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Virial exchange–correlation energy density in Hooke's atom

✍ Scribed by Kin-Chung Lam; Federico G. Cruz; Kieron Burke

Publisher
John Wiley and Sons
Year
1998
Tongue
English
Weight
211 KB
Volume
69
Category
Article
ISSN
0020-7608

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✦ Synopsis

Application of the virial theorem to the interelectronic Coulomb repulsion

shows that the virial of the exchange potential yields the exchange energy. However, the virial of the correlation potential does not yield the correlation energy. We have recently constructed a ''hypercorrelated'' potential whose virial is the correlation energy. We apply these ideas to a system which contains two interacting electrons in an external harmonic potential, Hooke's atom. This system can be solved analytically for a set of spring constants and numerically for any spring constant. By inverting the Kohn᎐Sham equations, the exact exchange and correlation potentials can be found. These exact values are compared with several popular approximate functionals, namely local spin density Ž . Ž . Ž . LSD , Perdew, Burke, and Ernzerhof PBE , and Becke and Lee᎐Yang᎐Parr BLYP . We illustrate our results for two values of the spring constant. At a moderate value, the density is comparable to the He atom, while for a low spring constant, we explore extremely low densities.

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