(23) |

Conserving *M*_{s} requires that the spins of *j* and *b* are equal. Therefore,

(24) |

After integrating over spin, this becomes in chemists' notation

(25) |

Time-reversal symmetry imposes certain conditions on the CI coefficients. In alpha and beta string notation [5], for

An analogous equation also holds for . This means that for a closed shell RHF reference, ( ) for singlets, and ( ) for triplets; thus only half of the CI coefficients must be computed explicitly. These sign rules are also evident from the observation that and are not spin eigenfunctions, but that the total CI wavefunction will be a spin eigenfunction (if the required determinants are present in the CI space). Using the determinant sign convention of Szabo and Ostlund [6], spin eigenfunctions (or CSFs) associated with the above determinants are

Using these relationships between CI coefficients, we obtain

= | (29) | ||

= | (30) |

Furthermore, and .

Consider how equations
(20)-(22) change when spin is
explicitly accounted for. There will be two pseudodensity matrices,

Due to equation (26), for singlets, and for triplets. Thus it is necessary to form only one of the Fock-like matrices, or . The former is constructed as

= | (33) | ||

= | (34) |

Finally is constructed according to eq (22). In terms of these quantities, the vector can be written

= | (35) | ||

= | (36) |