By introducing individual scaling factors for the same–spin and opposite–spin contributions to the
correlation energy most second–order methods can be modified to achieve 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 and ADC(2)
for ground and excited states is described in [14]. 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_{∞}) 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. 10.2 and ref. [140]). 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 [141] and Y. M. Rhee and M. Head–Gordon
in [142].

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

$ricc2

scs cos=1.2d0 css=0.3333d0

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 [14] 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 approach proposed by the Head-Gordon group for
MP2 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 the SOS
variants of CC2, CIS(D), CIS(D_{∞}), and ADC(2). The Laplace-transformed algorithm for the SOS
variants are activated by the additional data group $laplace:

$laplace

conv=4

conv=4

For further details on the Laplace-transformed implementation and how one can estimated
whether the (^{4})-scaling Laplace-transformed or (^{5})-scaling conventional RI implementation
is efficieint see Sec. 9.6.

Since Version 6.6 the (^{4})-scaling Laplace-transformed implementation is available for ground
and excited state gradients with CC2 and ADC(2).

- the spin (S
^{2}) expectation value for open-shell calculation can not be evaluated in the SCS or SOS approaches - for LT-SOS-CC2 (and the related CIS(D) and ADC(2) versions) the following further
limitations apply:
- only parallelized with MPI (no OpenMP parallelization)
- incompatible with the calculation of the D
_{1}and D_{2}diagnostics