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# 7.9.4 SOS-CIS(D) Model

(February 4, 2022)

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:

 $E^{\mathrm{SOS-CIS(D)}}=c_{U}\left\langle{\Psi^{\mathrm{CIS}}}\right|V\left|{U% _{2}^{\mathrm{OS}}\Psi^{\mathrm{HF}}}\right\rangle+c_{T}\left\langle{\Psi^{% \mathrm{CIS}}}\right|V\left|{T_{2}^{\mathrm{OS}}U_{1}\Psi^{\mathrm{{HF}}}}\right\rangle$ (7.50)

with the corresponding ground state energy

 $E^{\mathrm{SOS-MP2}}=c_{T}\left\langle{\Psi^{\mathrm{HF}}}\right|V\left|{T_{2}% ^{\mathrm{OS}}\Psi^{\mathrm{HF}}}\right\rangle$ (7.51)

More importantly, this SOS-CIS(D) energy can be evaluated with the 4th power of the molecular size by adopting Laplace transform technique.961 Accordingly, SOS-CIS(D) can be applied to the calculations of excitation energies for relatively large molecules.