A systematic study of techniques for treating noncovalent interactions within the computationally efficient density functional theory (DFT) framework is presented through comparison to benchmark-quality evaluations of binding strength compiled for molecular complexes of diverse size and nature. In particular, the efficacy of functionals deliberately crafted to encompass long-range forces, a posteriori DFT+dispersion corrections (DFT-D2 and DFT-D3), and exchange-hole dipole moment (XDM) theory is assessed against a large collection (469 energy points) of reference interaction energies at the CCSD(T) level of theory extrapolated to the estimated complete basis set limit. The established S22 [revised in J. Chem. Phys. 132, 144104 (2010)] and JSCH test sets of minimum-energy structures, as well as collections of dispersion-bound (NBC10) and hydrogen-bonded (HBC6) dissociation curves and a pairwise decomposition of a protein–ligand reaction site (HSG), comprise the chemical systems for this work. From evaluations of accuracy, consistency, and efficiency for PBE-D, BP86-D, B97-D, PBE0-D, B3LYP-D, B970-D, M05-2X, M06-2X, ωB97X-D, B2PLYP-D, XYG3, and B3LYP-XDM methodologies, it is concluded that distinct, often contrasting, groups of these elicit the best performance within the accessible double-ζ or robust triple-ζ basis set regimes and among hydrogen-bonded or dispersion-dominated complexes. For overall results, M05-2X, B97-D3, and B970-D2 yield superior values in conjunction with aug-cc-pVDZ, for a mean absolute deviation of 0.41 – 0.49 kcal/mol, and B3LYP-D3, B97-D3, ωB97X-D, and B2PLYP-D3 dominate with aug-cc-pVTZ, affording, together with XYG3/6-311+G(3df,2p), a mean absolute deviation of 0.33 – 0.38 kcal/mol.
REFERENCES
1.
E. A.
Meyer
, R. K.
Castellano
, and F.
Diederich
, Angew. Chem., Int. Ed. Engl.
42
, 1210
(2003
).2.
A.
Anbarasu
, S.
Anand
, M. M.
Babu
, and R.
Sethumadhavan
, Int. J. Biol. Macromol.
41
, 251
(2007
).3.
G. A.
Jeffrey
and W.
Saenger
, Hydrogen Bonding in Biological Structures
(Springer-Verlag
, Berlin
, 1991
).4.
L.
Brunsveld
, B. J. B.
Folmer
, E. W.
Meijer
, and R. P.
Sijbesma
, Chem. Rev.
101
, 4071
(2001
).5.
C. G.
Claessens
and J. F.
Stoddart
, J. Phys. Org. Chem.
10
, 254
(1997
).6.
T. C.
Dinadayalane
, L.
Gorb
, T.
Simeon
, and H.
Dodziuk
, Int. J. Quantum Chem.
107
, 2204
(2007
).7.
T.
Takatani
, E. G.
Hohenstein
, and C. D.
Sherrill
, J. Chem. Phys.
128
, 124111
(2008
).8.
S.
Grimme
, J. Chem. Phys.
118
, 9095
(2003
).9.
R. A.
Distasio
and M.
Head-Gordon
, Mol. Phys.
105
, 1073
(2007
).10.
A.
Tkatchenko
, R. A.
DiStasio
Jr., M.
Head-Gordon
, and M.
Scheffler
, J. Chem. Phys.
131
, 094106
(2009
).11.
M.
Pitoňák
, P.
Neogrády
, J.
Černý
, S.
Grimme
, and P.
Hobza
, ChemPhysChem
10
, 282
(2009
).12.
B.
Jeziorski
, R.
Moszynski
, and K.
Szalewicz
, Chem. Rev.
94
, 1887
(1994
).13.
A.
Heßelmann
, G.
Jansen
, and M.
Schütz
, J. Chem. Phys.
122
, 014103
(2005
).14.
E. G.
Hohenstein
and C. D.
Sherrill
, J. Chem. Phys.
133
, 104107
(2010
).15.
O. A. von
Lilienfeld
, I.
Tavernelli
, U.
Rothlisberger
, and D.
Sebastiani
, Phys. Rev. Lett.
93
, 153004
(2004
).16.
Q.
Wu
and W.
Yang
, J. Chem. Phys.
116
, 515
(2002
).17.
S.
Grimme
, J. Comput. Chem.
25
, 1463
(2004
).18.
S.
Grimme
, J. Comput. Chem.
27
, 1787
(2006
).19.
S.
Grimme
, J.
Antony
, S.
