# 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

Chemical Physics Letters **398**, 445 - 448 (2004)

# 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*(**r**_{1},**r**_{2})/*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.

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- http://dx.doi.org/10.1016/j.cplett.2004.08.043