Direct Calculation of First- and Second-Order Density Matrices. The Higher RPA Method

We present a procedure for approximately determining the first- and second-order density matrices of pure-state N-fermion systems. A higher random-phase approximation is used to derive a method in which the resulting density matrices are approximated self-consistently in an iterative scheme. As test calculations, the method is applied to the ground states of the helium, lithium, and beryllium atoms. The possibility and importance of obtaining error bounds involving the density matrices are discussed.