Complete solution to the inverse Kohn-Sham problem: From the density to the energy

Abstract

A complete solution to the inverse problem of Kohn-Sham (KS) density functional theory is proposed. Our method consists of two steps. First, the effective KS potential is determined from the ground-state density of a given system. Then, the knowledge of the potentials along a path in the space of densities is exploited in a line integration formula to determine numerically the KS energy of that system. A possible choice for the density path is proposed. A benchmark in the case of a simplified yet realistic nuclear system is shown to be successful, so the method seems promising for future applications.

Calculating Potential Energy Surfaces with Quantum Computers by Measuring Only the Density Along Adiabatic Transitions

“…The KS potential is defined as v normalK normalS = ∂ F ∂ ρ . In refs and , it was shown that energy differences between different external potentials can be calculated by using the line integral formula E normalK normalS ( ρ B ) − E normalK normalS ( ρ A ) = prefix∫ normald t ∫ normald r .25em v normalK normalS ( r , t ) ∂ ρ ( r , t ) ∂ t where ρ( r , t ) is such that the properties of eqs – are satisfied for all time points with external potential v ext ( r , t ). That is, the KS and fully interacting systems remain in the ground state, and the densities match.…”