Hartree-Fock band-structure calculations with the linear muffin-tin-orbital method: Application to C, Si, Ge, andα-Sn

A general formalism is presented for electronic structure calculations of solids in the Hartree-Fock approximation based on the linear muffin-tin-orbital (LMTO) method. The nonlocal exchange operator is evaluated in the basis of tight-binding muffin-tin orbitals with the atomic-sphere approximation. Since the LMTO minimal basis set by construction is orthogonal to the core states and fairly complete, well-converged calculations are obtained even for high-Z materials. The frozen-core approximation is used and relativistic effects are incorporated through the scalar relativistic approximation. No assumption of a weak pseudopotential is needed, and electronic states of high-angular-momentum character are treated straightforwardly. The method is applied to diamond, Si, Ge, and -Sn, for which the Hartree-Fock band structures and cohesive energies are presented and compared to the results of local-density calculations, to experiments, and, for C and Si, to previous Hartree-Fock calculations.