Evaluation of methods for obtaining dispersion energies used in density functional calculations of intermolecular interactions

  • Muhammad Shahbaz
  • Krzysztof Szalewicz
Regular Article
Part of the following topical collections:
  1. In Memoriam of János Ángyán


Since semilocal density functional theory (DFT) approximations cannot recover the dispersion components of interaction energies at intermonomer separations near van der Waals minima and larger, dispersion energies computed by methods other than semilocal DFTs are often added to DFT interaction energies such dispersion energies are assessed here by comparing them to accurate dispersion energies obtained from symmetry-adapted perturbation theory on a set of molecular dimers, including variations of intermonomer separations. The evaluated methods include nonlocal DFT correlation functionals, parameterized atom–atom dispersion functions originating from the asymptotic expansion, and methods based on models of atoms in molecules. In contrast to many published comparisons of such methods focused on total interaction energies, our comparisons evaluate the performance on the actual physical quantity for which these methods have been designed. This performance is discussed in the context of the physical soundness of the methods. Our results show that atom–atom functions reproduce dispersion energies best, with a mean absolute percentage error of the order of 10%. The nonlocal correlation functionals perform much worse, with errors in the range 24–49%, far from what could be called quantitative reproduction of this quantity. The only exception is the recently proposed damped asymptotic dispersion energy functional which gave an error of 12%. The atom-in-molecule methods also gave large errors, above 29%.


Density functional theory Dispersion energy Nonlocal correlation functional D3 vdW-DF VV09 VV10 MBD XDM DADE DFT+D 



We thank Dr. Marcin Modrzejewski for providing his code for the MBD calculations. This work was supported by the U.S. Army Research Laboratory and the Army Research Office under Grant W911NF-13-1-0387, as well as by the National Science Foundation Grant CHE-1566036. Computer resources were provided by the University of Delaware Computing Center.

Supplementary material

214_2019_2414_MOESM1_ESM.xlsx (157 kb)
Supplementary material 1 (xlsx 157 KB)


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Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of DelawareNewarkUSA

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