Density functional theory: coverage of dynamic and non-dynamic electron correlation effects

The electron correlation effects covered by density functional theory (DFT) can be assessed qualitatively by comparing DFT densities rho (r) with suit able reference densities obtained with wavefunction theory (WFT) methods th at cover typical electron correlation effects. The analysis of difference d ensities rho (DFT)-rho (WFT) reveals that LDA and GGA exchange (X) function als mimic non-dynamic correlation effects in an unspecified way. It is show n that these long range correlation effects are caused by the self-interact ion error (SIE) of standard X functionals. Self-interaction corrected (SIC) DFT exchange gives, similar to exact exchange, for the bonding region a de localized exchange hole, and does not cover any correlation effects. Hence, the exchange SIE is responsible for the fact that DFT densities often rese mble MP4 or MP2 densities. The correlation functional changes X-only DFT de nsities in a manner observed when higher order coupling effects between low er order N-electron correlation effects are included. Hybrid functionals le ad to changes in the density similar to those caused by SIC-DFT, which simp ly reflects the fact that hybrid functionals ave been developed to cover pa rt of the SIE and its long range correlation effects in a balanced manner. In the case of spin-unrestricted DFT (UDFT), non-dynamic electron correlati on effects enter the calculation both via the X functional and via the wave function, which may cause a double-counting of correlation effects. The use of UDFT in the form of permuted orbital and broken-symmetry DFT (PO-UDFT, BS-UDFT) can lead to reasonable descriptions of multireference systems prov ided certain conditions are fulfilled. More reliable, however, is a combina tion of DFT and WFT methods, which makes the routine description of multire ference systems possible. The development of such methods implies a separat ion of dynamic and non-dynamic correlation effects. Strategies for accompli shing this goal are discussed in general and tested in practice for CAS (co mplete active space)-DFT.