title: Reconstruction of Density Functionals from Kohn-Sham Potentials by Integration along Density Scaling Paths.
abstract: We demonstrate by specific examples that if a Kohn-Sham exchange-correlation potential is given explicitly in terms of the electron density and its derivatives, then one can easily reconstruct the parent density functional by evaluating analytically (or numerically with one-dimensional quadratures) the van Leeuwen-Baerends line integral (Phys. Rev. A 1995, 51, 170-178) along a path of (coordinate)-scaled densities. The choice of a density scaling path amounts to defining the gauge of the resultant exchange-correlation energy density. The well-known Levy-Perdew virial relation for exchange potentials can be viewed as an analytical line integral along the electron-number-conserving uniform density scaling path. Energies obtained from model exchange-correlation potentials should be interpreted with caution because the reconstructed density functional is unique (up to a gauge transformation) only if the model Kohn-Sham potential is a functional derivative.
authors.affiliation: Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada.
authors.forename: Alex P
authors.initials: AP
authors.lastname: Gaiduk
authors.affiliation: Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada.
authors.forename: Sergey K
authors.initials: SK
authors.lastname: Chulkov
authors.affiliation: Department of Chemistry, The University of Western Ontario, London, Ontario N6A 5B7, Canada.
authors.forename: Viktor N
authors.initials: VN
authors.lastname: Staroverov