# 7.2.4 Spin-Flip Extended CIS (SF-XCIS)

Spin-flip extended CIS (SF-XCIS)141 is a spin-complete extension of the spin-flip single excitation configuration interaction (SF-CIS) method.498 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.

Example 7.3  A SF-XCIS calculation of ground and excited states of trimethylenemethane (TMM) diradical, for which double substitutions make considerable contributions to low-lying excited states.

$molecule 0 3 C C 1 CC1 C 1 CC2 2 A2 C 1 CC2 2 A2 3 180.0 H 2 C2H 1 C2CH 3 0.0 H 2 C2H 1 C2CH 4 0.0 H 3 C3Hu 1 C3CHu 2 0.0 H 3 C3Hd 1 C3CHd 4 0.0 H 4 C3Hu 1 C3CHu 2 0.0 H 4 C3Hd 1 C3CHd 3 0.0 CC1 = 1.35 CC2 = 1.47 C2H = 1.083 C3Hu = 1.08 C3Hd = 1.08 C2CH = 121.2 C3CHu = 120.3 C3CHd = 121.3 A2 = 121.0$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