DOI: 10.1063/1.3382344
OpenAccess: Closed
This work is not Open Acccess. We may still have a PDF on file in the green box below.
Share this:
Get up to 30% off our standard price for selected sequencing services covering sample extraction, library preparation, sequencing, and bioinformatic analysis.
Find out more

A consistent and accurate <i>ab initio</i> parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu

Stefan Grimme,Jens Antony,Stephan Ehrlich,Helge Krieg

Intramolecular force
Molecule
Density functional theory
The method of dispersion correction as an add-on to standard Kohn-Sham density functional theory (DFT-D) has been refined regarding higher accuracy, broader range of applicability, and less empiricism. The main new ingredients are atom-pairwise specific dispersion coefficients and cutoff radii that are both computed from first principles. The coefficients for new eighth-order dispersion terms are computed using established recursion relations. System (geometry) dependent information is used for the first time in a DFT-D type approach by employing the new concept of fractional coordination numbers (CN). They are used to interpolate between dispersion coefficients of atoms in different chemical environments. The method only requires adjustment of two global parameters for each density functional, is asymptotically exact for a gas of weakly interacting neutral atoms, and easily allows the computation of atomic forces. Three-body nonadditivity terms are considered. The method has been assessed on standard benchmark sets for inter- and intramolecular noncovalent interactions with a particular emphasis on a consistent description of light and heavy element systems. The mean absolute deviations for the S22 benchmark set of noncovalent interactions for 11 standard density functionals decrease by 15%-40% compared to the previous (already accurate) DFT-D version. Spectacular improvements are found for a tripeptide-folding model and all tested metallic systems. The rectification of the long-range behavior and the use of more accurate C(6) coefficients also lead to a much better description of large (infinite) systems as shown for graphene sheets and the adsorption of benzene on an Ag(111) surface. For graphene it is found that the inclusion of three-body terms substantially (by about 10%) weakens the interlayer binding. We propose the revised DFT-D method as a general tool for the computation of the dispersion energy in molecules and solids of any kind with DFT and related (low-cost) electronic structure methods for large systems.


Referenced Papers:
DOI: 10.1002/9780470399545.ch1
·
2009
Cited 37 times
Computations of Noncovalent π Interactions
DOI: 10.1002/9780470399545.ch2
·
2009
Cited 24 times
Reliable Electronic Structure Computations for Weak Noncovalent Interactions in Clusters
DOI: 10.1021/jp070589p
·
2007
Cited 150 times
Is Spin-Component Scaled Second-Order Møller−Plesset Perturbation Theory an Appropriate Method for the Study of Noncovalent Interactions in Molecules?
DOI: 10.1063/1.1329889
·
2001
Cited 883 times
Hydrogen bonding and stacking interactions of nucleic acid base pairs: A density-functional-theory based treatment
DOI: 10.1063/1.2992078
·
2008
Cited 67 times
Accurate and efficient calculation of van der Waals interactions within density functional theory by local atomic potential approach
DOI: 10.1103/physrevb.78.045116
·
2008
Cited 69 times
Popular Kohn-Sham density functionals strongly overestimate many-body interactions in van der Waals systems
