(37) |

Unfortunately, for a UHF reference equations (26)-(28) no longer hold, so that the above equation can be simplified only to

(38) |

Even though spin has been integrated out, the overbars must be kept in the above equation because the spatial parts of spin orbitals

(39) |

and there is no general relationship between and . The pseudodensity matrices and are defined as in eq. (31) and (32), but they are no longer simply related. Thus it is necessary to compute two Fock-like matrices, according to

= | (40) | ||

= | (41) |

In contrast to RCIS, there are no longer separate singlet and triplet cases, since the UCIS eigenfunctions are not CSFs. After transforming to the MO basis by

= | (42) | ||

= | (43) |

the expressions for become

= | (44) | ||

= | (45) |