On the theory of metal nanoparticles based on quantum mechanical calculation

Abstract

Metal nanoparticles have attracted considerable attention owing to their unusual physical and chemical properties from those of their molecular and bulkcounterparts and are fundamental to surface science applications such as catalysts, optics, photonics, sensors, and spectroscopy. Traditionally, the opticalabsorption spectra are derived from the collective oscillations of free electrons of conduction band in metal nanoparticles as a consequence of incidentelectromagnetic radiation polarizing the nanoparticles. This phenomenon, known as the localized surface plasmon resonance, is unique to metallicnanostructures 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 thisclassical approach is still used widely. However, the theory cannot account for quantum confinement effects of the electronic structure, the fundamentalphysical 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 unoccupiedhigher energy-state of the conduction band of the particle. In this development we used time-independent Schrodinger equation of the ground-state energyof Thomas-Fermi-Dirac-Weizsacker atomic model and also the density function in the final Euler-Lagrange equation was algebraically substituted with theabsorption function. The total energy functional was computed numerically for isolated silver and gold nanospheres at various sizes. The electronictransitions within the conduction band are limited only by the Lagrange multiplier and the quantum number selection rules. The calculated absorption peaksfall within the experimental regimes. The results show a red-shift absorption peak increases with the increase of particle diameter corresponds to a decreasein the conduction band energy of metal nanoparticles.