Parallel calculation of electron multiple scattering using Lanczos algorithms

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 NR atoms and s, p, and d states for convergence, with NR between about 10 2 –10; for this case about 10 inversions of 9NR39NR 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 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.