Can density functional theory make use of experimentally determined ground-state electron densities via the Dirac density matrix for molecules of biological interest?

Abstract

Abstract More than four decades ago, March and Murray gave a perturbation theory of the single-particle(s) Dirac density matrix γ s ( r , r ′ ) to all orders in a given one-body potential energy V ( r ) . However, for density functional theory in orbital-free form, one requires the functional γ s [ ρ ] where ρ ( r ) is the ground-state electron density. Therefore, in the present study, a first-order non-linear differential equation is proposed for γ s in terms of ρ ( r ) and ∇ ρ ( r ) , plus the single-particle kinetic energy. Since this latter quantity is itself known to be a functional of ρ, the existence of such an equation for γ s would be a significant step along the road to determining the desired functional γ s [ ρ ] . As yet, we have succeeded in giving a rigorous proof of the proposed differential equation for γ s ( r , r ′ ) only for one- and two-level molecules. If it is subsequently proved for an arbitrary number of levels, which we believe should be possible, it would then allow γ s to be calculated for molecules of biological interest, from experimentally measured ground-state densities ρ ( r ) , as the approach is entirely orbital-free.