Density Functional-based tight binding

Abstract

Tight binding (TB) refers to a family of approximate quantum mechanical models that as-sume that the electrons of an atomic system are tightly bound to their nuclei. In the TB picture,molecules and solids form because the electrons of each atom interact with other electronsandnucleiofneighboringatoms.Theseinteratomicinteractions,1 betweenatomsthatarespatially close to each other, result in small fluctuations2 of the combined atomic electron den-sities, giving rise to chemical bonds!This way of thinking about atomic systems looks simple, but has strong physical grounds,which were rst realized for solids [1,2], but also apply to single molecules. This chapter willcon ne its discussion to molecules; fortunately, for historical reasons, the vast majority of theliterature on TB revolves around solids, in case the reader needs to supplement the content ofthis chapter with further reading on condensed matter systems (e.g., see Refs. [2e4]).