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 ${S}_{\mathrm{ij}}$. It vanishes beyond second-nearest neighbors and is tabulated. Tight-binding two-center forms with transfer integrals proportional to ${S}_{\mathrm{ij}}$ are derived.