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-$sr$DFT (or RAS-$sr$DFT) method¹³⁶ is based on the range separation of the electron-electron Coulomb operator (${\widehat{V}}_{ee}$) through the error function to describe long-range interactions,

where $r_{ij}$ is the inter electronic distance and the parameter $\mu$ controls the extend of short- and long-range interactions. Such splitting of ${\widehat{V}}_{ee}$ provides a well-defined approach to merge WFT with DFT by applying ${\widehat{V}}_{ee}^{lr,\mu }$ to RAS-CI and $V_{ee}^{lr,\mu }$ to DFT. Within the RAS-$sr$DFT approach, the energy of an electronic state can be expressed as:

where $\rho \equiv \rho [{\mathrm{\Psi }}^{\mu }]$, and $E_H^{sr,\mu }[\rho ]$ and $E_{xc}^{sr,\mu }[\rho ]$ 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).