A generally applicable atomic-charge dependent London dispersion correction

• Published in: The Journal of chemical physics Vol. 150; no. 15; pp. 154122 - 154140
• Main Authors: Caldeweyher, Eike, Ehlert, Sebastian, Hansen, Andreas, Neugebauer, Hagen, Spicher, Sebastian, Bannwarth, Christoph, Grimme, Stefan
• Format: Journal Article
• Language: English
• Published: United States American Institute of Physics 21.04.2019
• Subjects: Approximation; Benchmarks; Coefficients; Damping; Density functional theory; Dipoles; Dispersion; Electronegativity; Empirical analysis; Mathematical models; Model accuracy; Parameters; Physics; Quadrupole interaction; Quadrupoles; Radon; Thermochemical properties; Time dependence
• ISSN: 0021-9606; 1089-7690; 1089-7690
• DOI: 10.1063/1.5090222

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.