Tight Binding Methods

This page will introduce tight-binding methods as reduced electronic-structure models that bridge qualitative band theory, semiempirical Hamiltonians, and large-scale atomistic simulation. It will eventually connect localized orbital bases, parameterized matrix elements, band structures, and modern extensions used in molecules, solids, and low-dimensional materials.

Planned Scope

This chapter should eventually explain:

• how tight-binding models approximate the electronic Hamiltonian in a compact localized basis
• how hopping terms, on-site energies, and overlap assumptions shape the model
• how tight binding connects to band structures, density of states, and chemical bonding
• how semiempirical and density-functional tight-binding variants extend the basic framework
• where tight-binding methods are most useful and where they become unreliable

Status

This page is currently a placeholder so the theory navigation is complete. A full chapter outline and the first completed section can be added next.