Construction of ApproximatelyN-Representable Density Matrices

A method is given for obtaining the density matrix or matrices, expressible in terms of a given set of spin geminals, which are as nearly $N$ representable as possible. A measure of $N$ representability is introduced as the norm of the antisymmetric component of a normalized wave function leading to the density matrix. An error estimate is given for the maximum deviation of an energy calculated with the density matrix from that calculated with an antisymmetric wave function. Linear variational parameters may occur in the density matrix, and their number can be increased at the expense of $N$ representability. Implementation of the method requires diagonalization of a large matrix, and the consequences of truncation are considered. The method is also related to the problem of the exact $N$ representability of a given density matrix.