Abstract
Modern extensions of density functional theory such as the density functional theory plus U and the density functional theory plus dynamical mean field theory require choices, including selection of variable (charge vs spin density) for the density functional and specification of the correlated subspace. This paper examines these issues in the context of the ``plus U'' extensions of density functional theory, in which additional correlations on specified correlated orbitals are treated using a Hartree-Fock approximation. Differences between using charge-only or spin-density-dependent exchange-correlation functionals and between Wannier and projector-based definitions of the correlated orbitals are considered on the formal level and in the context of the structural energetics of the rare-earth nickelates. It is demonstrated that theories based on spin-dependent exchange-correlation functionals can lead to large and in some cases unphysical effective on-site exchange couplings. Wannier and projector-based definitions of the correlated orbitals lead to similar behavior near ambient pressure, but substantial differences are observed at large pressures. Implications for other beyond density functional methods such as the combination of density functional and dynamical mean field theory are discussed.
Highlights
Modern theories of electronic structure can be formally constructed in terms of functionals of observables of interest whose stationary points deliver the values of the observables[1]
Neither the local density approximation[3] (LDA) nor the generalized gradient approximation (GGA)[5] provide correct accounts of the structural energetics of layered and spinel manganites that exhibit cooperative Jahn-Teller distortions associated with the high spin state of Mn3+,6 because at ambient pressure both LDA and GGA incorrectly predict that the Mn ion is in a nominal |t42ge0g low-spin configuration instead of the proper high-spin |t32ge1g state
The spin-dependent generalized gradient approximation (SGGA)+U results of the structural transition in the rareearth nickelates show a re-entrant transition with pressure, and this is not observed in GGA+U calculations that are performed with a reasonable on-site exchange J = 1eV
Summary
Modern theories of electronic structure can be formally constructed in terms of functionals of observables of interest whose stationary points deliver the values of the observables[1]. The known implementations of SDFT fail to correctly describe many aspects of the physics and structure of strongly correlated electron systems, for example providing qualitatively incorrect structures for the rare-earth nickelates[12,13] (see, e.g. Ref. 1 for additional examples) These difficulties motivated the construction of new effective action theories that depend on the density or the spin-density, and on additional properties of a subspace of orbitals for which correlations are believed to be relevant[1,14].
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