Electron correlation energies from scaled exchange-correlation kernels: Importance of spatial versus temporal nonlocality

Within density functional theory, a coordinate-scaling relation for the cou pling-constant dependence of the exchange-correlation kernel f(xc)(r,r';ome ga) is utilized to express the correlation energy of a many-electron system in terms of f(xc). As a test of several of the available approximations fo r the exchange-correlation kernal, or equivalently the local-field factor, we calculate the uniform-gas correlation energy. While the random phase app roximation (f(xc) = 0) makes the correlation energy per electron too negati ve by about: 0.5 eV, the adiabatic local-density approximation [f(xc) = f(x c)(q = 0,omega =; 0)] makes a comparable error in the opposite direction. T he adiabatic nonlocal approximation [f(xc) = f(xc)(q, omega = 0)] reduces t his error to about 0.1 eV, and inclusion of the full frequency dependence [ f(xc) = f(xc)(q,omega)] in an approximate parametrization reduces it furthe r to less tl;an 0.02 eV. We also report the wave-vector analysis and the im aginary-frequency analysis of the correlation energy for each choice of ker nel.