Ehrlich
, and H.
Krieg
, J. Chem. Phys.
132
, 154104
(2010
).20.
A. D.
Becke
and E. R.
Johnson
, J. Chem. Phys.
122
, 154104
(2005
).21.
A. D.
Becke
and E. R.
Johnson
, J. Chem. Phys.
124
, 014104
(2006
).22.
J. G.
Angyan
, J. Chem. Phys.
127
, 024108
(2007
).23.
A. D.
Becke
and E. R.
Johnson
, J. Chem. Phys.
127
, 154108
(2007
).24.
A.
Heßelmann
, J. Chem. Phys.
130
, 084104
(2009
).25.
S. N.
Steinmann
and C.
Corminboeuf
, J. Chem. Theory Comput.
6
, 1990
(2010
).26.
X.
Xu
and W. A.
Goddard
, Proc. Natl. Acad. Sci. U.S.A.
101
, 2673
(2004
).27.
Y.
Zhao
and D. G.
Truhlar
, J. Phys. Chem. A
109
, 5656
(2005
).28.
Y.
Zhao
, N. E.
Schultz
, and D. G.
Truhlar
, J. Chem. Theory Comput.
2
, 364
(2006
).29.
Y.
Zhao
and D. G.
Truhlar
, Theor. Chem. Acc.
120
, 215
(2008
).30.
J.
Chai
and M.
Head-Gordon
, Phys. Chem. Chem. Phys.
10
, 6615
(2008
).31.
S.
Grimme
, J. Chem. Phys.
124
, 034108
(2006
).32.
T.
Schwabe
and S.
Grimme
, Phys. Chem. Chem. Phys.
9
, 3397
(2007
).33.
J.
Chai
and M.
Head-Gordon
, J. Chem. Phys.
131
, 174105
(2009
).34.
Y.
Zhang
, X.
Xu
, and W. A.
Goddard
, Proc. Natl. Acad. Sci. U.S.A.
106
, 4963
(2009
).35.
D. C.
Langreth
, M.
Dion
, H.
Rydberg
, E.
Schroder
, P.
Hyldgaard
, and B. I.
Lundqvist
, Int. J. Quantum Chem.
101
, 599
(2005
).36.
O. A.
Vydrov
and T. Van
Voorhis
, Phys. Rev. Lett.
103
, 063004
(2009
).37.
C. D.
Sherrill
, T.
Takatani
, and E. G.
Hohenstein
, J. Phys. Chem. A
113
, 10146
(2009
).38.
M.
Pitoňák
, K. E.
Riley
, Neogrády, and P.
Hobza
, ChemPhysChem
9
, 1636
(2008
).39.
E. C.
Lee
, D.
Kim
, P.
Jurečka
, P.
Tarakeshwar
, P.
Hobza
, and K. S.
Kim
, J. Phys. Chem. A
111
, 3446
(2007
).40.
K.
Raghavachari
, G. W.
Trucks
, J. A.
Pople
, and M.
Head-Gordon
, Chem. Phys. Lett.
157
, 479
(1989
).41.
T. J.
Lee
and G. E.
Scuseria
, “Achieving chemical accuracy with coupled-cluster theory
,” in Quantum Mechanical Electronic Structure Calculations with Chemical Accuracy
, edited by S. R.
Langhoff
(Kluwer Academic Publishers
, Dordrecht
, 1995
), pp. 47
–108
.42.
A. K.
Rappé
and E. R.
Bernstein
, J. Phys. Chem. A
104
, 6117
(2000
).43.
S.
Tsuzuki
and H. P.
Lüthi
, J. Chem. Phys.
114
, 3949
(2001
).44.
E. R.
Johnson
, R. A.
Wolkow
, and G. A.
DiLabio
, Chem. Phys. Lett.
394
, 334
(2004
).45.
F. O.
Kannemann
and A. D.
Becke
, J. Chem. Theory Comput.
5
, 719
(2009
).46.
W.
Koch
and M. C.
Holthausen
, A Chemist's Guide to Density Functional Theory
(Wiley-VCH
, New York
, 2001
).47.
Y.
Zhao
and D. G.
Truhlar
, Acc. Chem. Res.
41
, 157
(2008
).48.
E. R.
Johnson
, I. D.
Mackie
, and G. A.
DiLabio
, J. Phys. Org. Chem.
22
, 1127
(2009
).49.
J.
Gräfenstein
and D.
Cremer
, J. Chem. Phys.
130
, 124105
(2009
).50.
