ABSTRACT
The utility of density functional theory lies not only in its ability to calculate the atomistic structures of nanoscale and bulk materials from first principles, but to explain why one particular arrangement of atoms is favoured over another. This chapter discusses the physics that determines the relative accuracy of different functionals, with specific reference to the aspects most relevant to the description of the delocalised electronic states found in superatoms. It discusses methods for the interpretation of electronic structure, most of which centre on understanding the density of states (DOS). This is the finite particle equivalent of the band structure that is so critical for understanding the electronic properties of bulk materials and is extensively used in the description of superatoms. The interpretation of the DOS using spherical harmonics projections became particularly useful with the advent of chemically-synthesised, ligand-protected metal clusters for which simply counting the number of metal atoms is insufficient to understand the electronic structure.
