First-principles linear muffin-tin orbital atomic-sphere approximation calculations in real space

We have developed an approach, based on the linear muffin-tin orbital atomic-sphere approximation (LMTO-ASA) formalism and the recursion method, that allows us to perform first-principles density-functional calculations of electronic structure in real space. Using ${\mathrm{Zr}}_2$Fe as a test case, we compare our results with those obtained by using the standard reciprocal-space LMTO-ASA method. The scheme described here can be applied to nonperiodic systems and is also very useful in the study of complex metallic systems with a large number of atoms per unit cell. To illustrate the application of the first-principles real-space approach to a complex system, we calculate the electronic structure for a cluster of amorphous Zr. We use our results to evaluate the distribution of charge transfer among the sites of this randomly packed system. As a first guess we take the potential parameters to be the same for all atoms. The final self-consistent results show charge transfers that are almost an order of magnitude smaller than the ones obtained in the initial run. The major effect of the self-consistent process in this case is to rearrange the center of the bands in order to screen large charge fluctuations. This explains why the parametrized LMTO-ASA approach, where the relative position of the bands is fixed using approximate charge neutrality, works so well when applied to transition-metal alloys.