7.11.5 Spin Opposite Scaling ADC(2) Models

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, 1225, 592}

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

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

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.