Particle in a Cylinder, in a Sphere, and on a Helix

The particle in a box from an earlier chapter is useful as a model to treat the electron motion in linear molecular ‘wires’, rectangular surfaces, and cuboid nano-particles. In this chapter, similar models are developed for spherical and cylindrical nano-particles, and helical nano-wires. Applications of these models that have been reported in the literature are discussed. For example, the particle in a cylinder model has been applied to treat the absorption spectra of silver nano-rods. The particle in a sphere model can be used tom rationalize the occurrence of sodium nano-clusters with certain ‘magic’ numbers of Na atoms. The model also explains the behaviour of potassium under high pressure, where the element starts to behave like a transition metal. The particle on a helix has been used to rationalize the optical activity of helical pi-conjugated molecules.