First-Principles Study and Model of Dielectric Functions of Silver Nanoparticles

Dielectric functions of ultrafine silver nanoparticles with up to 586 atoms are computed using the density functional theory. A two-dimensional diagram method is developed to analyze the electronic transitions. It is found that the transitions can be categorized into intraband and interband. An analytical formulation is established for the imaginary part of the dielectric function arising from the intraband transitions by a statistical approach. The established semiempirical model is a unified one that allows prediction of dielectric functions covering all particle sizes. According to the model, the intraband transition approaches that in bulk materials for particles with a size larger than 10−20 nm depending on the wavelengths. The size effect for the interband transitions on the dielectric function is also investigated, and a faster convergence to the bulk behavior is observed.