Are Single Excitations Interacting?

For Slater determinants, and for Hartree-Fock references, Brillouin's theorem guarantees that single excitations will not contribute to the interacting space. However, if the reference is not obtained by the Hartree-Fock method, then single excitations may contribute (this is what McLean and Liu mean when they say that ``with the integral-independent subspaces single orbital excitations appear in first order, whereas with dependent subspaces they do not appear until second order.'') For CSF's, singly excited configurations may contribute, since these may contain doubly-excited determinants. Bunge observes,

For single excitations [from (s) (s) (p)] such as (s) s s (p), the dominant term does not belong to the coupling S(s) S(ss) P(p), but, rather, to S(s) P { S(ss) P(p) }. This can be explained in the following way: the first coupling involves only one-excited determinants, while the second one involves both one- and two-excited ones, the latter causing greater interaction with the HF configuration.

Nevertheless, due to the strong interaction of single excitations with the doubles, and also due to their importance in describing one-electron properties, we include all single excitations in our CI wavefunction.