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# 7.11.5 Spin Opposite Scaling ADC(2) Models

(December 20, 2021)

The spin-opposite scaling (SOS) approach originates from MP2 where it was realized that the same spin contributions can be completely neglected, if the opposite spin components are scaled appropriately. In a similar way it is possible to simplify the second order ADC equations by neglecting the same spin contributions in the ADC matrix, while the opposite-spin contributions are scaled with appropriate semi-empirical parameters. 449 Hellweg A., Grün S. A., Hättig C.
Phys. Chem. Chem. Phys.
(2008), 10, pp. 4119.
, 1225 Winter N. O., Hättig C.
J. Chem. Phys.
(2011), 134, pp. 184101.
, 592 Krauter C. M., Pernpointner M., Dreuw A.
J. Chem. Phys.
(2013), 138, pp. 044107.

Starting from the SOS-MP2 ground state the same scaling parameter $c_{T}=1.3$ is introduced into the ADC equations to scale the $t_{2}$ amplitudes. This alone, however, does not result in any computational savings or substantial improvements of the ADC(2) results. In addition, the opposite spin components in the ph/2p2h and 2p2h/ph coupling blocks have to be scaled using a second parameter $c_{c}$ to obtain a useful SOS-ADC(2)-s model. With this model the optimal value of the parameter $c_{c}$ has been found to be 1.17 for the calculation of singlet excited states. 1225 Winter N. O., Hättig C.
J. Chem. Phys.
(2011), 134, pp. 184101.

To extend the SOS approximation to the ADC(2)-x method yet another scaling parameter $c_{x}$ for the opposite spin components of the off-diagonal elements in the 2p2h/2p2h block has to be introduced. Here, the optimal values of the scaling parameters have been determined as $c_{c}=1.0$ and $c_{x}=0.9$ keeping $c_{T}$ unchanged. 592 Krauter C. M., Pernpointner M., Dreuw A.
J. Chem. Phys.
(2013), 138, pp. 044107.

The spin-opposite scaling models can be invoked by setting METHOD to either SOSADC(2) or SOSADC(2)-x. By default, the scaling parameters are chosen as the optimal values reported above, i.e., $c_{T}=1.3$ and $c_{c}=1.17$ for ADC(2)-s and $c_{T}=1.3$, $c_{c}=1.0$, and $c_{x}=0.9$ for ADC(2)-x. However, it is possible to adjust any of the three parameters by setting ADC_C_T, ADC_C_C, or ADC_C_X, respectively.