Approximate Solution of the Representability Problem

Approximate solution of the ensemble representability problem for density operators of arbitrary order is obtained. This solution is closely related to the ``Q condition'' of A.J.Coleman. The representability conditions are formulated in orbital representation and are easy to use. They are tested numerically on the base of CI calculation of simple atomic and molecular systems. General scheme of construction of the contraction operator right inverses is proposed and the explicit expression for the right inverse associated with the expansion operator is derived as an example. Two algorithms for direct 2-density matrix determination are described.