Density functionals with spin-density accuracy for open shells

Abstract

Electrons in zero external magnetic field can be studied with density functional theory (DFT) or with spin-DFT (SDFT). The latter is normally used for open shell systems because its approximations appear to model better the exchange and correlation (xc) functional, but also because so far the application of DFT implied a closed-shell-like approximation. Correcting this error for open shells allows the approximate DFT xc functionals to become as accurate as those in SDFT. In the limit of zero magnetic field, the Kohn-Sham equations of SDFT emerge as the generalised KS equations of DFT.

Approaching periodic systems in ensemble density functional theory via finite one-dimensional models

“…The development of accurate weight-dependent density-functional approximations (DFAs) for EDFT is an ongoing challenge. Existing ensemble approximations to E w xc include the quasi-LDA (qLDA) functional [38,39], the 'ghost'-corrected exact exchange (EXX) functional [40,41], the exact ensemble exchange functional (EEXX), [42] local system-dependent and excitation-specific ensemble exchange functionals for double excitations (CC-S) [43] and for single excitations [61], a universal weight-dependent local correlation functional (eVWN5) based on finite UEGs [43], and the orbital-dependent second-order perturbative approximation (PT2) for the ensemble correlation energy functional [44,62]. As noted in all the aforementioned works, ensemble HXC has special complications beyond those of GS DFT, such as the consideration that ensemble Hartree and exchange are not naturally separated in EDFT [45].…”

DFT exchange: sharing perspectives on the workhorse of quantum chemistry and materials science

“…Recently, we managed to write down such a density functional for the magnetization density in DFT (not spin DFT) for open-shell systems in the absence of an external magnetic field. 657 4.4.3 Gould. Much recent work on ensemble DFT (see Section 3.7) and DFAs is focused on excited states.…”

“…Recently, we managed to write down such a density functional for the magnetization density in DFT (not spin DFT) for open-shell systems in the absence of an external magnetic field. 657 …”

Improving the exchange and correlation potential in density functional approximations through constraints

“…One of the integers N , N + 1 is an odd number, corresponding to an open shell system. The LDA exchange energy for open shells contains an error ("ghost-exchange error" [26]) in modelling exchange with half the electrons spin-up and half spin-down. In a forthcoming publication [26], we propose how to correct this error, still within LDA (not local spin density approximation).…”

“…The LDA exchange energy for open shells contains an error ("ghost-exchange error" [26]) in modelling exchange with half the electrons spin-up and half spin-down. In a forthcoming publication [26], we propose how to correct this error, still within LDA (not local spin density approximation). Hence, in the KS calculation for an odd number of electrons (either for N or for N + 1), we employ our method to correct for the ghost-exchange error, in order to improve the accuracy of the resulting CLDA xc potential and density.…”