7.9.3 SOS-CIS(D) Model

As in MP2 case, the accuracy of CIS(D) calculations can be improved by semi-empirically scaling the opposite-spin components of CIS(D) expression:

$$E^{\mathrm{SOS}-\mathrm{CIS}(\mathrm{D})}=c_U⟨{\mathrm{\Psi }}^{\mathrm{CIS}}\left|V\right|U_2^{\mathrm{OS}}{\mathrm{\Psi }}^{\mathrm{HF}}⟩+c_T⟨{\mathrm{\Psi }}^{\mathrm{CIS}}\left|V\right|T_2^{\mathrm{OS}}{U}_1\mathrm{\Psi }{}^{\mathrm{HF}}⟩$$

(7.39)

with the corresponding ground state energy

$$E^{\mathrm{SOS}-\mathrm{MP2}}=c_T⟨{\mathrm{\Psi }}^{\mathrm{HF}}\left|V\right|T_2^{\mathrm{OS}}{\mathrm{\Psi }}^{\mathrm{HF}}⟩$$

(7.40)

More importantly, this SOS-CIS(D) energy can be evaluated with the 4th power of the molecular size by adopting Laplace transform technique.⁸¹⁵ Accordingly, SOS-CIS(D) can be applied to the calculations of excitation energies for relatively large molecules.