Minimal basis sets in the linear muffin-tin orbital method: Application to the diamond-structure crystals C, Si, and Ge

It is shown that in the muffin-tin orbital (MTO) method a minimal basis set suffices for the calculation of one-electron energies and wave functions, provided that the higher partial waves, ₋ (E, r), are included by means of L\"owdin downfolding. In terms of a recently proposed transformation theory the downfolding can be considered as the transformation to a set of MTO's whose tails can be continuously and differentiably augmented by the higher partial waves. Simplified linearization schemes provide Hamiltonian and overlap matrices in terms of energy-independent, linear muffin-tin orbitals (LMTO's). By application to band-structure and total-energy calculations for C, Si, and Ge it is demonstrated that a minimal basis set consisting of only one s and three p atom-centered LMTO's plus one s LMTO at the tetrahedral, interstitial site (that is, a total of five orbitals per atom) is sufficient for the calculation of ground-state properties.