A Generally Applicable Atomic-Charge Dependent London Dispersion Correction Scheme
Sebastian Ehlert1 , Eike Caldeweyher1 , Andreas Hansen1 , Hagen Neugebauer1 , Sebastian Spicher1 , Christoph Bannwarth2 , Stefan Grimme1
1Mulliken Center for Theoretical Chemistry, Beringstr. 4, D-53115 Bonn, Germany
2Department of Chemistry, Stanford University, Stanford, CA 94305, United States of America
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 modelling 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 pre-computed 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 3.9% 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 force-fields or semiempirical models.
[1] Caldeweyher, E. and Bannwarth, C. and Grimme S. J. Phys. Chem. 2017, 147, 034112.
[2] Caldeweyher, E. and Ehlert, S. and Hansen, A. and Neugebauer, H. and Spicher, S. and Bannwarth, C. and Grimme S. ChemRxiv, 2018, Preprint. DOI: 10.26434/chemrxiv.7430216.v1