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

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Prediction and Calculation of Crystal Structures

Part of the book series: Topics in Current Chemistry ((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.

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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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Authors and Affiliations

  1. Mulliken Center for Theoretical Chemistry, Institut für Physikalische und Theoretische Chemie der Universität Bonn, Beringstraße 4, 53115, Bonn, Germany

    Jan Gerit Brandenburg & Stefan Grimme

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  1. Jan Gerit Brandenburg
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  2. Stefan Grimme
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Correspondence to Stefan Grimme .

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Editors and Affiliations

  1. Dept. of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, USA

    Sule Atahan-Evrenk

  2. Dept. of Chemistry and Chemical Biology, Harvard University, Cambridge, Massachusetts, USA

    Alan Aspuru-Guzik

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Brandenburg, J.G., Grimme, S. (2013). Dispersion Corrected Hartree–Fock and Density Functional Theory for Organic Crystal Structure Prediction. In: Atahan-Evrenk, S., Aspuru-Guzik, A. (eds) Prediction and Calculation of Crystal Structures. Topics in Current Chemistry, vol 345. Springer, Cham. https://doi.org/10.1007/128_2013_488

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