We provide a new interpretation of how electron correlations are represented within the local-density approximation for exchange by deducing via Harbola-Sahni theory the corresponding pair-correlation density. The expression differs from that in the literature and contains, in addition to the uniform electron-gas result, a term proportional to the gradient of the density. Thus, the nonuniformity of the electron density is explicitly incorporated in the approximation, and constitutes thereby the reason underlying its success.
Sahni, Viraht, Slamet, Marlina. "Interpretation of Electron Correlation in Local-Density Approximation for Exchange." Physical Review B 48.3 (1993): 1910-1913.