Issue 3; Other Information: PBD: 20 Jan 2000; ISSN 0020-7608
- Country of Publication:
- United States
- Language:
- English
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