Normalizing e DFT,λ c (r) by ρ(r) gives the conventional gauge for the correlation energy density per particle in the DFT literature . This conventional gauge represents the correlation energy density through the electrostatic potential of the λ-dependent correlation hole (r) is already known, the true value of our strategy lies in its generality, as it enables us to move beyond DFT's correlation energy density and obtain e c (r), linked to the traditional quantum-chemical E λ c (Eqs. 2 and 3). This is the main objective of the next section where we derive e c (r).