Change in analytic structure of first-order density matrix as a functional of electron density due to inter-particle correlation: a two-electron model example

Density matrix functional theory is currently attracting a good deal of attention because of its potential for quantum chemistry. Here we focus on the correlated first-order density matrix γ(r,r′), which is known, of course formally in general, to be a functional of the electron density ρ(r) = γ(r,r). By explicit construction, we show that the functional derivative δγ(r1,r2)/δρ(r) has its analytical structure crucially changed by inter-particle correlation in the solvable two-electron spin-compensated ground-state of the model proposed by Moshinsky in 1968. Here, there is both harmonic confinement to the nucleus of the two electrons with opposed spins, as well as Hookean inter-particle interaction. Provided one retains harmonic confinement, some more modest progress is possible for a general inter-particle force law.