REGULAR ARTICLE Ab initio dynamic correlation effects in density functional theories: a density based study for argon Karol Jankowski • Krzysztof Nowakowski • Ireneusz Grabowski • Jan Wasilewski Received: 20 May 2009 / Accepted: 9 September 2009 / Published online: 4 October 2009 Ó Springer-Verlag 2009 Abstract In an attempt to get more insight into the links between the coverage of dynamic electron correlation effects defined in traditional wave function theories (WFT) by density functional theories (DFT) we have performed comprehensive studies for the Ar atom, for which the dynamic correlation effects play the dominant role. A density-based approach directly hinged on difference radial density (DRD) distributions defined with respect the Har- tree-Fock radial density has been employed for analyzing the impact of dynamic correlation effects on the density. The DRD-distributions calculated by ab initio methods have been compared with their DFT counterparts generated for representatives of several generations of broadly used exchange-correlation functionals and for the recently developed orbital-dependent OEP2 exchange-correlation functional (Bartlett et al. in J Chem Phys 122:034104, 2005). For the local, generalized-gradient, and hybrid functionals it has been found that the dynamic WFT cor- relation effects on the density are to a significant extent accounted for by densities resulting from exchange-only calculations. It has been shown that the removal of self- interaction errors does not change this result. It has been demonstrated that the VWN5 and LYP correlation func- tionals do not represent any substantial dynamical corre- lation effects on the electron density, whereas these effects are well represented by the orbital-dependent OEP2 cor- relation functional. Critical comparison of the results of the present investigations with various published results obtained for more complex many-electron systems has been made. Attention has been paid to bringing into shar- per relief the differences between the conclusions reached when using energy- or density-based criteria. Keywords Electron correlation  Radial density  Density functional theory  Ab initio densities 1 Introduction To satisfy the hard-to-meet requirement for quantum- mechanical theories describing in a reliable way many- electron systems of increasing sizes and complexity is the central problem of both main categories of contemporary many-electron-theory methods: the traditional ab initio or wave function theory (WFT) methods, which are more or less directly grounded on the concept of the wave function, and the density functional theory (DFT) [26, 32], essen- tially based on the concept of electron density. WFT methods offer, in principle, better instruments of control- ling the ways of increasing the accuracy of results but become prohibitively expensive for larger systems, whereas the much cheaper, most widely used DFT approaches still suffer various reliability problems pri- marily caused by the lack of knowledge of the exact form of the functionals for exchange and correlation. To overcome the reliability problems of these approa- ches, enormous efforts have been invested in the search for possibly realistic representations of the unknown exchange and correlation functionals (to get some flavor of this important problem see, e.g., the discussion in Ref. [51]). Dedicated to Professor Sandor Suhai on the occasion of his 65th birthday and published as part of the Suhai Festschrift Issue. K. Jankowski (&)  K. Nowakowski  I. Grabowski  J. Wasilewski Faculty of Physics, Astronomy, and Informatics, Nicolaus Copernicus University, 87-100 Torun ´, Poland e-mail: karoljan@fizyka.umk.pl I. Grabowski e-mail: ig@fizyka.umk.pl 123 Theor Chem Acc (2010) 125:433–444 DOI 10.1007/s00214-009-0638-5