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Density functional theory for molecular and periodic systems using density fitting and continuous fast multipole method: Analytical gradients
Author(s) -
Łazarski Roman,
Burow Asbjörn Manfred,
Grajciar Lukáš,
Sierka Marek
Publication year - 2016
Publication title -
journal of computational chemistry
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.907
H-Index - 188
eISSN - 1096-987X
pISSN - 0192-8651
DOI - 10.1002/jcc.24477
Subject(s) - density functional theory , multipole expansion , fast multipole method , atomic orbital , gaussian , computation , basis (linear algebra) , scaling , coulomb , basis function , statistical physics , physics , computational physics , computational chemistry , mathematics , quantum mechanics , chemistry , algorithm , geometry , electron
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.