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From explicit to implicit density functionals
Author(s) -
Engel E.,
Dreizler R. M.
Publication year - 1999
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/(sici)1096-987x(19990115)20:1<31::aid-jcc6>3.0.co;2-p
Subject(s) - eigenvalues and eigenvectors , multiplicative function , perturbation theory (quantum mechanics) , van der waals force , limit (mathematics) , mathematics , integral equation , perturbation (astronomy) , physics , statistical physics , mathematical analysis , quantum mechanics , molecule
The concept of orbital‐ and eigenvalue‐dependent exchange‐correlation (xc) energy functionals is reviewed. We show how such functionals can be derived in a systematic fashion via a perturbation expansion, utilizing the Kohn–Sham system as a noninteracting reference system. We demonstrate that the second‐order contribution to this expansion of the xc‐energy functional includes the leading term of the van der Waals interaction. The optimized‐potential method (OPM), which allows the calculation of the multiplicative xc‐potential corresponding to an orbital‐ and eigenvalue‐dependent xc‐energy functional via an integral equation, is discussed in detail. We examine an approximate analytical solution of the OPM integral equation, pointing out that, for eigenvalue‐dependent functionals, the three paths used in the literature for the derivation of this approximation yield different results. Finally, a number of illustrative results, both for the exchange‐only limit and for the combination of the exact exchange with various correlation functionals, are given. © 1999 John Wiley & Sons, Inc. J Comput Chem 20: 31–50, 1999