Using random numbers to obtain Kohn-Sham potential for a given density

Abstract

Most of the density-to-potential inversion methods developed over the years follow a general algorithm vxci+1(r)=vxci(r)+Δvxc(r), where Δvxc(r)=δS[ρ]δρ(r)∣ρi(r)-δS[ρ]δρ(r)∣ρ0(r) and S[ρ] is an appropriately chosen density functional. In this work we show that this algorithm can be used with random numbers to obtain the exchange–correlation potential for a given density. This obviates the need to evaluate the functional S[ρ] in each iterative step. The method is demonstrated by calculating exchange–correlation potential of atoms, clusters and the Hookium.