| Abstract: | The Colle–Salvetti second-order reduced density matrix (2-matrix) is an approximation to the 2-matrix obtained from a wave function that is a product of a reference wave function containing little or no correlation times a product of correlation factors that are functions of the coordinates of pairs of electrons. A formal proof is given for the non-N-representability for the Colle–Salvetti 2-matrix using the nonnegativity condition of the 2-matrix. The nonnegativity condition of the particle-hole overlap matrix (G matrix) is also not satisfied. The proof is valid for Colle–Salvetti 2-matrices obtained from both the Hartree–Fock and small multiconfigurational-self-consistent-field wave functions. Even though the Colle–Salvetti 2-matrix is not N-representable, it does satisfy the Pauli principle component of the G-matrix condition because it reduces to an N-representable first-order reduced density matrix. © 1993 John Wiley & Sons, Inc. |
