Dynamical and static dipole polarizability of metal clusters studied within different density functional approximations

Abstract

We study the linear response of pure and doped metal clusters to spin-dependent and spin-independent external fields within the framework of the time-dependent density functional theory. As test cases we have considered the response of clusters with spin-saturated configurations ( ${\mathrm{Na}}_9^{+}$ , ${\mathrm{Na}}_8$ , ${\mathrm{Na}}_{21}^{+}$ , ${\mathrm{Na}}_{20}$ , ${\mathrm{Na}}_{40}$ , ${\mathrm{Na}}_4\mathrm{Pb}$ and ${\mathrm{Na}}_6\mathrm{Pb}$ ) and with spin-polarized configurations ( ${\mathrm{Na}}_6^{+}$ , ${\mathrm{Na}}_5\mathrm{Pb}$ , ${\mathrm{Al}}_{11}\mathrm{Fe}$ , ${\mathrm{Al}}_{18}$ and ${\mathrm{Al}}_{18}\mathrm{Fe}$ ). For spin-dependent excitations we have obtained in all the pure and doped sodium clusters a strongly collective spin mode of surface type lying at lower energies than the unperturbed particle-hole excitations. This mode uncouples cleanly from the electric dipole mode in the case of spin-saturated clusters, but for spin-polarized clusters these two modes turn out to be intertwined in the responses to spin-dependent and to spin-independent fields. We have performed the calculations within two different exchange-correlation potentials, the first constructed from the local density approximation by Perdew and Wang and the second constructed by Parr and Ghosh starting from the strongly non-local Amaldi Approximation. The latter incorporates the correct $-1\mathrm{/}\mathit{r}$ long-range behaviour leading to calculated static polarizabilities and photoabsorption spectra closer to experiments that the results from local density calculations. For the doped clusters ${\mathrm{Na}}_{\mathit{n}}\mathrm{Pn}$ and ${\mathrm{Al}}_{\mathit{n}}\mathrm{Fe}$ we have compared the results obtained within two descriptions of the atoms surrounding the central impurity atom, namely the jellium model and the spherical average of the pseudopotentials method. The polarizabilities of ${\mathrm{Al}}_{\mathit{n}}\mathrm{Fe}$ clusters with $\mathit{n}⩽18$ , calculated within the two ionic models are similar and for $\mathit{n}\mathrm{>}9$ are also similar to those of pure ${\mathrm{Al}}_{\mathit{n}}$ clusters. The main difference between jellium and pseudopotential models when describing doped ${\mathrm{Al}}_{\mathit{n}}\mathit{F}\mathit{e}$ clusters is obtained for the dipole response at several tens of eV for certain sizes where the last occupied d orbital has different occupation number in the pseudopotential model than in the jellium model.