Gradient corrections to the local spin density approximation for the exchange-correlation energy Exc are increasingly useful in quantum chemistry and solid state physics. We present elementary physical arguments which explain the qualitative dependencies of the exchange and correlation energies upon the local density, local spin polarization, and reduced density gradient. The nearly local behavior of the generalized gradient approximation for Exc at valence-electron densities, due to strong cancellation between the nonlocalities of exchange and correlation, is shared by the exact linear response of the uniform electron gas. We further test and develop our rationale for the chemical and solid-state consequences of gradient corrections. We also partially explain the “conjointness” between the exchange energy and the noninteracting kinetic energy, whose generalized gradient approximation is tested here. An appendix presents the full expression for the gradient-corrected correlation potential.

Perdew, J. P., Ernzerhof, M., Zupan, A., & Burke, K. (1998). Nonlocality of the density functional for exchange and correlation: Physical origins and chemical consequences. The Journal of Chemical Physics, 108(4), 1522–1531.