Parallel calculation of electron multiple scattering using Lanczos algorithms

Abstract

Real space multiple scattering calculations of the electronic density of states and x-ray spectra in solids typically scale as the cube of the system and basis set size, and hence are highly demanding computationally. For example, such x-ray absorption near edge structure (XANES) calculations typically require clusters of order $N_R$ atoms and s, p, and d states for convergence, with $N_R$ between about ${10}^2–{10}^3;$ for this case about ${10}^2$ inversions of ${9N}_R\times {9N}_R$ matrices are needed, one for each energy point. We discuss here two ways to speed up these calculations: (1) message passing interface (MPI) parallel processing and (2) fast, Lanczos multiple scattering algorithms. Together these algorithms can reduce computation times typically by two orders of magnitude. These are both implemented in a generalization of the ab initio self-consistent FEFF8 code, which thus makes practical XANES calculations in complex systems with of order ${10}^3$ atoms. The Lanczos algorithm also yields a natural crossover between full and finite-order multiple scattering with increasing energy, thus differentiating the extended and near-edge regimes.