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Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients
Authors:Roman ?azarski  Asbjörn Manfred Burow  Luká? Grajciar  Marek Sierka
Institution:1. Otto‐Schott‐Institut für Materialforschung (OSIM), Friedrich‐Schiller‐Universit?t Jena, Jena, Germany;2. Department of Chemistry, Chair of Theoretical Chemistry, University of Munich (LMU), Munich, Germany
Abstract:A full implementation of analytical energy gradients for molecular and periodic systems is reported in the TURBOMOLE program package within the framework of Kohn–Sham density functional theory using Gaussian‐type orbitals as basis functions. Its key component is a combination of density fitting (DF) approximation and continuous fast multipole method (CFMM) that allows for an efficient calculation of the Coulomb energy gradient. For exchange‐correlation part the hierarchical numerical integration scheme (Burow and Sierka, Journal of Chemical Theory and Computation 2011, 7, 3097) is extended to energy gradients. Computational efficiency and asymptotic O(N) scaling behavior of the implementation is demonstrated for various molecular and periodic model systems, with the largest unit cell of hematite containing 640 atoms and 19,072 basis functions. The overall computational effort of energy gradient is comparable to that of the Kohn–Sham matrix formation. © 2016 Wiley Periodicals, Inc.
Keywords:ab initio calculations  density‐functional theory  Gaussian‐basis sets  continuous fast multipole method  density fitting
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