7.2.6 Spin-Adapted Spin-Flip CIS

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}