Laboratoire de Physique Théorique
Toulouse - UMR 5152

While density functional theory (DFT) based on local or semi-local approximations to exchange and correlation has been successful in describing a broad variety of systems, remaining problems are often attributed to ’self-interaction’ or ’strong correlation’.

The most prominent quantitative definition of the self-interaction error was given by Perdew and Zunger in 1981 in combination with a scheme for its correction [1]. A unified concept and a more general definition of self-interaction errors was given more recently [2]. A commonly used DFT approach to strong correlation relies on the Hubbard model in the DFT+U scheme [3].

The existence of different ’flavors’ of self-interaction correction [4-10] represents, at first glance, its weak theoretical foundation. A closer look reveals that many of the concepts can in fact be understood as approximations to a more general form of non-local exchange-correlation functionals, i.e., orbital-density dependent energy functionals. Beside long-range non-locality and a correct asymptotic Kohn-Sham potential, this class of functionals has the potential to bridge the gap between the strongly interacting and the independent particle regime, while it can still be embedded in the framework of Kohn-Sham DFT.

A short introduction to the fundamental concepts of ’strong correlation’ and ’self-interaction’ will be given. Strengths and weaknesses of different approaches to SIC will be illustrated with examples ranging from benchmark cases (molecules and atomization energies) to state-of-the-art applications in theoretical spectroscopy and computational material design (Rydberg states, transition metal oxides). An extended DFT+U method, derived from the concepts of self-interaction correction, will be presented. The talk will be concluded by a discussion of the pro’s and con’s of the novel functional form including comparison with alternative DFT approaches to non-locality, self-interaction free formulations and strong-correlation.

[1] J.P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981). [2] A. Ruzsinszky et al., J. Chem. Phys. ?126, 104102 (2007). [3] V.I. Anisimov et al., J. Phys. : Condens. Matter 9, 767 (1997). [4] C. Legrand et al., J. Phys. B 35, 1115 (2002). [5] U. Lundin and O. Eriksson, Int. J. Quantum Chem. 81, 247 (2001). [6] T. Körzdörfer et al., J. Chem. Phys. 129, 014110 (2008). [7] S. Klüpfel et al., J. Chem. Phys. 137, 124102 (2012). [8] A. Svane, Phys. Rev. B 53, 4275 (1996). [9] A. Valdes et al., PCCP 14, 49 (2012). [10] I. Dabo, Phys. Rev. B 82, 115121 (2010).