So far we have assumed the utilised orbital basis to be semicanonical, which is equivalent to asserting that for the given orbital basis, Brillouin's theorem must hold. The most direct consequence of Brillouin's theorem is that only doubly excited determinants influence the correlation energy. For a noncanonical orbital basis, however, there is an additional nonzero contribution from singly excited determinants. Within MBPT theory, the first order singly excited amplitudes t a i (1) are given as: