From Eq. 42, we can see that in the MPAC framework, the contributions from the Hartree ( Ĵ) and exchange ( K) terms vanish in e λ c (r) as λ → 0, leaving only the electronrepulsion term. In this way, MPAC's e λ c (r) reduces to its DFT counterpart in the λ → 0 limit in the sense that only the electron-repulsion term contributes to its initial slope. This highlights another common feature between MPAC's and DFT's correlation energy densities (in addition to being derived with the same gauge strategy from Sec. III).