Time-dependent DFT for metals
For metals the interband part of the dielectric function is due to transitions from (partially)-occupied bands to (partially)-unoccupied bands. Now there is also a term, which is called the intraband part of the dielectric function, which is due to transitions within the same partially-occupied band. The macroscopic dielectric function εe(ω) is now calculated as
εe(ω)=1+4πχe(ω) - 4πiσe(ω)/ω.Convergence and reproducibility: For TD-DFT calculations on metals a dense sampling of reciprocal space is required, i.e. the results converge slowly with the KSPACE parameter. The dielectric function might even not reproduce well across different machines. (Usually results that are not yet converged with the KSPACE parameter, like the energy, are reproducible across different platforms). Nevertheless, when the KSPACE parameter is chosen sufficiently high, the same result will be obtained on all machines. For instance for Cu the machine dependence was less than 0.01 for the dielectric function with KSPACE=11. In short: check for the convergence of the dielectric function with respect to the KSPACE parameter.
