Microscopic electronic susceptibility, χ(ω,q₁₁,z,z'), of the jellium half-space: a successful average-density ansatz for complex frequency

Using time-dependent local density theory and a Lang-Kohn zero-order density profile n⁰(z), the authors present accurate values of the jellium half-space susceptibility chi ( omega ,q₁₁,z,z') for complex frequencies omega in the upper half-plane. For r_s=2.07 the numerically-obtained susceptibility is compared with a useful mimic function, chi ^bulk( omega ,q₁₁, mod z-z' mod :n), based on the response of a uniform electron gas of density n equal to an average of n⁰(z) between the points z and z'. This is found to be an excellent approximation away from the real frequency axis, especially when the surface-parallel wavevector q₁₁ is large.