For many-electron systems, the generalized electron-pair density function g(q;a,b) represents the probability density function for the magnitude lari+brjl of two-electron vector ari+brj to be q, where a and b are real-valued parameters. For Hartree-Fock wave functions, decomposition of g(q;a,b) into spi.~-orbital-pair components gij(q;a,b) shows that the second moments _(a,b)~(ij), associated with g'J(q;a,b), satisfy several rigorous sum rules which connect one- and two-electron properties of spin-orbitals 1 and j. The same is also true in momentum space. As an illustrative application, the orbital kinetic energies of the Rn atom are separated into the relative motion and center-of-mass motion contributions of electrons in two relevant orbitals.
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