Exchange-correlation potential virial theorem

Differential Virial Theorem and Exchange-Correlation Potential.99... 

DIFFERENTIAL VIRIAL THEOREM AND EXCHANGE-CORRELATION POTENTIAL... 

We have applied a slight variation of this general idea to the exchange-correlation potential of the He atom [18], The virial theorem applied to the Kohn-Sham system yields [39] ... 

However, in the second set of data, reporting scans of the PES for a limited set of small molecules, it appears that the geometries obtained are satisfactory. Moreover, the nature of the technique used for the determination of Exc, namely the use of a "senior" Exe functional, or the use of the virial theorem, as well as the use of a line integration (not reported here), leads to quite similar geometries. This point is in accord with a similar conclusion obtained by van Gisbergen et ol. in their frequency-dependent polarizabilities [75] they choose to use a "mixed scheme" where a different approximation for fxc and Vxc were used, whereas fxc is the functional derivative of the exchange-correlation potential Vxc, with respect to the time-dependent density. 

Holas A, March NH (1995) Exact exchange-correlation potential and approximate exchange potential in terms of density matrices. Phys Rev A 51 2040-2048 Nagy A, March NH (1997) Differential and local virial theorem. Mol Phys 91 597-602 Ehrenfest P (1927) Bemerkung fiber die angenaherte Gfiltigkeit der klassischen Mechanik innerhalb der Quantenmechanik. Z Phys A 45 455-457... 

We propose instead a type of middle ground. " From an examination of spin polarized and BS approaches, and some general results based on the virial theorem, we employ a strategy where general exchange and correlation effects are built into the potential j/xc (called dynamic correlation), while important wave function specific correlation effects are built into the BS method (called nondynamic or near-degeneracy correlation). 

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