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Modern extensions of density functional theory such as the density functionaltheory plus U and the density functional theory plus dynamical mean-fieldtheory require choices, including selection of variable (charge vs spindensity) for the density functional and specification of the correlatedsubspace. This paper examines these issues in the context of the "plus U"extensions of density functional theory, in which additional correlations onspecified correlated orbitals are treated using a Hartree-Fock approximation.Differences between using charge-only or spin-density-dependentexchange-correlation functionals and between Wannier and projector-baseddefinitions of the correlated orbitals are considered on the formal level andin the context of the structural energetics of the rare earth nickelates. It isdemonstrated that theories based on spin-dependent exchange-correlationfunctionals can lead to large and in some cases unphysical effective on-siteexchange couplings. Wannier and projector-based definitions of the correlatedorbitals lead to similar behavior near ambient pressure, but substantialdifferences are observed at large pressures. Implications for other beyonddensity functional methods such as the combination of density functional anddynamical mean field theory are discussed.

Density functional versus spin-density functional and the choice of  correlated subspace in multi-variable effective action theories of electronic  structure