N -representability problem within the framework of the contracted Schrödinger equation

A a procedure is proposed by which, in the course of an iterative solution of the second-order contracted Schr\"odinger equation, The N representability of the second-order reduced density matrix can be tested with increasing stringency. This procedure was suggested by an extended study of the G conditions and from the contraction into the two-electron space of an N-fermion relation, expressing in matrix form the antisymmetry and normalization properties of the N-electron wave function. Several relations are reported.