This talk will discuss real-space multiple-scattering, electronic-structure methods, which, by use of electronic screening concepts, have produced O(N) scaling of energy calculations (N is the number of atoms per unit cell, not electrons). Such real-space methods are a type of "divide-and-conquer" scheme using a 'local interaction zone'. These all-electron, DFT methods directly solve for the system's Green's function, and allow, e.g., structural defects and chemical and magnetic disorder to be addressed. In band-gap materials, the method is O(N) with a small prefactor. In metallic systems, i.e. those with a continuum electronic spectrum, accuracy and scaling (up to 2000 atoms on a workstation) of the real-space O(N) methodology is compared to converged k-space results, as well as a real- and k-space hybrid method. For metallic systems with N > 400, the complex non-Hermitian matrices involved are 98% (or more) sparse. For large N, iterative methods (and related preconditioning) become necessary, although not as efficient as standard inversion, and provide trivial parallelization. Examples are given where such real-space "divide-and-conquer" schemes, such as (screened) Linear Scaling Multiple Scattering, do and do not converge. This work was performed under the auspices of the U.S. Department of Energy through the Frederick Seitz Materials Research Laboratory at the University of Illinois Urbana-Champaign grant DEFG02-91ER45439. [Please visit, use and contribute to the Software Archive at the Materials Computation Center at http://www.mcc.uiuc.edu.]
Copyright. All Rights Reserved.