where p † /q denote creation and annihilation operatos corresponding to spin orbitals φ p /φ q , and indices p, q run over all spin-orbitals. The trace of γ equals the number of electrons and its eigenvalues are non-negative numbers between 0 and 1. The magnitude of these eigenvalues, called occupation numbers, reflects the relative weights of configurations in which the respective NO is occupied. For example, for a single Slater determinant Φ composed of a subset of {φ p }, γ pq is a diagonal matrix with γ pp = 1 for the orbitals occupied in Φ and zero otherwise. Thus, molecular orbitals from a Hartree-Fock calculation are also natural orbitals of the underlying Hartree-Fock wave-function. Moreover, because all occupied orbitals have unit occupancy and all virtual orbitals have zero occupancy, any unitary transformation within the occupied or virtual space yields a set of Hartree-Fock natural orbitals. For multideterminantal wave-functions, the occupation numbers become fractional.