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

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

Abstract

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.

Keywords

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

Abbreviations

ANCOPT

Approximate normal coordinate rational function optimization program

AO

Gaussian atomic orbitals

B3LYP

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

BSE

Basis set error

BSIE

Basis set incompleteness error

BSSE

Basis set superposition error

CN

Coordination number

CRYSTAL09

Crystalline orbital program

D3

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

DF

Density functional

DFT

Density Functional Theory

DFT-D3

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

gCP

Geometrical counterpoise correction

GGA

Generalized gradient approximation

HF

Hartree–Fock

HF-3c

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

MAD

Mean absolute deviation

MBD

Many-body dispersion interaction by Tkatchenko and Scheffler

MD

Mean deviation

Me-TBTQ

Centro-methyl tribenzotriquinazene

MINIX

Combination of polarized minimal basis and SVP basis

PAW

Projector augmented plane-wave

PBE

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

RMSD

Root mean square deviation

RPA

Random phase approximation

RPBE

Revised version of the PBE functional

SAPT

Symmetry Adapted Perturbation Theory

SCF

Self-consistent field

SD

Standard deviation

SIE

Self interaction error

SRB

Short-range basis incompleteness correction

SVP

Polarized split-valence basis set of Ahlrichs

TBTQ

Tribenzotriquinazene

TS

Tkatchenko and Scheffler dispersion correction

VASP

Vienna ab initio simulation package

vdW

Van der Waals

VV10

Vydrov and van Voorhis non-local correlation functional

X23

Benchmark set of 23 small organic crystals

XDM

Exchange-dipole model of Becke and Johnson

ZPV

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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