Charge densities for singlet and triplet electron pairs

Analytic properties of charge densities associated with singlet and triplet electron pairs, ρ 0 ( r ) and ρ 1 ( r ), are presented. In an N ‐electron system with total spin S , distributions ρ 0 ( r ) and ρ 1 ( r ) are independent of the spin projection quantum number M (spin rotation invariance), as opposed to the usual spin‐up and spin‐down electron densities, ρ α ( r ) and ρ β ( r ). We derive equations showing that in the case of a wave function which is a spin‐eigenfunction, ρ 0 ( r ) and ρ 1 ( r ) are linear combinations of the total charge density ρ( r ) and the uncompensated spin density ρ s ( r )=[ρ α ( r )−ρ β ( r )]/2 M . For a wave function which is not an eigenfunction of \documentclass{article}\pagestyle{empty}\begin{document}$\mathcal{S}^{2}$\end{document} , no such relationship exists. In a related discussion, a definition of the high‐spin solution corresponding to a given spin‐unrestricted Hartree–Fock wave function is proposed, and a notion of effectively unpaired electrons is introduced. The distributions ρ 0 ( r ) and ρ 1 ( r ) are shown not to be invariant under spin coupling between isolated systems. © 2000 John Wiley & Sons, Inc. Int J Quant Chem 77: 651–660, 2000