where Φ 0 is the ground-state reference determinant, Φ CIS the CIS wave function, and V the perturbation potential operator. The first of the two terms in Eq. 3 is called the "direct term", as it involves the excitation of two electrons from the ground-state determinant through the double excitation operator Û2 . In the second term in Eq. 3 the CIS wave function is generated first with the single excitation operator Û1 followed by the excitation of two additional electrons with T2 . As those electrons are CIS-inactive, this term is also referred to as the "indirect term". The indirect term has a direct analogy to MP2. In MP2, doubles excitations are generated from the reference determinant, and in CIS(D), from the CIS determinant. This connection is important when discussing the SCS versions of CIS(D). The interested reader can find the exact definitions of the singles and doubles excitation operators in the original literature. The SCS idea and its applications to different electronic structure methods has been extensively reviewed and dates back to Grimme's idea to separately scale same-(SS) and opposite-spin (OS) contributions to the electron correlation in MP2. In 2003, Izgorodina and Grimme then applied this idea to the indirect term in CIS(D), but left the direct term unchanged: