Expansion of the density-functional energy components Ec and Tc in terms of moments of the electron density

Starting from known identities in density-functional theory, it is shown that for finite electronic systems the density functionals E-c(lambda)[rho] and T-c(lambda)[rho] can be expanded in terms of powers of the classical moments [x(q)y(r)z(s)rho] of the electron density, with the expansion coefficients of the two series related in a simple way. For neutral atoms and coupling constant lambda=1, two-term universal linear expansions are demonstrated to be reasonably accurate: E-c[rho] = -0.1659[rho]ln Z + 0.000 40[r rho]Z and T-c[rho] = 0.1659[rho]ln Z-0.000 80[r rho]Z, where Z is the atomic number. The factors In Z and Z in these formulas are rationalized. [S1050-2947(99)02702-X].