Third-generation muffin-tin orbitals

By the example of sp^3-bonded semiconductors, we illustrate what 3rd-generation muffin-tin orbitals (MTOs) are. We demonstrate that they can be downfolded to smaller and smaller basis sets: sp^3d^10,sp^3, and bond orbitals. For isolated bands, it is possible to generate Wannier functions a priori. Also for bands, which overlap other bands, Wannier-like MTOs can be generated a priori. Hence, MTOs have a unique capability for providing chemical understanding.