Charge densities for singlet and triplet electron pairs

Analytic properties of charge densities associated with singlet and triplet electron pairs, pg(r) and pl(r), are presented. In an N-electron system wi th total spin S, distributions rho(0)(r) and rho(1)(r) are independent of t he spin projection quantum number M (spin rotation invariance), as opposed to the usual spin-up and spin-down electron densities, rho(0)(r) and rho(1) (r). We derive equations showing that in the case of a wave function which is a spin-eigenfunction, rho(alpha)(r) and rho(beta)(r) are linear combinat ions of the total charge density rho(r) and the uncompensated spin density rho(s)(r) = [rho(alpha)(r) - rho(beta)(r)]/2M. For a wave function which is not an eigenfunction of S-2, no such relationship exists. In a related dis cussion, a definition of the high-spin solution corresponding to a given sp in-unrestricted Hartree-Fock wave function is proposed, and a notion of eff ectively unpaired electrons is introduced. The distributions rho(0)(r) and rho(1)(r) are shown not to be invariant under spin coupling between isolate d systems. (C) 2000 John Wiley & Sons, Inc.