Spin-flip extended CIS (SF-XCIS)^{Casanova:2008b} is a
spin-complete extension of the spin-flip single excitation configuration
interaction (SF-CIS) method.^{Krylov:2001b}
The method includes all configurations in which no more
than one virtual level of the high spin triplet reference
becomes occupied and no more than one doubly occupied level becomes vacant.

SF-XCIS is defined only from a restricted open shell Hartree-Fock triplet ground state reference. The final SF-XCIS wave functions correspond to spin-pure ${M}_{S}=0$ (singlet or triplet) states. The fully balanced treatment of the half-occupied reference orbitals makes it very suitable for applications with two strongly correlated electrons, such as single bond dissociation, systems with important diradical character or the study of excited states with significant double excitation character.

The computational cost of SF-XCIS scales in the same way with molecule size as CIS itself, with a pre-factor 13 times larger.

$molecule 0 3 C C 1 CC1 C 1 CC2 2 A2 C 1 CC2 2 A2 3 180.0 H 2 C2H 1 C2CH 3 0.0 H 2 C2H 1 C2CH 4 0.0 H 3 C3Hu 1 C3CHu 2 0.0 H 3 C3Hd 1 C3CHd 4 0.0 H 4 C3Hu 1 C3CHu 2 0.0 H 4 C3Hd 1 C3CHd 3 0.0 CC1 = 1.35 CC2 = 1.47 C2H = 1.083 C3Hu = 1.08 C3Hd = 1.08 C2CH = 121.2 C3CHu = 120.3 C3CHd = 121.3 A2 = 121.0 $end $rem UNRESTRICTED = false SF-XCIS runs from ROHF triplet reference EXCHANGE = HF BASIS = 6-31G* SCF_CONVERGENCE = 10 SCF_ALGORITHM = DM MAX_SCF_CYCLES = 100 SPIN_FLIP_XCIS = true Do SF-XCIS CIS_N_ROOTS = 3 CIS_SINGLETS = true Do singlets CIS_TRIPLETS = true Do triplets $end