Although the third determinant is a double substitution as far as spin-orbitals are concerned, it is only a single substitution when spatial orbital occupations are considered. Hence, it is very reasonable to assume that this CSF may be of comparable importance to the singles included in ROCIS. The extended CIS method (XCIS) is a spin-adapted CI method including these ``extended single'' substitutions.

It is helpful to first verify that eq. (86) is indeed
an eigenfunction of
.
Using previous results for ROCIS,
it is trivial to see that

(87) |

It remains to be seen what is the effect of acting on .

= | |||

= | (88) |

The factor acts on unpaired spins; thus,

= | |||

= | |||

= | (89) |

The result of has already been worked out in eq. (60). Thus overall,

(90) |

and it is easy to see that

(91) |

Hence (eq. 86) is a CSF.