The so-called D4 model is presented for the accurate computation of London dispersion interactions in density functional theory approximations (DFT-D4) and generally for atomistic modeling methods. In this successor to the DFT-D3 model, the atomic coordination-dependent dipole polarizabilities are scaled based on atomic partial charges which can be taken from various sources. For this purpose, a new charge-dependent parameter-economic scaling function is designed. Classical charges are obtained from an atomic electronegativity equilibration procedure for which efficient analytical derivatives with respect to nuclear positions are developed. A numerical Casimir-Polder integration of the atom-in-molecule dynamic polarizabilities then yields charge- and geometry-dependent dipole-dipole dispersion coefficients. Similar to the D3 model, the dynamic polarizabilities are precomputed by time-dependent DFT and all elements up to radon (Z = 86) are covered. The two-body dispersion energy expression has the usual sum-over-atom-pairs form and includes dipole-dipole as well as dipole-quadrupole interactions. For a benchmark set of 1225 molecular dipole-dipole dispersion coefficients, the D4 model achieves an unprecedented accuracy with a mean relative deviation of 3.8% compared to 4.7% for D3. In addition to the two-body part, three-body effects are described by an Axilrod-Teller-Muto term. A common many-body dispersion expansion was extensively tested, and an energy correction based on D4 polarizabilities is found to be advantageous for larger systems. Becke-Johnson-type damping parameters for DFT-D4 are determined for more than 60 common density functionals. For various standard energy benchmark sets, DFT-D4 slightly but consistently outperforms DFT-D3. Especially for metal containing systems, the introduced charge dependence of the dispersion coefficients improves thermochemical properties. We suggest (DFT-)D4 as a physically improved and more sophisticated dispersion model in place of DFT-D3 for DFT calculations as well as other low-cost approaches like semi-empirical models.
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21 April 2019
Research Article|
April 19 2019
A generally applicable atomic-charge dependent London dispersion correction
Eike Caldeweyher
;
Eike Caldeweyher
1
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn
, Beringstr. 4, D-53115 Bonn, Germany
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Sebastian Ehlert
;
Sebastian Ehlert
1
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn
, Beringstr. 4, D-53115 Bonn, Germany
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Andreas Hansen
;
Andreas Hansen
1
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn
, Beringstr. 4, D-53115 Bonn, Germany
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Hagen Neugebauer
;
Hagen Neugebauer
1
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn
, Beringstr. 4, D-53115 Bonn, Germany
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Sebastian Spicher
;
Sebastian Spicher
1
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn
, Beringstr. 4, D-53115 Bonn, Germany
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Christoph Bannwarth
;
Christoph Bannwarth
1
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn
, Beringstr. 4, D-53115 Bonn, Germany
2
Department of Chemistry, Stanford University
, Stanford, California 94305, USA
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Stefan Grimme
Stefan Grimme
a)
1
Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn
, Beringstr. 4, D-53115 Bonn, Germany
a)Author to whom correspondence should be addressed: grimme@thch.uni-bonn.de
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a)Author to whom correspondence should be addressed: grimme@thch.uni-bonn.de
J. Chem. Phys. 150, 154122 (2019)
Article history
Received:
January 25 2019
Accepted:
March 22 2019
Citation
Eike Caldeweyher, Sebastian Ehlert, Andreas Hansen, Hagen Neugebauer, Sebastian Spicher, Christoph Bannwarth, Stefan Grimme; A generally applicable atomic-charge dependent London dispersion correction. J. Chem. Phys. 21 April 2019; 150 (15): 154122. https://doi.org/10.1063/1.5090222
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