Convergence and reliability of the Rehr-Albers formalism in multiple-scattering calculations of photoelectron diffraction

The Rehr-Albers (RA) separable Green's-function formalism, which is based o n an expansion series, has been successful in speeding up multiple-scatteri ng cluster calculations for photoelectron diffraction simulations, particul arly in its second-order version. The performance of this formalism is expl ored here in terms of computational speed, convergence over orders of multi ple scattering, over orders of approximation, and over cluster size, by com parison with exact cluster-based formalisms. It is found that the second-or der RA approximation [characterized by (6x6) scattering matrices] is adequa te for many situations, particularly if the initial state from which photoe mission occurs is of s or p type. For the most general and quantitative app lications, higher-order versions of RA may become necessary for d initial s tates [third-order, i.e., (10x 10) matrices] and f initial states [fourth-o rder, i.e., (15x15) matrices]. However, the required RA order decreases as an electron wave proceeds along a multiple-scattering path, and this can be exploited, together with the selective and automated cutoff of weakly cont ributing matrix elements and paths, to yield computer time savings of at le ast an order of magnitude with no significant loss of accuracy. Cluster siz es of up to approximately 100 atoms should be sufficient for most problems that require about 5% accuracy in diffracted intensities. Excellent sensiti vity to structure is seen in comparisons of second-order theory with variab le geometry to exact theory as a fictitious "experiment." Our implementatio n of the Rehr-Albers formalism thus represents a versatile, quantitative, a nd efficient method for the accurate simulation of photoelectron diffractio n. [S0163-1829(98)04943-1].