What correlation effects are covered by density functional theory?

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The electron density distribution ρ(r) generated by a DFT calculation was systematically studied by comparison with a series of reference densities obtained by wavefunction theory (WFT) methods that cover typical electron correlation effects. As a sensitive indicator for correlation effects the dipole moment of the CO molecule was used. The analysis reveals that typical LDA and GGA exchange functional already simulate effects that are actually reminiscent of pair and three-electron correlation effects covered by MP2, MP4, and CCSD(T) in WFT. Correlation functionals contract the density towards the bond and the valence region thus taking negative charge out of the van der Waals region. It is shown that these improvements are relevant for the description of van der Waals interactions. Similar to certain correlated single-determinant WFT methods, BLYP and other GGA functionals underestimate ionic terms needed for a correct description of polar bonds. This is compensated for in hybrid functionals by mixing in HF exchange. The balanced mixing of local and non-local exchange and correlation effects leads to the correct description of polar bonds as in the B3LYP description of the CO molecule. The density obtained with B3LYP is closer to CCSD and CCSD(T) than to MP2 or MP4, which indicates that the B3LYP hybrid functional mimics those pair and three-electron correlation effects, which in WFT are only covered by coupled cluster methods.