On the extremum property of electron density functions in position and momentum spaces

For statistically uncorrelated wave functions, the electron density ρ(r) is known to be an extremum function of the generalized electron-pair density g(q;a,b), which smoothly connects ρ(r), the electron-pair intracule (relative motion) density h(u), and the electron-pair extracule (center-of-mass motion) density d(R). The present systematic examination of the numerical Hartree–Fock results of moments 〈rn〉, 〈un〉, 〈Rn〉 and density values at the origin ρ(0), h(0), d(0) for 102 neutral atoms and 96 singly charged ions suggests that ρ(r) is local maximum for a small q and is local minimum for a large q of the function g(q;a,b). Analogous results are obtained for the momentum-space counterparts Π(p) and ḡ(t;a,b).