Density functional theory: Approximating quasiparticle density functional

Abstract

A constructive approach for deriving the approximating quasiparticle energy density functional is proposed. As a matter of fact, the proposed approach is the direct development of the Kohn-Sham quasiparticle concept and the Levy-Valone approach. The approach presented takes into account a pseudopotential character of the exchange-correlation part of the density functional and results in a system of functional equations to obtain ground-state energies of many-electron systems. Preamble and IntroductionThe density functional theory has a long history begun by the fundamental works by Thomas and Gombas [7] (also see Ref. 8). A large volume of literature is devoted to the density functional theory [9-521. The density functional theory has some advantages in the quantum theory of atoms, molecules, and solid state, which are the result of one-particle pictures of many-body systems adopted there, and it simplifies computational problems. The density functional theory is a powerful approach that does not exhaust all of their possibilities.In the literature there exists a view that the density functional theory has the correct mathematical foundation based on the Hohenberg-Kohn theorem [16], which is the formal justification of the density functional theory. What does the Hohenberg-Kohn theorem represent?This theorem states the existence of the universal energy density functional for a fixed N-particle system where p(r) is the density of this system with and not of Vext(r). Therefore, F [ p ] is also universal because it only needs to be computed once for all times and for all many-particle systems. Then the groundstate energy and the ground-state density p(r) are determined from the variational

Density functional calculation of transition metal cluster energy surfaces

“…The first term in (19) is the classical Coulomb energy; the second one describes the interaction of the vm-th quasi-particle with its exchange-correlation "hole" [9], and the last terms are Weizsacker's and Hartree's quanties of the v,-th quasi-particle self-energy, respectively.…”

“…The above-developed QFC approach leads one to the generalization of ordinary density functional calculation [7] of the ground-state energy of clusters in nonlocal pseudopotential spirit by Gilbert's theorem [8] and the ideology of the approximating quasi-particle density functional method [9]. The AQDF method, one of the QFC theory's applications to computing of compact quasi-molecules, represents a wide class of nonlocal density functional methods, which are wellknown as orbital density functional methods [lo].…”

“…is some quantum field order parameter of m-quasi-molecule exact ground state obtained by the variational procedure (9). Thus, phase transitions of electron microstructure in condensed ground states may be described in terms of quantum electron field order parameters (gk (2) (12)…”

Four‐dimensional density and energy density functional

“…A very interesting constructive approach was proposed by Levy [3] and Valone [4]. Recently, an alternative approach is being examined by Beznosjuk and Kryachko [5].…”