Charge densities for singlet and triplet electron pairs

✍ Scribed by Viktor N. Staroverov; Ernest R. Davidson

• Book ID: 101257422
• Publisher: John Wiley and Sons
• Year: 2000
• Tongue: English
• Weight: 464 KB
• Volume: 77
• Category: Article
• ISSN: 0020-7608
• DOI: 10.1002/(sici)1097-461x(2000)77:3<651::aid-qua6>3.0.co;2-n

✦ Synopsis

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)]/2M. For a wave function which is not an eigenfunction of S 2 , 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.