Bounds on the PNOF5 natural geminal occupation numbers

The nonlinear N-representability condition obtained by Casida [2] is checked for the eigenvalues of the reconstructed two-particle reduced density matrix used in the Piris natural orbital functional 5 (PNOF5). The distinguished difference, with respect to other necessary N-representability conditions, is that the bounds on the natural geminal occupation numbers depend only on one-fermion properties, namely, the system one-particle reduced density matrix and the 1-matrix of the natural geminal associated with the eigenvalue to be bounded. It is shown that PNOF5 satisfies this N-representability necessary condition.