Abstract: | The problem of pure-state N-representability of the two-particle spin-dependent density function ρ(x1, x2) is considered for an N-electron system, and a procedure for finding an N-representable ρ(x1, x2) is advanced. The problem is formulated in the framework of a family of N × N matrices formed from integrals of auxiliary two-particle functions θn(x1, x2) converging at n → ∞ to ρ(x1, x2)/N(N?1)]. The simple requirement of positive definiteness of these matrices is shown to play a decisive role in finding an N-representable ρ(x1, x2). The results obtained may open new possibilities for using ρ(x1, x2) in the density-functional theory. © 1997 John Wiley & Sons, Inc. Int J Quant Chem 65 : 127–142, 1997 |