Antiadiabatic limit of the exchange-correlation kernels of an inhomogeneous electron gas

We express the high-frequency (antiadiabatic) limit of the exchange-correlation (xc) kernels of an inhomogeneous electron gas in terms of the following equilibrium properties: the ground-state density, the xc kinetic stress tensor, the pair-correlation function and the ground-state xc potential. Of these quantities, the first three are amenable to exact evaluation by quantum Monte Carlo methods while the last can be obtained from the inversion of the Kohn-Sham equation for the ground-state orbitals. The exact scalar kernel, in this limit, is found to be of very long range in space, at variance with the kernel that is used in the standard local density approximation. The antiadiabatic xc kernels will be useful in calculations of excitation energies by time-dependent density-functional theory in atoms, molecules, and solids, and provide a solid basis for interpolation between the low- and high-frequency limits of the xc kernels.

Figure 1

High-frequency limit of the longitudinal xc kernel for the homogenous electron gas plotted as function of $q$ for different values of $r_s$. Asymptotically the only finite contribution is due to the term containing the correlation kinetic energy.

Figure 2

Here the quantity in Fig. 1 is plotted by neglecting $f_{\text{xc}\text{L}}^{\left(2\right)}\left(q,\infty \right)$ [Eq. (B4)].

Figure 3

High-frequency limit of the transverse xc kernel for the homogenous electron gas plotted as function of $q$ for different values of $r_s$. Asymptotically the only finite contribution is due to the term containing the correlation kinetic energy.