DOI: 10.1002/jcc.20570
·
2007
Cited 580 times
Density functional theory augmented with an empirical dispersion term. Interaction energies and geometries of 80 noncovalent complexes compared with<i>ab initio</i>quantum mechanics calculations
DOI: 10.1021/ct900410j
·
2010
Cited 103 times
Describing Both Dispersion Interactions and Electronic Structure Using Density Functional Theory: The Case of Metal−Phthalocyanine Dimers
DOI: 10.1002/qua.20315
·
2005
Cited 307 times
Van der Waals density functional theory with applications
DOI: 10.1063/1.3315418
·
2010
Cited 25 times
Dipole oscillator strength distributions with improved high-energy behavior: Dipole sum rules and dispersion coefficients for Ne, Ar, Kr, and Xe revisited
DOI: 10.1063/1.1627293
·
2003
Cited 785 times
Gaussian basis sets of quadruple zeta valence quality for atoms H–Kr
DOI: 10.1021/ct9005882
·
2010
Cited 128 times
Accurate Intermolecular Interaction Energies from a Combination of MP2 and TDDFT Response Theory
DOI: 10.1103/physrevlett.103.263201
·
2009
Cited 148 times
Dispersionless Density Functional Theory
DOI: 10.1063/1.1723844
·
1943
Cited 1,253 times
Interaction of the van der Waals Type Between Three Atoms
DOI: 10.1103/physrevlett.77.3865
·
1996
Cited 120,160 times
Generalized Gradient Approximation Made Simple
DOI: 10.1021/jp800974k
·
2008
Cited 21 times
Toward an Accurate and Efficient Theory of Physisorption. I. Development of an Augmented Density-Functional Theory Model
DOI: 10.1007/s00214-007-0250-5
·
2007
Cited 394 times
Optimized accurate auxiliary basis sets for RI-MP2 and RI-CC2 calculations for the atoms Rb to Rn
DOI: 10.1039/b704725h
·
2007
Cited 901 times
Double-hybrid density functionals with long-range dispersion corrections: higher accuracy and extended applicability
DOI: 10.1080/00268970412331333474
·
2005
Cited 100 times
Van der Waals interactions studied by density functional theory
DOI: 10.1021/jp0720791
·
2007
Cited 210 times
Noncovalent Interactions between Graphene Sheets and in Multishell (Hyper)Fullerenes
DOI: 10.1039/b508541a
·
2005
Cited 14,462 times
Balanced basis sets of split valence, triple zeta valence and quadruple zeta valence quality for H to Rn: Design and assessment of accuracy
DOI: 10.1063/1.3256238
·
2009
Cited 14 times
The van der Waals coefficients between carbon nanostructures and small molecules: A time-dependent density functional theory study
DOI: 10.1039/b509242f
·
2005
Cited 191 times
A short-range gradient-corrected density functional in long-range coupled-cluster calculations for rare gas dimers
DOI: 10.1063/1.1622924
·
2003
Cited 1,625 times
Systematically convergent basis sets with relativistic pseudopotentials. II. Small-core pseudopotentials and correlation consistent basis sets for the post-<i>d</i> group 16–18 elements
DOI: 10.1063/1.3282265
·
2010
Cited 9 times
Van der Waals density functional from multipole dispersion interactions
DOI: 10.1063/1.447150
·
1984
Cited 1,276 times
An improved simple model for the van der Waals potential based on universal damping functions for the dispersion coefficients
DOI: 10.1039/b803508c
·
2008
Cited 50 times
Analysis of non-covalent interactions in (bio)organic molecules using orbital-partitioned localized MP2
DOI: 10.1103/physrevb.74.235401
·
2006
Cited 28 times
Ab initioquantum force field for simulations of nanostructures
DOI: 10.1021/jp050036j
·
2005
Cited 216 times
Accurate Calculation of the Heats of Formation for Large Main Group Compounds with Spin-Component Scaled MP2 Methods
DOI: 10.1016/0009-2614(95)00621-a
·
1995
