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.
Cite
@article{arxiv.cond-mat/0203083,
title = {Third-generation muffin-tin orbitals},
author = {O. K. Andersen and T. Saha-Dasgupta and S. Ezhov},
journal= {arXiv preprint arXiv:cond-mat/0203083},
year = {2007}
}