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Linear Scaling Self-Consistent Field Calculations with Millions of Atoms in the Condensed Phase

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Department of Materials, ETH Zurich, Wolfgang-Pauli-Strasse 27, 8093 Zurich, Switzerland
Physical Chemistry Institute, University of Zurich, Winterthurerstrasse 190, CH-8057 Zurich, Switzerland
§On leave from the National Institute of Chemistry, Ljubljana, Slovenia.
Cite this: J. Chem. Theory Comput. 2012, 8, 10, 3565–3573
Publication Date (Web):February 29, 2012
https://doi.org/10.1021/ct200897x
Copyright © 2012 American Chemical Society

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    Abstract

    In this work, the applicability and performance of a linear scaling algorithm is investigated for three-dimensional condensed phase systems. A simple but robust approach based on the matrix sign function is employed together with a thresholding matrix multiplication that does not require a prescribed sparsity pattern. Semiempirical methods and density functional theory have been tested. We demonstrate that self-consistent calculations with 1 million atoms are feasible for simple systems. With this approach, the computational cost of the calculation depends strongly on basis set quality. In the current implementation, high quality calculations for dense systems are limited to a few hundred thousand atoms. We report on the sparsities of the involved matrices as obtained at convergence and for intermediate iterations. We investigate how determining the chemical potential impacts the computational cost for very large systems.

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