Cited 2,240 times
Auxiliary basis sets to approximate Coulomb potentials
DOI: 10.1063/1.2139668
·
2006
Cited 164 times
Exchange-hole dipole moment and the dispersion interaction: High-order dispersion coefficients
DOI: 10.1021/ct800308k
·
2008
Cited 566 times
Assessment of the Performance of the M05−2X and M06−2X Exchange-Correlation Functionals for Noncovalent Interactions in Biomolecules
DOI: 10.1021/jp050536c
·
2005
Cited 1,175 times
Design of Density Functionals That Are Broadly Accurate for Thermochemistry, Thermochemical Kinetics, and Nonbonded Interactions
DOI: 10.1021/jp062225n
·
2006
Cited 46 times
Adsorption Energies, Inter-adsorbate Interactions, and the Two Binding Sites within Monolayer Benzene on Ag(111)†
DOI: 10.1063/1.1677610
·
1972
Cited 130 times
Calculation of Coefficients in the Power Series Expansion of the Long‐Range Dispersion Force between Atoms
DOI: 10.1021/ja070616p
·
2007
Cited 419 times
A Double Concave Hydrocarbon Buckycatcher
DOI: 10.1063/1.478522
·
1999
Cited 11,104 times
Toward reliable density functional methods without adjustable parameters: The PBE0 model
DOI: 10.2320/matertrans.mf200911
·
2009
Cited 35 times
A Universal Damping Function for Empirical Dispersion Correction on Density Functional Theory
DOI: 10.1021/jp906086x
·
2009
Cited 121 times
Potential Energy Curves for Cation−π Interactions: Off-Axis Configurations Are Also Attractive
DOI: 10.1002/(sici)1096-987x(19990115)20:1<12::aid-jcc4>3.0.co;2-u
·
1999
Cited 100 times
Toward the description of van der Waals interactions within density functional theory
DOI: 10.1103/physrevb.79.201105
·
2009
Cited 139 times
Linear-scaling self-consistent implementation of the van der Waals density functional
DOI: 10.1103/physrev.73.360
·
1948
Cited 2,044 times
The Influence of Retardation on the London-van der Waals Forces
DOI: 10.1103/physrevlett.96.073201
·
2006
Cited 239 times
Asymptotics of the Dispersion Interaction: Analytic Benchmarks for van der Waals Energy Functionals
DOI: 10.1063/1.3269802
·
2009
Cited 175 times
Density functional method including weak interactions: Dispersion coefficients based on the local response approximation
DOI: 10.1063/1.2178795
·
2006
Cited 97 times
Estimated MP2 and CCSD(T) interaction energies of n-alkane dimers at the basis set limit: Comparison of the methods of Helgaker et al. and Feller
DOI: 10.1103/physrevb.37.785
·
1988
Cited 75,585 times
Development of the Colle-Salvetti correlation-energy formula into a functional of the electron density
DOI: 10.1063/1.2065267
·
2005
Cited 905 times
A density-functional model of the dispersion interaction
DOI: 10.1002/chem.200400091
·
2004
Cited 146 times
On the Importance of Electron Correlation Effects for theπ-π Interactions in Cyclophanes
DOI: 10.1021/jp002631l
·
2000
Cited 117 times
Binding Enthalpies for Alkali Cation−Benzene Complexes Revisited
DOI: 10.1103/physrevb.33.8822
·
1986
Cited 15,173 times
Density-functional approximation for the correlation energy of the inhomogeneous electron gas
DOI: 10.1103/physrevlett.91.146401
·
2003
Cited 5,028 times
Climbing the Density Functional Ladder: Nonempirical Meta–Generalized Gradient Approximation Designed for Molecules and Solids
DOI: 10.1021/ct900536n
·
2010
Cited 18 times
Applications of Screened Hybrid Density Functionals with Empirical Dispersion Corrections to Rare Gas Dimers and Solids
DOI: 10.1063/1.1949201
·
2005
Cited 622 times
A post-Hartree–Fock model of intermolecular interactions
DOI: 10.1039/b204199p
·
2002
Cited 1,042 times
