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 rs=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.
Dobson, J., & Harris, G. (1987). Microscopic electronic susceptibility, χ (ω, q11, z, z'), of the jellium halfspace: a successful average-density ansatz for complex frequency. Journal of Physics Condensed Matter, 20(36), 6127-6136. https://doi.org/10.1088/0022-3719/20/36/014