Analytical expressions for the local-held factor G(q) and the exchange-correlation kernel K-xc(r) of the homogeneous electron gas

We present an analytical expression-for the local-field factor G(q) of the homogeneous electron gas which reproduces recently published quantum Monte Carlo data by Moroni, Ceperley, and Senatore [Phys. Rev. Lett. 75, 689 (1995)], reflects the theoretically known asymptotic behaviors for both small-and large-q limits, and allows us to express the exchange-correlation kernel K-xc analytically in both the direct and reciprocal space. The last property is particularly useful in numerical applications to real solids.