C. D.
Sherrill
, “Computations of noncovalent π interactions
,” in Reviews in Computational Chemistry
, edited by K. B.
Lipkowitz
and T. R.
Cundari
(Wiley
, Hoboken
, 2009
), Vol. 26
, pp. 1
–38
.51.
M. E.
Foster
and K.
Sohlberg
, Phys. Chem. Chem. Phys.
12
, 307
(2010
).52.
K. E.
Riley
, M.
Pitoňák
, P.
Jurečka
, and P.
Hobza
, Chem. Rev.
110
, 5023
(2010
).53.
Y.
Zhao
, B. J.
Lynch
, and D. G.
Truhlar
, J. Phys. Chem. A
108
, 4786
(2004
).54.
J.
Antony
and S.
Grimme
, Phys. Chem. Chem. Phys.
8
, 5287
(2006
).55.
P.
Jurečka
, J.
Šponer
, J.
Černý
, and P.
Hobza
, Phys. Chem. Chem. Phys.
8
, 1985
(2006
).56.
P.
Jurecka
, J.
Cerny
, P.
Hobza
, and D. R.
Salahub
, J. Comput. Chem.
28
, 555
(2007
).57.
E. G.
Hohenstein
, S. T.
Chill
, and C. D.
Sherrill
, J. Chem. Theory Comput.
4
, 1996
(2008
).58.
K. E.
Riley
, M.
Pitonak
, J.
Cerny
, and P.
Hobza
, J. Chem. Theory Comput.
6
, 66
(2010
).59.
A.
Vazquez-Mayagoitia
, C. D.
Sherrill
, E.
Apra
, and B. G.
Sumpter
, J. Chem. Theory Comput.
6
, 727
(2010
).60.
K. S.
Thanthiriwatte
, E. G.
Hohenstein
, L. A.
Burns
, and C. D.
Sherrill
, J. Chem. Theory Comput.
7
, 88
(2011
).61.
L.
Gráfová
, M.
Pitoňák
, J.
Řezáč
, and P.
Hobza
, J. Chem. Theory Comput.
6
, 2365
(2010
).62.
F. O.
Kannemann
and A. D.
Becke
, J. Chem. Theory Comput.
6
, 1081
(2010
).63.
M. O.
Sinnokrot
and C. D.
Sherrill
, J. Phys. Chem. A
108
, 10200
(2004
).64.
L. F.
Molnar
, X.
He
, B.
Wang
, and K. M.
Merz
, J. Chem. Phys.
131
, 065102
(2009
).65.
The DFT-D2 s6 parameter for the B970 functional was obtained by minimizing the mean absolute percent deviation for the S22 test set calculated with uncounterpoise-corrected and equally weighted aug-cc-pVDZ and aug-cc-pVTZ basis sets. A more thorough procedure, taking into account BSSE-corrected interaction energies, shifts the recommended parameter only slightly, to 0.80.
66.
See http://www.uni-muenster.de/Chemie.oc/grimme/ for a FORTRAN program implementing the DFT-D3 method and a file with available C6 coefficients. Westfalische Wilhelms-Universitat Munster, Organisch-Chemisches Institut, Theoretische Organische Chemie, Grimme Research Group, Corrensstrasse 40, D-48149 Munster, email: [email protected].
67.
J. P.
Perdew
, K.
Burke
, and M.
Ernzerhof
, Phys. Rev. Lett.
77
, 3865
(1996
).68.
C.
Adamo
and V.
Barone
, J. Chem. Phys.
110
, 6158
(1999
).69.
M.
Ernzerhof
and G. E.
Scuseria
, J. Chem. Phys.
110
, 5029
(1999
).70.
A. D.
Becke
, Phys. Rev. A
38
, 3098
(1988
).71.
J. P.
Perdew
, Phys. Rev. B
33
, 8822
(1986
).72.
A. D.
Becke
, J. Chem. Phys.
98
, 5648
(1993
).73.
P. J.
Stephens
, F. J.
Devlin
, C. F.
Chabalowski
, and M. J.
Frisch
, J. Phys. Chem.
98
, 11623
(1994
).74.
C.
Lee
, W.
Yang
, and R. G.
Parr
, Phys. Rev. B
37
, 785
(1988
).75.
It is acknowledged that the “exact HF exchange” energy computed within a DFT method is always slightly higher than the quantity produced by HF theory, due to imprecision in representing the solution to the HF ansatz by KS orbitals. See Ch. 5.3 of Ref. 46 for further discussion. Nevertheless, the present work continues the widespread conventional use of the term.
