Construction of integrable model Kohn-Sham potentials by analysis of the structure of functional derivatives

Abstract

A directly approximated exchange-correlation potential should, by construction, be a functional derivative of some density functional in order to avoid unphysical results. Using generalized gradient approximations (GGAs) as an example, we show that functional derivatives of explicit density functionals have a very rigid inner structure, the knowledge of which allows one to build the entire functional derivative from a small part. Based on this analysis, we develop a method for direct construction of integrable Kohn-Sham potentials. As an illustration, we transform the model potential of van Leeuwen and Baerends (which is not a functional derivative) into a semilocal exchange potential that has a parent GGA, yields accurate energies, and is free from the artifacts inherent in existing semilocal potential approximations.

Assessment of density functional methods with correct asymptotic behavior

“…[33]). Due to the inclusion of the gradient-dependent exchange potential, the LB94 (or LBα) potential is not a functional derivative [44,46]. In this work, the exchange energy from the LB94 (or LBα) exchange potential is calculated by the popular Levy-Perdew virial relation [61]:…”

“…Besides, as these model potentials are not variationally stable, the associated XC energies are not well-defined, and the predicted properties need to be carefully interpreted. The proposals made by Staroverov and co-workers [45,46] are useful for transforming a model GGA exchange potential (which is not a functional derivative) into an exchange potential that has a parent GGA functional. However, for the LB94 potential (an AC model potential with no parent GGA functional) [33], the transformed potential no longer has the correct (−1/r) asymptote [46].…”

A generalized gradient approximation for exchange derived from the model potential of van Leeuwen and Baerends

“…It is quite feasible, at least at the level of generalized gradient approximations, to develop model potentials that are by construction functional derivatives. 30,31 However, even in that case the presence of r in the Levy-Perdew energy density leads to unappealing artifacts for extended systems. 32,33 What is desired is a method for turning model Kohn-Sham potentials into properly invariant energy functionals with positionindependent energy densities.…”

Comparison between exact and semilocal exchange potentials: An all-electron study for solids

“…16,17 Therefore several studies have focused on the search for better semilocal approximations for v x rather than E x . Among these studies there are the early works of Engel and Vosko, 17 Baerends and co-workers, [18][19][20][21] and the more recent works of Becke and Johnson, 22 Staroverov and co-workers, [23][24][25][26] Armiento et al, 27,28 and others. 29,30 It is worth mentioning that all these approximations for v x can be categorized in one of these two groups, namely, those which are functional derivative of a functional E x and those which are not (such potentials were termed stray in Ref.…”