N-Representability Problem for an Odd Number of Fermions

Abstract

The $N$-representability problem for the first- and second-order density matrices is considered when $N$ is an odd integer. Attention is restricted to those density matrices derivable from functions whose natural spin orbitals have certain paired properties. Neither pairing of spatial orbitals nor special spin properties are required in general, but they are discussed as special cases. New sufficient conditions for $N$-representability of the first-order density matrix are given. The second-order density matrix is studied in detail. Special cases in which the $N$-representability problem for the second-order density matrix can be solved are considered.