76.
A. D.
Becke
, J. Chem. Phys.
107
, 8554
(1997
).77.
L. A.
Curtiss
, K.
Raghavachari
, P. C.
Redfern
, and J. A.
Pople
, J. Chem. Phys.
106
, 1063
(1997
).78.
L. A.
Curtiss
, P. C.
Redfern
, K.
Raghavachari
, and J. A.
Pople
, J. Chem. Phys.
109
, 42
(1998
).79.
Y.
Zhao
and D. G.
Truhlar
, J. Chem. Theory Comput.
3
, 289
(2007
).80.
L. A.
Curtiss
, K.
Raghavachari
, P. C.
Redfern
, and J. A.
Pople
, J. Chem. Phys.
112
, 7374
(2000
).81.
A. D.
Becke
and M. R.
Roussel
, Phys. Rev. A
39
, 3761
(1989
).82.
J.
Kong
, Z. T.
Gan
, E.
Proynov
, M.
Freindorf
, and T. R.
Furlani
, Phys. Rev. A
79
, 042510
(2009
).83.
L. A.
Burns
, K. S.
Thanthiriwatte
, J.
Kong
, and C. D.
Sherrill
, “Improved performance for the exchange-hole dipole moment method: A reparameterization and assessment
,” (unpublished).84.
A.
Halkier
, T.
Helgaker
, P.
Jørgensen
, W.
Klopper
, H.
Koch
, J.
Olsen
, and A. K.
Wilson
, Chem. Phys. Lett.
286
, 243
(1998
).85.
See supplementary material at http://dx.doi.org/10.1063/1.3545971 for Tables 1–5 elaborating the reference CBS extrapolation level for individual test set members; Table 6 defining summary error statistics; Tables 7–14 containing MA%D and MA%BD counterparts to Tables VII and III–VI; Tables 15–16 compiling MAD results for alternate DFT-D3 parameters; and a shocking number of tables detailing interaction energies. Text files with electronic energies and interaction energies are also available, along with Cartesian coordinates for all test set members.
86.
Y.
Zhao
and D. G.
Truhlar
, J. Chem. Theory Comput.
1
, 415
(2005
).87.
J.
Řezáč
, P.
Jurečka
, K. E.
Riley
, J.
Černý
, H.
Valdes
, K.
Pluháčková
, K.
Berka
, T.
Řezáč
, M.
Pitoňák
, J.
Vondrášek
, and P.
Hobza
, Collect. Czech. Chem. Commun.
73
, 1261
(2008
). http://www.begdb.com.88.
T.
Takatani
, E. G.
Hohenstein
, M.
Malagoli
, M. S.
Marshall
, and C. D.
Sherrill
, J. Chem. Phys.
132
, 144104
(2010
).89.
T.
Takatani
and C. D.
Sherrill
, Phys. Chem. Chem. Phys.
9
, 6106
(2007
).90.
E. G.
Hohenstein
and C. D.
Sherrill
, J. Phys. Chem. A
113
, 878
(2009
).91.
J.
Faver
, M. L.
Benson
, X.
He
, B. P.
Roberts
, B.
Wang
, M. S.
Marshall
, M. R.
Kennedy
, C. D.
Sherrill
, and K. M.
Merz
Jr., “Formal Estimation of Errors in Computed Absolute Interaction Energies for Protein–Ligand Complexes
,” J. Chem. Theory Comput.
(in press) (2011
).92.
As was verified through inspection of base pair classification and comparison of recomputed MP2/aug-cc-pVDZ interaction energies with those in the published table, the interaction energy and label of JSCH-40 is properly associated with the geometry in file 100, represented as JSCH-40←100. Similarly, JSCH-41←102, JSCH-42←41, JSCH-45← 46, JSCH-46←45, JSCH-99←40, JSCH-100← 99, and JSCH-102←42, for a total of eight reassignments.
93.
T. H.
Dunning
, J. Chem. Phys.
90
, 1007
(1989
).94.
R. A.
Kendall
, T. H.
Dunning
, and R. J.
Harrison
, J. Chem. Phys.
96
, 6796
(1992
).95.
S. F.
Boys
and F.
Bernardi
, Mol. Phys.
19
, 553
(1970
).96.
E. J.
Bylaska
, W. A.
de Jong
, N.
Govind
, K.
Kowalski
, T. P.
Straatsma
, M.
Valiev
, D.
Wang
, E.
Apra
, T. L.
Windus
, J.
Hammond
, P.
Nichols
, S.
