On the size-consistency of the reduced-density-matrix method and the unitary invariant diagonal N-representability conditions

A promising variational approach for determining the ground state energy and its properties is by using the second-order reduced density matrix (2-RDM). However, the leading obstacle with this approach is the N-representability problem. By employing a subset of conditions (typically the P, Q, G, T1 and T2′ conditions) results comparable to those of CCSD(T) can be achieved. However, these conditions do not guarantee size-consistency. In this work, we show that size-consistency can be satisfied if the 2-RDM satisfies the following conditions: (i) the 2-RDM is unitary invariant diagonal N-representable; (ii) the 2-RDM corresponding to each (unspecified) subsystem is the eigenstate of the number of corresponding electrons; and (iii) the 2-RDM satisfies at least one of the P, Q, G, T1 and T2′ conditions. This is the first time that a computationally feasible (though demanding) sufficient condition for the RDM method that guarantees size-consistency in all chemical systems has been published in the literature.