A fully direct RI-HF algorithm: Implementation, optimised auxiliary basis sets, demonstration of accuracy and efficiency
DOI: 10.1080/00268970701635543
·
2007
Cited 29 times
Structure and binding energies of the porphine dimer
DOI: 10.1016/0009-2614(93)89151-7
·
1993
Cited 1,361 times
Integral approximations for LCAO-SCF calculations
DOI: 10.1063/1.3244209
·
2009
Cited 281 times
Long-range corrected double-hybrid density functionals
DOI: 10.1063/1.1884601
·
2005
Cited 428 times
Exchange-hole dipole moment and the dispersion interaction
DOI: 10.1002/jcc.20495
·
2006
Cited 19,117 times
Semiempirical GGA-type density functional constructed with a long-range dispersion correction
DOI: 10.1103/physrevlett.80.890
·
1998
Cited 1,883 times
Comment on “Generalized Gradient Approximation Made Simple”
DOI: 10.1103/physrevb.76.155425
·
2007
Cited 146 times
Potassium intercalation in graphite: A van der Waals density-functional study
DOI: 10.1063/1.1424928
·
2002
Cited 710 times
Empirical correction to density functional theory for van der Waals interactions
DOI: 10.1063/1.1305880
·
2000
Cited 847 times
Small-core multiconfiguration-Dirac–Hartree–Fock-adjusted pseudopotentials for post-<b><i>d</i></b> main group elements: Application to PbH and PbO
DOI: 10.1063/1.3021474
·
2008
Cited 149 times
Delocalization errors in density functionals and implications for main-group thermochemistry
DOI: 10.1103/physrevlett.76.102
·
1996
Cited 405 times
van der Waals Interactions in Density-Functional Theory
DOI: 10.1021/ct900126q
·
2009
Cited 50 times
Convergence of the CCSD(T) Correction Term for the Stacked Complex Methyl Adenine−Methyl Thymine: Comparison with Lower-Cost Alternatives
DOI: 10.1039/b608262a
·
2006
Cited 207 times
Treating dispersion effects in extended systems by hybrid MP2:DFT calculations—protonation of isobutene in zeolite ferrierite
DOI: 10.1063/1.467146
·
1994
Cited 7,080 times
Fully optimized contracted Gaussian basis sets of triple zeta valence quality for atoms Li to Kr
DOI: 10.1063/1.463012
·
1992
Cited 125 times
<i>Ab</i><i>initio</i>dispersion coefficients for interactions involving rare‐gas atoms
DOI: 10.1103/physrevlett.102.073005
·
2009
Cited 3,896 times
Accurate Molecular Van Der Waals Interactions from Ground-State Electron Density and Free-Atom Reference Data
DOI: 10.1021/ar700208h
·
2008
Cited 312 times
Theoretical Thermodynamics for Large Molecules: Walking the Thin Line between Accuracy and Computational Cost
DOI: 10.1103/physrevlett.93.153004
·
2004
Cited 462 times
Optimization of Effective Atom Centered Potentials for London Dispersion Forces in Density Functional Theory
DOI: 10.1039/b907260h
·
2009
Cited 44 times
Cooperativity in noncovalent interactions of biologically relevant molecules
DOI: 10.1103/physreva.79.042510
·
2009
Cited 50 times
Efficient computation of the dispersion interaction with density-functional theory
DOI: 10.1063/1.3079822
·
2009
Cited 98 times
An efficient algorithm for the density-functional theory treatment of dispersion interactions
DOI: 10.1039/b600027d
·
2006
Cited 1,475 times
Benchmark database of accurate (MP2 and CCSD(T) complete basis set limit) interaction energies of small model complexes, DNA base pairs, and amino acid pairs
DOI: 10.1021/ct9002509
·
2009
Cited 67 times
Unified Inter- and Intramolecular Dispersion Correction Formula for Generalized Gradient Approximation Density Functional Theory
DOI: 10.1063/1.1637034
·
2004
Cited 264 times
Dispersion corrections to density functionals for water aromatic interactions
DOI: 10.1063/1.3336452
·
2010
Cited 36 times
