Description of magnetic interactions in strongly correlated solids via range-separated hybrid functionals Pablo Rivero, 1 Ibério de P. R. Moreira, 1 Gustavo E. Scuseria, 2 and Francesc Illas 1 1 Departament de Química Física and Institut de Química Teòrica i Computacional (IQTCUB), Universitat de Barcelona, C/Martí i Franquès 1, E-08028 Barcelona, Spain 2 Department of Chemistry, Rice University, 6100 Main Street, Houston, Texas 77005-1892, USA Received 20 February 2009; revised manuscript received 28 April 2009; published 25 June 2009 The performance of two range-separated hybrid HSE and LC-PBE exchange-correlation functionals for describing narrow-band magnetic solids and, more precisely, for predicting magnetic coupling constants has been investigated for a large set of systems for which accurate experimental data exist. The set includes superconducting cuprates parent compounds and transition-metal oxides and fluorides exhibiting a broad range of magnetic coupling values. Both HSE and LC-PBE provide an overall improvement over the description arising from standard hybrid functionals such as the well-known B3LYP. Nevertheless, the two range-separated hybrid functionals still overestimate antiferromagnetic and ferromagnetic interactions although significantly less than B3LYP. The increased accuracy of LC-PBE suggests that the approximations and exact constraints included in the definition of this long-range corrected hybrid functional have important consequences for the accurate description of exchange and correlation effects of the electronic structure of magnetic solids and other systems exhibiting localized spins. DOI: 10.1103/PhysRevB.79.245129 PACS numbers: 71.15.-m I. INTRODUCTION The discovery of high-temperature superconductivity in doped cuprates in 1986 Ref. 1 sparked substantial interest in strongly correlated systems and triggered a huge amount of work from both theory and experiment. 2–6 In fact, super- conducting cuprates provide one of the most typical ex- amples of strongly correlated systems, a wide class of mate- rials that show unusual electronic and magnetic properties. In solid-state physics, the term strong correlation is applied to emphasize the situations where the electrons tend to be lo- calized and strongly interacting. 7 Consequently, the resulting electronic structure of these solids is not well-described, most often not even in a qualitatively correct manner, by simple one-electron theories such as the local-density ap- proximation LDA of density-functional theory DFT 8–10 or even by the more sophisticated generalized gradient approaches, 11 usually referred to as GGA. This is somehow different from the meaning that electron correlation has in quantum chemistry where it is defined with respect to the Hartree-Fock model. 7,12 The apparently simple NiO is surely the archetype of strongly correlated materials, it has a par- tially filled 3d band with the Ni 2+ cations almost in a 3d 8 configuration and therefore from band theory arguments it would be expected to be a good conductor. However, taking into account the strong Coulomb repulsion between d elec- trons, an electron correlation effect, NiO appears to be pre- dicted to behave as an antiferromagnetic wide band-gap insulator, 13 as observed in experiments. Thus, strongly corre- lated materials have electronic structures that do not follow simple free-electron-like models. A careful discussion about the limitations of current DFT methods was recently pro- vided by Yang and co-workers. 14,15 In spite of significant advances, the mechanism for high critical temperature remains essentially unknown, in part due to the difficulties in describing accurately their electronic structure; however, there are strong indications that it is re- lated to the magnetic structure. 16,17 The recent discovery of superconductivity in a new family of compounds derived from LaOFeAs 18,19 has renewed interest in strongly corre- lated magnetic solids and stimulated further research. In the case of cuprates, the strong correlation in the 3d shell pro- vokes the unpaired electrons to be essentially localized at the Cu 2+ site leading to an antiferromagnetic insulator. Recently, it has been suggested that the electronic structure of the LaOFeAs parent compounds has strong similarity with that of the cuprates, being described as a strongly frustrated an- tiferromagnetic insulator. 20 However, this similarity only emerges when the description of the electronic structure of this material arises from methods that go well beyond LDA and GGA approximations to the unknown universal exchange-correlation functional of DFT. In fact, the lack of wave-function methods other than Hartree-Fock 21,22 and second-order perturbation theory 23,24 based methods fully exploiting translational symmetry or making use of appropri- ate periodic boundary conditions, makes DFT the standard approach to explore the electronic structure of solids, with most applications relying precisely on LDA and GGA meth- ods. However, we already mentioned that LDA and GGA fail to describe the antiferromagnetic insulating character of the electronic structure of strongly correlated systems and, in particular, of high-T c superconducting parent compounds and predict them to be metallic conductors. In some cases, this deficiency of LDA and GGA can be remedied by directly introducing a correction to the LDA or GGA potential. This is the case of the LDA+ U or GGA+ U methods, 25 which are able to correctly describe the antiferromagnetic insulating ground state of strongly correlated systems such as Ce 2 O 3 Ref. 26 or LaOFeAs Refs. 20 and 27, but at the cost of incorporating parameters that are external to the theory and material-dependent. In addition, recent work has shown that these approaches still have difficulties in describing the mag- PHYSICAL REVIEW B 79, 245129 2009 1098-0121/2009/7924/2451299 ©2009 The American Physical Society 245129-1