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# 7.2.6 Spin-Adapted Spin-Flip CIS

(February 4, 2022)

Spin-Adapted Spin-Flip CIS (SA-SF-CIS)1273 is a spin-complete extension of the spin-flip single excitation configuration interaction (SF-CIS) method.601 Unlike SF-XCIS, SA-SF-CIS only includes the minimal set of electronic configurations needed to remove the spin contamination in the conventional SF-CIS method. The target SA-SF-CIS states have spin eigenvalues one less than the reference ROHF state, i.e., if singlet states ($S=0$) are targeted then the reference state should be a triplet ($S=1$), or if doublet states ($S=1/2$) are targeted then the reference state should be a quartet ($S=3/2$). The SA-SF-CIS approach uses a tensor equation-of-motion formalism,1273 such that the dimension of the CI vectors in SA-SF-CIS remains exactly the same as that in conventional SF-CIS. A DFT correction to SA-SF-CIS (i.e., SA-SF-TDDFT) can be added.1273 As with other SF-TDDFT methods,1274 the BH&HLYP functional has become something of a de facto standard choice.459, Herbert:2022

Example 7.4  An SA-SF-DFT calculation of singlet ground and excited states of ethylene.

$molecule 0 3 C C 1 B1 H 1 B2 2 A1 H 1 B3 2 A2 3 D1 H 2 B4 1 A3 3 D2 H 2 B5 1 A4 3 D3 B1 1.32808942 B2 1.08687297 B3 1.08687297 B4 1.08687297 B5 1.08687297 A1 121.62604150 A2 121.62604150 A3 121.62604150 A4 121.62604150 D1 180.00000000 D2 0.00000000 D3 180.00000000$end

$rem EXCHANGE bhhlyp BASIS cc-pvtz BASIS2 sto-3g UNRESTRICTED false CIS_N_ROOTS 5 SASF_RPA 1 CIS_TRIPLETS false$end


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