Density functional study of 1,3,5-trinitro-1,3,5-triazine molecular crystal with van der Waals interactions
DOI: 10.1063/1.2190220
·
2006
Cited 743 times
A post-Hartree-Fock model of intermolecular interactions: Inclusion of higher-order corrections
DOI: 10.1021/ct900489g
·
2010
Cited 327 times
A General Database for Main Group Thermochemistry, Kinetics, and Noncovalent Interactions − Assessment of Common and Reparameterized (<i>meta</i>-)GGA Density Functionals
DOI: 10.1063/1.1412004
·
2001
Cited 528 times
Towards extending the applicability of density functional theory to weakly bound systems
DOI: 10.1016/s0009-2614(98)00862-8
·
1998
Cited 2,121 times
RI-MP2: optimized auxiliary basis sets and demonstration of efficiency
DOI: 10.1007/s002140050269
·
1997
Cited 1,182 times
RI-MP2: first derivatives and global consistency
DOI: 10.1021/ar700111a
·
2008
Cited 5,355 times
Density Functionals with Broad Applicability in Chemistry
DOI: 10.1002/(sici)1097-461x(1998)66:2<131::aid-qua4>3.0.co;2-w
·
1998
Cited 67 times
Relativistic pseudopotential calculations on Xe2, RnXe, and Rn2: The van der Waals properties of radon
DOI: 10.1063/1.1287055
·
2000
Cited 37 times
The He–OCS van der Waals potential from model calculations: Bound states, stable structures, and vibrational couplings
DOI: 10.1021/jp047289h
·
2004
Cited 283 times
The Vibronic Structure of Electronic Absorption Spectra of Large Molecules: A Time-Dependent Density Functional Study on the Influence of “Exact” Hartree−Fock Exchange
DOI: 10.1103/physreva.38.3098
·
1988
Cited 40,963 times
Density-functional exchange-energy approximation with correct asymptotic behavior
DOI: 10.1021/jp066504m
·
2007
Cited 64 times
Resolution of Identity Density Functional Theory Augmented with an Empirical Dispersion Term (RI-DFT-D): A Promising Tool for Studying Isolated Small Peptides
DOI: 10.1063/1.2148954
·
2006
Cited 2,364 times
Semiempirical hybrid density functional with perturbative second-order correlation
DOI: 10.1002/anie.200600448
·
2006
Cited 340 times
Seemingly Simple Stereoelectronic Effects in Alkane Isomers and the Implications for Kohn–Sham Density Functional Theory
DOI: 10.1039/b717744e
·
2008
Cited 187 times
Computational characterization and modeling of buckyball tweezers: density functional study of concave–convex π⋯π interactions
DOI: 10.1039/b907148b
·
2009
Cited 1,284 times
Density functional theory for transition metals and transition metal chemistry
DOI: 10.1103/physrevlett.103.063004
·
2009
Cited 297 times
Nonlocal van der Waals Density Functional Made Simple
DOI: 10.1002/poc.1606
·
2009
Cited 300 times
Dispersion interactions in density-functional theory
DOI: 10.1002/chem.200500465
·
2005
Cited 148 times
Structure and IR Spectrum of Phenylalanyl-Glycyl-Glycine Tripetide in the Gas-Phase: IR/UV Experiments, Ab Initio Quantum Chemical Calculations, and Molecular Dynamic Simulations
DOI: 10.1021/ct800511q
·
2009
Cited 199 times
“Mindless” DFT Benchmarking
DOI: 10.1039/b810189b
·
2008
Cited 7,832 times
Long-range corrected hybrid density functionals with damped atom–atom dispersion corrections
DOI: 10.1080/00268979909482993
·
1999
Cited 87 times
The MP2 limit correction applied to coupled cluster calculations of the electronic dissociation energies of the hydrogen fluoride and water dimers
DOI: 10.1021/jp8111556
·
2009
Cited 1,012 times
Consistent van der Waals Radii for the Whole Main Group
DOI: 10.1002/jcc.20078
·
2004
Cited 3,751 times
Accurate description of van der Waals complexes by density functional theory including empirical corrections
