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# 7.12.4 Short-Range Density Functional Correlation within RAS-CI

(February 4, 2022)

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) method171 is based on the range separation of the electron-electron Coulomb operator ($\hat{V}_{ee}$) through the error function to describe long-range interactions,

 $\displaystyle\hat{V}_{ee}^{lr,\mu}=\sum_{i (7.112) $\displaystyle\hat{V}_{ee}^{sr,\mu}=\hat{V}_{ee}-\hat{V}_{ee}^{lr,\mu}$ (7.113)

where $r_{ij}$ is the inter electronic distance and the parameter $\mu$ controls the extend of short- and long-range interactions. Such splitting of $\hat{V}_{ee}$ provides a well-defined approach to merge WFT with DFT by applying $\hat{V}_{ee}^{lr,\mu}$ 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:

 $E^{\text{RAS-}sr\text{DFT}}=\min_{\Psi^{\mu}}\left[\langle\Psi^{\mu}|\hat{T}+% \hat{V}_{ne}+\hat{V}_{ee}^{lr,\mu}|\Psi^{\mu}\rangle+E_{H}^{sr,\mu}[\rho]+E_{% xc}^{sr,\mu}[\rho]\right]$ (7.114)

where $\rho\equiv\rho[\Psi^{\mu}]$, 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 5.3.3 and 5.3.4).