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7.13 Restricted Active Space Spin-Flip (RAS-SF) and Configuration Interaction (RAS-CI)

7.13.2 The Restricted Active Space (RAS) Scheme

(July 10, 2023)

In the RAS formalism, one divides the orbital space into three subspaces called RAS1, RAS2 and RAS3 (Fig. 7.2). The RAS-CI states are defined by the number of orbitals and the restrictions in each subspace.

Orbital subspaces in RAS-CI employing a ROHF triplet reference.
Figure 7.2: Orbital subspaces in RAS-CI employing a ROHF triplet reference.

The single reference RAS-CI electronic wave functions are obtained by applying a spin-flipping or excitation operator R^ on the reference determinant |ϕ(0).

|ΨRAS=R^|ϕ(0) (7.114)

The R^ operator must obey the restrictions imposed in the subspaces RAS1, RAS2 and RAS3, and can be decomposed as:

R^=r^RAS2+r^h+r^p+r^hp+r^2h+r^2p+ (7.115)

where r^RAS2 contains all possible electronic promotions within the RAS2 space, that is, a reduced full CI, and the rest of the terms generate configurations with different number of holes (h super-index) in RAS1 and electrons in RAS3 (p super-index). The current implementation truncates this series up to the inclusion of hole and particle contributions, i.e., the first three terms on the right hand side of Eq. (7.115).