The electronic structures of aluminum, copper, and silver were investigated in bulk, thin-film and nanoparticle forms using first-principles band structure methods. The density of states (DOS) and partial density of states (PDOS) were also calculated. The calculations show the progression from continuous bands to subbands to discrete states as spatial confinement is imposed by going from bulk to thin film to particle forms. The choice of metals in this study allows for the comparison of the degree of localization of the d-electrons on inter-band transitions, which, in part, governs the optical properties of the metals.

The associated optical properties described by the imaginary component of the dielectric function, ε₂(ω), were also investigated. The interband contributions to ε₂(ω) were calculated from the band structure, while the intraband contributions were calculated using the Drude theory for free electrons. Both contributions to ε₂(ω)are needed to understand the optical properties of metals and to interpret their reflectance spectra. The interband transitions need to be considered to explain reflectivity at energies lower than the plasma frequencies, but not all interband transitions result in reflectance peaks since they are significantly weaker compared to the intraband contributions at lower energies.

We have studied the dependence of the DOS, PDOS and ε₂(ω) on the choice of exchange potentials by comparing results obtained using the generalized gradient approximation (GGA) and the Heyd-Scuseria-Ernzerhof (HSE) hybrid functional. In copper, where ultraviolet photoelectron spectroscopy data are available, the HSE potential leads to better agreement with the experiment than when using the GGA potential, and HSE reproduces correctly the variation of binding energy of the d electrons as spatial confinement is imposed. The corresponding dependence of exchange potential for silver exists, but is less severe.