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 gamma(r,r'), which is known, of course formally in general, to be a functional of the electron density rho(r) = gamma(r,r). By explicit construction, we show that the functional derivative deltagamma(r(1),r(2))/deltarho(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. (C) 2004 Published by Elsevier B.V.