## 3 Results  
The Drude-Lorentz model is mostly used to fit the experimental data for different metals and frequency intervals [20; 27; 28]. Thus, we first made sure that the proposed algorithm can correctly fit the experimentally measured permittivities. The optimal values for the model parameters obtained for the experimental data tabulated in the _Handbook on Optical Constants of Metals_ ([PERSON], 2012) [29] are given in Table 2 (\(\Gamma_{j}\) and \(\omega_{j}\) are in eV). The model was fitted in the 0.05-6 eV range with \(k=4\) interband oscillators and the plasma frequencies given in Table 1 at 300 K. Figure 1 shows a general good agreement between our model and experimental data for all considered metals. The results of ab initio calculations and the optimized Drude-Lorentz model at different electron temperatures are shown in Figure 2 for Cr, W, and Ti and in Figure 3 for Fe, Au, and Ni, with the values of the optimization parameters given in Tables 3 and 4, respectively. The fitting range 0.05-6 eV was chosen to correspond to the photon energies used for laser-induced nanostructuring. Figures 2 and 3 reveal that the proposed algorithm performed well for most of the cases, especially to reproduce the imaginary part behaviour. The discrepancies appear for the real part of Au permittivity at 300 K and 10,000 K as the global-optimization method is less well-suited to reproduce strong local oscillations. This is also related to the fact that density functional theory calculations using the LDA potential cannot properly reproduce bound electrons and thus are not accurate for Au. However, it is interesting to note that at a higher electron temperature, the Au permittivity becomes \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Metal** & \(T_{e}\) **(K)** & \(n_{e}\) **(10\({}^{23}\) cm\({}^{-3}\))** & \(\hbar\omega_{p}\) **(eV)** \\ \hline \multirow{3}{*}{Cr} & 300 & 1.67 & 15.17 \\  & 10,000 & 1.67 & 15.17 \\  & 25,000 & 1.67 & 15.17 \\ \hline \multirow{3}{*}{W} & 300 & 1.40 & 13.88 \\  & 10,000 & 1.40 & 13.88 \\  & 25000 & 1.52 & 14.50 \\ \hline \multirow{3}{*}{Ti} & 300 & 0.79 & 10.45 \\  & 10,000 & 0.79 & 10.45 \\  & 25,000 & 0.85 & 10.82 \\ \hline \multirow{3}{*}{Fe} & 300 & 1.11 & 12.36 \\  & 15,000 & 1.28 & 13.28 \\  & 30,000 & 1.45 & 14.14 \\ \hline \multirow{3}{*}{Au} & 300 & 1.42 & 13.98 \\  & 10,000 & 1.47 & 14.26 \\  & 25,000 & 1.65 & 15.10 \\ \hline \multirow{3}{*}{Ni} & 300 & 1.28 & 13.28 \\  & 10,000 & 1.55 & 14.63 \\  & 25,000 & 1.83 & 15.87 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Free-electron densities \(n_{e}\) and plasma frequencies \(\omega_{p}\) for different metals at different electron temperatures \(T_{e}\). \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Coefficient** & **Cr** & **W** & **Ti** & **Fe** & **Au** & **Ni** \\ \hline \(f_{0}\) & 0.100 & 0.182 & 0.067 & 0.103 & 0.144 & 0.139 \\ \(\Gamma_{0}\) & 0.042 & 0.053 & 0.036 & 0.016 & 0.001 & 0.038 \\ \(f_{1}\) & 0.198 & 0.014 & 0.082 & 0.652 & 0.192 & 0.107  
smoother, and the Drude-Lorentz fitting model proves to be more efficient. The same statement is true for most of the metals excited at high \(T_{e}\). For higher electron temperatures, the Fermi-Dirac distribution of electrons becomes less abrupt around the Fermi level \(E_{f}\), spreading the allowed optical transitions on a larger energy domain. This softens the peak effects of the density of states (DOS), leading to a smoother permittivity describing the optical transitions of the smeared electrons. Electron distribution smearing intrinsically decreases the error in the calculation of optical transitions around the sharp features of the electron DOS within the \(d\) band for transition metals. Remarkably, the ab initio permittivity is more accurate at high electron temperatures and probably less dependent on the inherent variation of the experimental material preparation process.