Spin-component scaling approaches (SCS/SOS)

By introducing individually scaling factors to the same-spin and opposite-spin contributions of the correlation energy second-order methods can be modified for a (hopefully) better performance. SCS-MP2 has first been proposed by S. Grimme and SOS-MP2 by Y. Jung et al. (see below). The generalization of SCS and SOS to CC2 for ground and excited states is described in [109]. It uses the same scaling factors as proposed for the original SCS- and SOS-MP2 approaches (see below). In the ricc2 program we have also implemented SCS and SOS variants of CIS(D) for excitation energies and of CIS(D_∞) and ADC(2) for excitation energies and gradients, which are derived from SCS-CC2 and SOS-CC2 in exactly the same manner as the unmodified methods can be derived as approximations to CC2 (see Sec. 9.2 and ref. [110]). Please note, that the SCS-CIS(D) and SOS-CIS(D) approximations obtained in this way and implemented in ricc2 differ from the spin-component scaled SCS- and SOS-CIS(D) methods proposed by, respectively, S. Grimme and E. I. Ugorodina in [111] and Y. M. Rhee and M. Head-Gordon in [112].

A line with scaling factors has to be added in the $ricc2 data group:

$ricc2
scs  cos=1.2d0  css=0.3333d0

cos denotes the scaling factor for the opposite-spin component, css the same-spin component.

As an abbreviation
scs
can be inserted in $ricc2. In this case, the SCS parameters cos=6/5 and css=1/3 proposed S. Grimme (S. Grimme, J. Chem. Phys. 118 (2003) 9095.)are used. These parameters are also recommended in [109] for the SCS variants of CC2, CIS(D), CIS(D_∞), and ADC(2) for ground and excited states.

Also, just
sos
can be used as a keyword, to switch to the SOS-MP2 approach proposed by the Head-Gordon group with scaling factors of cos=1.3 and css=0.0 (Y., Jung, R.C. Lochan, A.D. Dutoi, and M. Head-Gordon, J. Chem. Phys. 121 (2004) 9793.), which are also recommended for SOS variants of CC2, CIS(D), CIS(D_∞), and ADC(2).