Development of a CAS-DFT method covering non-dynamical and dynamical electron correlation in a balanced way

CAS-DFT (Complete Active Space Density Functional Theory) is presented as a method that allows an economical, simultaneous treatment of non-dynamical and dynamical correlation effects for electronic systems with multi-reference character. Central problems of CAS-DFT concern the effective coupling between wave function and DFT method, the double counting of dynamical correlation effects, the choice of the proper input quantities for the DFT functional, the balanced treatment of core and active orbital correlation, of equal-spin and opposite-spin correlation effects, and the inclusion of spin polarization to handle closed- and open-shell systems in a balanced way. We present CAS-DFT2(CS,SPP,FOS,DS) (CAS-DFT using level 2 for the distinction of core and active orbital correlations, carried out with the Colle–Salvetti functional, using the Stoll–Pavlidou–Preuss functional for equal-spin correlation corrections, including spin polarization in the scaling procedure, and correcting with the Davidson–Staroverov density for low-spin cases). The method is free of any self-interaction error and size extensive provided the active space is properly chosen. For the three lowest states of methylene, stringent and less stringent tests are used to demonstrate the performance of the new CAS-DFT method for six different active spaces.