(1) where the second term on the right is the Hubbard energy which depends on the density through the occupations, {n σ m }. These are the eigenvalues of the 5×5 occupation matrix n σ mm ′ = i,k f σ i,k ⟨Ψ σ i,k |ϕm⟩ ⟨ϕ m ′ |Ψ σ i,k ⟩, with f σ i,k being Fermi-Dirac occupations. The |Ψ σ i,k ⟩ are the Kohn-Sham wave functions of band index i, and the {|ϕm⟩} projectors are here the 3d atomic-like functions. The density-corrected scheme consists in performing a full self consistent calculation using the self consistent U, and by keeping only the first term of the total energy of equation 1. By removing the Hubbard term from the adiabatic energy difference, we remove the bias of DFT+U towards HS which arises from the penalizing Hubbard term being systematically larger for LS. We recently demonstrated that this method allows to compute adiabatic energy differences of Fe(II) molecular and crystalline complexes with excellent agreement with coupled cluster-corrected CASPT2 and with experimentallyextracted values. The Hubbard-U density corrected adiabatic energy difference between HS and LS is thus computed as follows