Dispersion Corrected Hartree–Fock and Density Functional Theory for Organic Crystal Structure Prediction

  • Jan Gerit Brandenburg
  • Stefan GrimmeEmail author
Part of the Topics in Current Chemistry book series (TOPCURRCHEM, volume 345)


We present and evaluate dispersion corrected Hartree–Fock (HF) and Density Functional Theory (DFT) based quantum chemical methods for organic crystal structure prediction. The necessity of correcting for missing long-range electron correlation, also known as van der Waals (vdW) interaction, is pointed out and some methodological issues such as inclusion of three-body dispersion terms are discussed. One of the most efficient and widely used methods is the semi-classical dispersion correction D3. Its applicability for the calculation of sublimation energies is investigated for the benchmark set X23 consisting of 23 small organic crystals. For PBE-D3 the mean absolute deviation (MAD) is below the estimated experimental uncertainty of 1.3 kcal/mol. For two larger π-systems, the equilibrium crystal geometry is investigated and very good agreement with experimental data is found. Since these calculations are carried out with huge plane-wave basis sets they are rather time consuming and routinely applicable only to systems with less than about 200 atoms in the unit cell. Aiming at crystal structure prediction, which involves screening of many structures, a pre-sorting with faster methods is mandatory. Small, atom-centered basis sets can speed up the computation significantly but they suffer greatly from basis set errors. We present the recently developed geometrical counterpoise correction gCP. It is a fast semi-empirical method which corrects for most of the inter- and intramolecular basis set superposition error. For HF calculations with nearly minimal basis sets, we additionally correct for short-range basis incompleteness. We combine all three terms in the HF-3c denoted scheme which performs very well for the X23 sublimation energies with an MAD of only 1.5 kcal/mol, which is close to the huge basis set DFT-D3 result.


Counterpoise correction Crystal structure prediction Density Functional Theory Dispersion correction Hartree–Fock 



Approximate normal coordinate rational function optimization program


Gaussian atomic orbitals


Combination of Becke’s three-parameter hybrid functional B3 and the correlation functional LYP of Lee, Yang, and Parr


Basis set error


Basis set incompleteness error


Basis set superposition error


Coordination number


Crystalline orbital program


Third version of a semi-classical first-principles dispersion correction


Density functional


Density Functional Theory


Density Functional Theory with atom-pairwise and three-body dispersion correction


Geometrical counterpoise correction


Generalized gradient approximation




Dispersion corrected Hartree–Fock with semi-empirical basis set corrections


Mean absolute deviation


Many-body dispersion interaction by Tkatchenko and Scheffler


Mean deviation


Centro-methyl tribenzotriquinazene


Combination of polarized minimal basis and SVP basis


Projector augmented plane-wave


Generalized gradient-approximated functional of Perdew, Burke, and Ernzerhof


Root mean square deviation


Random phase approximation


Revised version of the PBE functional


Symmetry Adapted Perturbation Theory


Self-consistent field


Standard deviation


Self interaction error


Short-range basis incompleteness correction


Polarized split-valence basis set of Ahlrichs




Tkatchenko and Scheffler dispersion correction


Vienna ab initio simulation package


Van der Waals


Vydrov and van Voorhis non-local correlation functional


Benchmark set of 23 small organic crystals


Exchange-dipole model of Becke and Johnson


Zero point vibrational energy


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© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  1. 1.Mulliken Center for Theoretical ChemistryInstitut für Physikalische und Theoretische Chemie der Universität BonnBonnGermany

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