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

7.12.3 Short-Range Density Functional Correlation within RAS-CI

Alternatively, effective dynamic correlation can be introduced into the RAS-CI wave function by means of short-range density functional correlation energy. The idea relies on the different ability of wave function methods and DFT to treat non-dynamic and dynamic correlations. Concretely, the RAS-CI-srDFT (or RAS-srDFT) method136 is based on the range separation of the electron-electron Coulomb operator (V^ee) through the error function to describe long-range interactions,

V^eelr,μ=i<jerf(μrij)rij (7.92)
V^eesr,μ=V^ee-V^eelr,μ (7.93)

where rij is the inter electronic distance and the parameter μ controls the extend of short- and long-range interactions. Such splitting of V^ee provides a well-defined approach to merge WFT with DFT by applying V^eelr,μ to RAS-CI and Veelr,μ to DFT. Within the RAS-srDFT approach, the energy of an electronic state can be expressed as:

ERAS-srDFT=minΨμ[Ψμ|T^+V^ne+V^eelr,μ|Ψμ+EHsr,μ[ρ]+Excsr,μ[ρ]] (7.94)

where ρρ[Ψμ], and EHsr,μ[ρ] and Excsr,μ[ρ] are the short-range Hartree and exchange-correlation energy functionals, respectively. The RAS-CI wave function can be combined with different short-range exchange and correlation functionals (Sections 5.3.2 and 5.3.3).