Variational reduced-density-matrix theory: strength of Hamiltonian-dependent positivity conditions

Variational reduced-density-matrix (RDM) theory, employing the 2-RDM as the primary variable, has the potential to overcome the scaling limitations of configuration interaction to provide accurate electronic ground-state energies. A significant aspect of variational RDM theory is the inclusion of N-representability conditions which ensure that the 2-RDM corresponds to the N-particle wavefunction. Recent implementations of the method have mainly considered Hamiltonian-independent positivity conditions. In this Letter, we evaluate the strength of two Hamiltonian-dependent conditions. While one of the conditions is proven inactive, the positivity of the matrix S H j i = 〈 ψ | C ˆ i † [ H ˆ , C ˆ j ] | ψ 〉 provides additional N-representability conditions that may be beneficial in future RDM calculations.