Application of the LCAO method for energy band calculation in nanocrystals

摘要

On the basis of the LCAO method, the energy band width of a conduction electron in a one dimensional crystal is found to be 4ã. The quantity ã is a measure of overlapping interactions among the atomic orbitals of a conduction electron. In the present work, this method is applied to a copper (f.c.c.) nanocrystal of size equal to 10a (a being the lattice constant) to see the nature of dependence of ã on the nanocrystal size. It is found that ã increases inversely as the size of nanocrystals. This agrees well with the observation that the energy band widths in nanocrystals are wider compared to those of the corresponding bulk materials.