Hirata
, M. T.
Hackler
, Y.
Zhao
, P.-D.
Fan
, R. J.
Harrison
, M.
Dupuis
, D. M. A.
Smith
, J.
Nieplocha
, V.
Tipparaju
, M.
Krishnan
, Q.
Wu
, T.
Van Voorhis
, A. A.
Auer
, M.
Nooijen
, E.
Brown
, G.
Cisneros
, G. I.
Fann
, H.
Fruchtl
, J.
Garza
, K.
Hirao
, R.
Kendall
, J. A.
Nichols
, K.
Tsemekhman
, K.
Wolinski
, J.
Anchell
, D.
Bernholdt
, P.
Borowski
, T.
Clark
, D.
Clerc
, H.
Dachsel
, M.
Deegan
, K.
Dyall
, D.
Elwood
, E.
Glendening
, M.
Gutowski
, A.
Hess
, J.
Jaffe
, B.
Johnson
, J.
Ju
, R.
Kobayashi
, R.
Kutteh
, Z.
Lin
, R.
Littlefield
, X.
Long
, B.
Meng
, T.
Nakajima
, S.
Niu
, L.
Pollack
, M.
Rosing
, G.
Sandrone
, M.
Stave
, H.
Taylor
, G.
Thomas
, J.
van Lenthe
, A.
Wong
, and Z.
Zhang
, NWChem, A Computational Chemistry Package for Parallel Computers, version 5.1
(Pacific Northwest National Laboratory
, Richland
, 2007
).97.
Y.
Shao
, L. F.
Molnar
, Y.
Jung
, J.
Kussmann
, C.
Ochsenfeld
, S. T.
Brown
, A. T. B.
Gilbert
, L. V.
Slipchenko
, S. V.
Levchenko
, D. P.
O'Neill
, R. A.
DiStasio
Jr., R. C.
Lochan
, T.
Wang
, G. J. O.
Beran
, N. A.
Besley
, J. M.
Herbert
, C. Y.
Lin
, T.
Van Voorhis
, S. H.
Chien
, A.
Sodt
, R. P.
Steele
, V. A.
Rassolov
, P. E.
Maslen
, P. P.
Korambath
, R. D.
Adamson
, B.
Austin
, J.
Baker
, E. F. C.
Byrd
, H.
Dachsel
, R. J.
Doerksen
, A.
Dreuw
, B. D.
Dunietz
, A. D.
Dutoi
, T. R.
Furlani
, S. R.
Gwaltney
, A.
Heyden
, S.
Hirata
, C.-P.
Hsu
, G.
Kedziora
, R. Z.
Khalliulin
, P.
Klunzinger
, A. M.
Lee
, M. S.
Lee
, W.
Liang
, I.
Lotan
, N.
Nair
, B.
Peters
, E. I.
Proynov
, P. A.
Pieniazek
, Y. M.
Rhee
, J.
Ritchie
, E.
Rosta
, C. D.
Sherrill
, A. C.
Simmonett
, J. E.
Subotnik
, H. L.
Woodcock
, W.
Zhang
, A. T.
Bell
, A. K.
Chakraborty
, D. M.
Chipman
, F. J.
Keil
, A.
Warshel
, W. J.
Hehre
, H. F.
Schaefer
, J.
Kong
, A. I.
Krylov
, P. M. W.
Gill
, and M.
Head-Gordon
, Phys. Chem. Chem. Phys.
8
, 3172
(2006
).98.
E. R.
Johnson
, A. D.
Becke
, C. D.
Sherrill
, and G. A.
DiLabio
, J. Chem. Phys.
131
, 034111
(2009
).99.
J. A.
Pople
, in Energy, Structure and Reactivity: Proceedings of the 1972 Boulder Summer Research Conference on Theoretical Chemistry
, edited by D. W.
Smith
and W. B.
McRae
, (Wiley
, New York
, 1973
) p. 51
.100.
A.
Karton
, D.
Gruzman
, and J. M. L.
Martin
, J. Phys. Chem. A
113
, 8434
(2009
).101.
E.
Papajak
and D. G.
Truhlar
, J. Chem. Theory Comput.
6
, 597
(2010
).102.
I. Y.
Zhang
, Y.
Luo
, and X.
Xu
, J. Chem. Phys.
133
, 104105
(2010
).103.
J. P.
Perdew
and K.
Schmidt
, AIP Conf. Proc.
577
, 1
(2001
).© 2011 American Institute of Physics.
2011
American Institute of Physics
You do not currently have access to this content.
