USE OF THE LLOYD FORMULA FOR BINARY-ALLOYS

The generalized Lloyd formula and the trace of the Green's function are equivalent expressions for the number of states of electrons in solids. The comparison of these two approaches enables one to estimate the accuracy of the number-of-states calculations. We study the accuracy of the Lloyd formula and of the trace of the Green's function for the number of states of a binary random alloy as a function of the cutoff parameter l(max) in the orbital momentum representation. We show that for transition metals truncation at l(max) = 2 leads to an essential loss of accuracy. It is necessary to take into consideration the contributions of s, p, d, and f electrons in both approaches to obtain their numerical equivalence. All higher-l contributions can be neglected. We propose a quadratic extrapolation scheme to solve the coherent-potential-approximation equation in one iteration. We show that the use of the tetrahedron technique for the Brillouin-zone integration for calculation of the tau matrix of an alloy allows us to obtain high-precision results with minimum computational efforts. The proposed procedures reduce computational time at least by a factor of 100 in comparison with the standard approaches.