Electronic densities of states of semi-infinite disordered chains: Comparisons of exact and analytic calculations

Results of exact and analytic calculations of the electronic densities of states (DOSs) associated with semi-infinite substitutionally disordered chains are presented using the exact position-space renormalization-group (PSRG) method, the augmented-space (AS) formalism, and the embedded-cluster method (ECM). In addition to total DOSs, the PSRG method allows the calculation of exact partial DOSs associated with local atomic configurations in a disordered material. Comparisons with the exact results indicate that as in the case of infinite materials the ECM provides a reliable method for the calculation of single-particle properties, such as the DOS, of semi-infinite systems. Furthermore, the ECM is found to be much more accurate than the AS formalism, especially in the case of concentrated substitutionally disordered alloys.