The effect of the local field and dipole-dipole interactions on the absorption spectra of noble metals and the plasmon resonance of their nanoparticles

An analysis of the effect of free and bound electrons on the optical properties of noble metals and their nanoparticles is performed, based on the Drude-Lorentz model. It is shown that the shifts in the absorption bands of plasmons localized in spherical nanoparticles with respect to the zero frequency of free electrons in a bulk metal can be estimated using the theory of resonant dipole-dipole interactions. The calculation includes account for differences between the effective and average electromagnetic fields. It is established that the difference in oscillator strength for free electrons in the bulk metal, obtained using the Drude-Lorentz model, and the microscopic oscillators in the corresponding spherical nanoparticle, is due to background polarization. This occurs at the expense of high-frequency excitation of the bound electrons. These results show that interparticle interactions in the noble metals in the quasi-static approximation can be regarded as dipole-dipole interactions of point dipoles with a concentration equal to the concentration of free electrons.