Implementation of empirical dispersion corrections to density functional theory for periodic systems

Abstract

A recently developed empirical dispersion correction (Grimme et al., J. Chem. Phys. 2010, 132, 154104) to standard density functional theory (DFT-D3) is implemented in the plane-wave program package VASP. The DFT-D3 implementation is compared with an implementation of the earlier DFT-D2 version (Grimme, J. Comput. Chem. 2004, 25, 1463; Grimme, J. Comput. Chem. 2006, 27, 1787). Summation of empirical pair potential terms is performed over all atom pairs in the reference cell and over atoms in shells of neighboring cells until convergence of the dispersion energy is obtained. For DFT-D3, the definition of coordination numbers has to be modified with respect to the molecular version to ensure convergence. The effect of three-center terms as implemented in the original molecular DFT-D3 version is investigated. The empirical parameters are taken from the original DFT-D3 version where they had been optimized for a reference set of small molecules. As the coordination numbers of atoms in bulk and surfaces are much larger than in the reference compounds, this effect has to be discussed. The results of test calculations for bulk properties of metals, metal oxides, benzene, and graphite indicate that the original parameters are also suitable for solid-state systems. In particular, the interlayer distance in bulk graphite and lattice constants of molecular crystals is considerably improved over standard functionals. With the molecular standard parameters (Grimme et al., J. Chem. Phys. 2010, 132, 154104; Grimme, J. Comput. Chem. 2006, 27, 1787) a slight overbinding is observed for ionic oxides where dispersion should not contribute to the bond. For simple adsorbate systems, such as Xe atoms and benzene on Ag(111), the DFT-D implementations reproduce experimental results with a similar accuracy as more sophisticated approaches based on perturbation theory (Rohlfing and Bredow, Phys. Rev. Lett. 2008, 101, 266106).

Van der Waals interactions in selected allotropes of phosphorus

“…Taking into account all results, the complete description of the phosphorus system with DFT-D2 provides a benchmark for this method combining accuracy and cost-effectiveness. In this context, it has to be mentioned that the recent developments of D3 [69] and D3BJ [70] came up with a more sound physical background and accuracy [71] to serve as a basis for continuative work on the heavier homologues of phosphorous.…”

Theoretical study of stability and charge-transport properties of coronene molecule and some of its halogenated derivatives: A path to ambipolar organic-based materials?

“…Geometry optimizations for dimer systems are thus done at the cost-efficient BLYP-D3/def2-SVP level. The final calculations on binding energies also incorporate a further (three-body) correction 59 depending on system size, 60,61 and are done with a larger basis set (BLYP-D3/def2-TZVP) and can be thus considered to be nearly free of basis sets incompleteness issues.…”

Importance of dispersion in density functional calculations of cesium chloride and its related halides

“…Of these various methods, the DFT + D2 approach is the most widely used. Recently the DFT + D3 method was privately implemented 26 but is not yet publicly available. Beyond these methods there are many alternative dispersion corrections, including those of Becke, Johnson, 27,28 and co-workers who have derived schemes to determine the dispersion parameters for any system, including solids, from the properties of the exchange hole.…”