NONLOCAL DENSITY FUNCTIONALS AND THE LINEAR-RESPONSE OF THE HOMOGENEOUS ELECTRON-GAS

The known and usable truly nonlocal functionals for exchange-correlati on energy of the inhomogeneous electron gas are the ADA (average densi ty approximation) and the WDA (weighted density approximation). ADA, b y design, yields the correct linear response function of the uniform e lectron gas. The WDA is constructed so that it is exact in the opposit e limit of one-electron systems, and it was conjectured that the WDA i s also accurate in the uniform gas limit. To test this conjecture, we derive an expression for the linear response of the uniform gas in the WDA, and calculate it for several flavors of the WDA. We then compare the results with the Monte Carlo data on the exchange-correlation loc al-held correction, and identify the weak points of conventional WDA i n the homogeneous limit. We suggest how the WDA can be modified to imp rove the response function. The resulting approximation is a good one in both opposite limits. Future testing should show whether it will al so be better than conventional WDA and ADA for practical nonlocal dens ity-functional calculations.