Fast full-potential calculations with a converged basis of atom-centered linear muffin-tin orbitals: Structural and dynamic properties of silicon

For fast and accurate density-functional calculations we devise a small basis set consisting of atom-centered linear muffin-tin orbitals (LMTO's). For the test case Si, an absolute total energy convergence of 0.02 eV/atom is obtained with 22 LMTO's/atom. The calculated lattice constant, elastic constants, phonon frequencies, mode Gr\"uneisen, and strain parameters, as well as the energy-volume curves for various crystalline phases are in accord with experimental data. This includes to 0.43-eV/atom energy difference between the diamond and bcc phases. Compared with pseudopotential plane-wave (PP-PW) calculations, our full-potential LMTO calculations are at least as accurate. In contrast with the PP-PW method, and in common with the linear augmented plane-wave method, the LMTO method can treat materials with atoms of any kind. By virtue of its 5--10 times smaller basis set, it is much faster.