Time-Dependent Density-Functional Theory beyond the Local-Density Approximation

Approximations for the ground-state exchange-correlation potential of density-functional theory have reached a high level of sophistication. By contrast, time- or frequency-dependent exchange-correlation potentials are still being treated in a local approximation. Here we propose a novel approximation scheme, which effectively brings the power of the generalized gradient approximation (GGA) and meta-GGA to time-dependent density-functional theory. The theory should allow a more accurate treatment of strongly inhomogeneous electronic systems (e.g. molecular junctions) while remaining essentially exact for slowly varying densities and slowly varying external potentials.

Figure 1

The bulk viscosity $\zeta (\omega )$ (in units of $\hslash n_0$) for several values of the reduced gradient $s=|\nabla n_0|/2k_F{n}_0$ at $r_s=3$. $s=0$ corresponds to the uniform gas. The same RPA value of ${\mu }_{\mathrm{xc}}(0)$ for all $s$ is taken from Table I of Ref. 25.

Figure 2

The shear viscosity $\eta (\omega )$ plotted at $r_s=3$. The units and notations are the same as in Fig. 1.