Comparing ab initio density-functional and wave function theories: The impact of correlation on the electronic density and the role of the correlation potential

Abstract

The framework of ab initio density-functional theory (DFT) has been introduced as a way to provide a seamless connection between the Kohn-Sham (KS) formulation of DFT and wave-function based ab initio approaches [R. J. Bartlett, I. Grabowski, S. Hirata, and S. Ivanov, J. Chem. Phys. 122, 034104 (2005)]. Recently, an analysis of the impact of dynamical correlation effects on the density of the neon atom was presented [K. Jankowski, K. Nowakowski, I. Grabowski, and J. Wasilewski, J. Chem. Phys. 130, 164102 (2009)], contrasting the behaviour for a variety of standard density functionals with that of ab initio approaches based on second-order Møller-Plesset (MP2) and coupled cluster theories at the singles-doubles (CCSD) and singles-doubles perturbative triples [CCSD(T)] levels. In the present work, we consider ab initio density functionals based on second-order many-body perturbation theory and coupled cluster perturbation theory in a similar manner, for a range of small atomic and molecular systems. For comparison, we also consider results obtained from MP2, CCSD, and CCSD(T) calculations. In addition to this density based analysis, we determine the KS correlation potentials corresponding to these densities and compare them with those obtained for a range of ab initio density functionals via the optimized effective potential method. The correlation energies, densities, and potentials calculated using ab initio DFT display a similar systematic behaviour to those derived from electronic densities calculated using ab initio wave function theories. In contrast, typical explicit density functionals for the correlation energy, such as VWN5 and LYP, do not show behaviour consistent with this picture of dynamical correlation, although they may provide some degree of correction for already erroneous explicitly density-dependent exchange-only functionals. The results presented here using orbital dependent ab initio density functionals show that they provide a treatment of exchange and correlation contributions within the KS framework that is more consistent with traditional ab initio wave function based methods.

Self-consistent double-hybrid density-functional theory using the optimized-effective-potential method

“…Note that this is in spite of the fact that LYP correlation energies are usually reasonably accurate. On the contrary, the OEP-GL2 correlation potentials tend to be largely overestimated, as previously observed [27,65]. Overall, the OEP-1DH correlation potentials at λ = 0.65 have fairly reasonable shapes, providing a good compromise between the understructured BLYP and the overestimated OEP-GL2 correlation potentials.…”

“…The analysis of the correlated densities provides a useful tool for the detailed examination of the correlation effects on the electronic density and for the test of exchange-correlation approximations in DFT [65,66,[84][85][86][87]. Thus, in Figure 7 we report correlated densities calculated by OEP-1DH at the recommended value of λ = 0.65, as well as the correlated densities obtained at the extreme values of λ, corresponding to KS BLYP (λ = 0) and OEP-GL2 (λ = 1).…”

Increasing the applicability of density functional theory. III. Do consistent Kohn-Sham density functional methods exist?

“…However, due to the very large amount of relaxation in the core, our EXX + MBPT2 based OEP is not sufficient, so we had to add 0.5 K intoĥ s . Presumably, the pure OEP would be much better if the correlation functional were from CCSD, and beyond as presented elsewhere 34,47 though that would be overkill for applications. IP-EOM-CCSD does a good job in core relaxation reducing the error to ∼2 eV in cc-pCVTZ bases, but additional relaxation effects 48 even further reduce it to 1 eV.…”

A density difference based analysis of orbital-dependent exchange-correlation functionals

“…This method has been found to provide a stable alternative to the other second-order correlated OEP2-KS theories 17,27,[41][42][43] , where problems with convergence, overestimation of the correlation energy, and in many cases poor quality of the correlation potentials were encountered 19,21,24,27,42 . Recently the scaled-oppositespin version of the second-order correlated OEP method (SOS-OEP2) was also proposed 33 .…”