On the theory of metal nanoparticles based on quantum mechanical calculation.

Metal nanoparticles have attracted considerable attention owing to their unusual physical and chemical properties from those of their molecular and bulk counterparts and are fundamental to surface science applications such as catalysts, optics, photonics, sensors, and spectroscopy. Traditionally, the optical absorption spectra are derived from the collective oscillations of free electrons of conduction band in metal nanoparticles as a consequence of incident electromagnetic radiation polarizing the nanoparticles. This phenomenon, known as the localized surface plasmon resonance, is unique to metallic nanostructures and has been modelled by Gustav Mei in 1908 based on the Maxwell’s equations. It is the most-cited scientific paper of 20th century and this classical approach is still used widely. However, the theory cannot account for quantum confinement effects of the electronic structure, the fundamental physical properties of metal nanoparticles. More satisfying treatment of photons interacting with metal nanoparticles is by a quantum theory approach. When UV-visible light impinging on a metal nanoparticle, occupied ground-state conduction electrons absorb photons and excite to higher unoccupied higher energy-state of the conduction band of the particle. In this development we used time-independent Schrodinger equation of the ground-state energy of Thomas-Fermi-Dirac-Weizsacker atomic model and also the density function in the final Euler-Lagrange equation was algebraically substituted with the absorption function. The total energy functional was computed numerically for isolated silver and gold nanospheres at various sizes. The electronic transitions within the conduction band are limited only by the Lagrange multiplier and the quantum number selection rules. The calculated absorption peaks fall within the experimental regimes. The results show a red-shift absorption peak increases with the increase of particle diameter corresponds to a decrease in the conduction band energy of metal nanoparticles.

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