A simple algorithm for the Kohn–Sham inversion problem applicable to general target densities

Abstract

A simple algorithm for the Kohn-Sham inversion problem is presented. The method is found to converge towards a nearby ν-representable Kohn-Sham density irrespective of the fact whether the initial target density has been νrepresentable or not. For the proposed procedure the target density can be of general nature. The algorithm can handle Hartree-Fock and post Hartree-Fock, spin-unpolarized and polarized states equally well. Additionally, experimental densities and even general gedanken densities can be treated. The algorithm is easy to implement and does not require an additional procedure to adjust eigenvalues.

A general penalty method for density‐to‐potential inversion

“…The exchange-correlation potentials obtained for different systems by using functionals S[ρ] of Equations (37)(38)(39)(40) are shown in Figures 1-3.…”

“…To do this, several inversion schemes have been proposed. [ 26–42 ] Most of them utilize optimization approaches based on the fundamental principles of DFT. [ 1,43,44 ] These approaches either minimize the noninteracting kinetic energy of electrons with the constraint that the corresponding orbitals lead to the given density ρ 0 ( r ) [ 30,31,43 ] or maximize the functional given in Equation ) by varying the KS potential.…”

Accurate effective potential for density amplitude and the corresponding Kohn-Sham exchange-correlation potential calculated from approximate wavefunctions

“…For a finite basis set calculation the ρ KS (r) = ρ(r) and the resulting potential is an approximation to the true potential conjugate to density ρ(r). The exchange-correlation potential obtained from other existing popular density-to-potential inversion methods [20][21][22][23][24][25][26][33][34][35]38,40,41,[63][64][65][66] depends upon what type of density it corresponds to and for a basis-set density it could show unphysical behavior. However, exchangecorrelation potential obtained by RKS method is found to be free from such pathological features.…”

“…In the following we will denote the exchange-correlation potential obtained by inversion of density as v ρ xc (r). There are several methods [20][21][22][23][24][25][26][33][34][35]38,40,41,[63][64][65] proposed for this inversion and most of them have been shown 66 to emanate from a single algorithm based on the Levy-Perdew-Sahni (LPS) equation 67 for the square root of the density. However, these methods are highly sensitive to the correctness of the density and its derivatives for a given v ext (r) and can lead to v ρ xc (r) having spurious features in them 31,64,[68][69][70][71] .…”

A general penalty method for density-to-potential inversion

“…As noted earlier, knowing v xc (r) exactly is of interest by itself and is also important to provide insights [20][21][22][23][24][25][26][27][28][29][30][31][32][33][34][35][36][37] into the working of approximate exchange-correlation functionals E xc [ρ]. To do this several inversion schemes have been proposed [38][39][40][41][42][43][44][45][46][47][48][49][50][51][52][53][54] . Most of them employ optimization approaches based on fundamental principles of DFT 1,55,56 .…”