Explicit, First-Principles Tight-Binding Theory

The minimal base of muffin-tin orbitals is transformed exactly into a tight-binding base. The linear transformations, the orbitals, and the Hamiltonian, overlap, and Green's function matrices are expressed in terms of one matrix, the canonical structure matrix Sᵢⱼ. It vanishes beyond second-nearest neighbors and is tabulated. Tight-binding two-center forms with transfer integrals proportional to Sᵢⱼ are derived.