DOI: 10.1007/s10910-008-9451-y
·
2009
Cited 20 times
A perspective on the link between the exchange(-correlation) hole and dispersion forces
DOI: 10.1063/1.464913
·
1993
Cited 77,987 times
Density‐functional thermochemistry. III. The role of exact exchange
DOI: 10.1021/j100096a001
·
1994
Cited 15,672 times
Ab Initio Calculation of Vibrational Absorption and Circular Dichroism Spectra Using Density Functional Force Fields
DOI: 10.1021/jp053905d
·
2005
Cited 73 times
Binding Energy Curves from Nonempirical Density Functionals II. van der Waals Bonds in Rare-Gas and Alkaline-Earth Diatomics
DOI: 10.1088/0953-8984/22/2/022201
·
2010
Cited 1,961 times
Chemical accuracy for the van der Waals density functional
DOI: 10.1021/jp710918f
·
2008
Cited 135 times
A Prototype for Graphene Material Simulation: Structures and Interaction Potentials of Coronene Dimers
DOI: 10.1103/physrevb.69.155406
·
2004
Cited 886 times
Interlayer cohesive energy of graphite from thermal desorption of polyaromatic hydrocarbons
DOI: 10.1002/chem.200800987
·
2009
Cited 1,443 times
Molecular Single-Bond Covalent Radii for Elements 1-118
DOI: 10.1039/b615319b
·
2007
Cited 632 times
Density functional theory with dispersion corrections for supramolecular structures, aggregates, and complexes of (bio)organic molecules
DOI: 10.1103/physrevb.34.7406
·
1986
Cited 2,255 times
Erratum: Density-functional approximation for the correlation energy of the inhomogeneous electron gas
DOI: 10.1002/jcc.21022
·
2009
Cited 63 times
Noncovalent interactions in supramolecular complexes: A study on corannulene and the double concave buckycatcher
DOI: 10.1021/jp0112774
·
2001
Cited 157 times
Comment on “Using Kohn−Sham Orbitals in Symmetry-Adapted Perturbation Theory To Investigate Intermolecular Interactions”
DOI: 10.1002/047086334x
·
2006
Cited 163 times
Intermolecular Interactions
Related Papers:
DOI: 10.1016/s0009-2614(98)01351-7
·
1999
Cited 13 times
The intermolecular interaction between amines and F2. An ab initio study
DOI: 10.1016/s0166-1280(98)00085-2
·
1998
Cited 17 times
Computational study of water and ammonia dimers with density functional theory methods
DOI: 10.1016/j.saa.2006.07.029
·
2007
Cited 39 times
Molecular structures and vibrational frequencies of xanthine and its methyl derivatives (caffeine and theobromine) by ab initio Hartree–Fock and density functional theory calculations
DOI: 10.1002/1099-1395(200102)14:2<109::aid-poc344>3.0.co;2-j
·
2001
Cited 19 times
Ab initio study of the mechanisms of intermolecular and intramolecular [4?+?2] cycloaddition reactions of conjugated enynes
DOI: 10.1002/chin.199237068
·
1992
ChemInform Abstract: Empirical Force-Field Models for the Transition States of Intramolecular Diels-Alder Reactions Based Upon ab initio Transition Structures.
DOI: 10.1088/1674-1056/24/7/073301
·
2015
Assignment of terahertz vibrational modes of L-glutamine using density functional theory within generalized-gradient approximation
MAG: 2381502431
·
2007
DENSITY FUNCTIONAL THEORY CALCULATIONS ON TAUTOMERISM OF 2-THIOPYRIMIDINE
MAG: 239649814
·
2011
(E)-1-[4-(2-hydroxy-5-methoxybenzylideneamino)-phenyl]ethanone and (E)-1-[4-(2-hydroxy-4-methoxybenzylideneamino) phenyl]ethanone:X-ray and DFT-calculated structures
DOI: 10.1021/ja00038a052
·
1992
Cited 59 times
Empirical force field models for the transition states of intramolecular Diels-Alder reactions based upon ab initio transition structures
MAG: 2996419808
·
1996
ab initio Calculations on Intramolecular and Intermolecular Hydrogen Bonded Clusters