Parallel calculation of electron multiple scattering using Lanczos algorithms

TLDR

Real‑space multiple‑scattering calculations of electronic density of states and XANES scale as the cube of system size, requiring large atomic clusters and many matrix inversions, which makes them computationally demanding. The study aims to accelerate these calculations by employing MPI parallel processing and fast Lanczos multiple‑scattering algorithms. The authors implement MPI parallelism and a fast Lanczos algorithm within the FEFF8 code to achieve this acceleration. These methods reduce computation times by roughly two orders of magnitude, enable practical XANES for systems with ~10³ atoms, and provide an energy‑dependent crossover between full and finite‑order multiple scattering that distinguishes extended and near‑edge regimes.

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 ${9N}_{R}\ifmmode\times\else\texttimes\fi{}{9N}_{R}$ 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.