Kelkkanen, Kari André

Lundqvist, Bengt

Nørskov, Jens Kehlet

André K. Kelkkanen

Bengt I. Lundqvist

Jens K. Nørskov

MUCC (Crossref)

Density functional for van der Waals forces accounts for hydrogen bond in benchmark set of water hexamers

A recent extensive study has investigated how various exchange-correlation (XC) functionals treat hydrogen bonds in water hexamers and has shown traditional generalized gradient approximation and hybrid functionals used in density-functional (DF) theory to give the wrong dissociation-energy trend of low-lying isomers and van der Waals (vdW) dispersion forces to give key contributions to the dissociation energy. The question raised whether functionals that incorporate vdW forces implicitly into the XC functional predict the correct lowest-energy structure for the water hexamer and yield accurate total dissociation energy is here answered affirmatively for the vdW-DF [M. Dion , Phys. Rev. Lett.92, 246401 (2004)]

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Downloaded from orbit.dtu.dk on: Dec 17, 2017Density functional for van der Waals forces accounts for hydrogen bond in benchmarkset of water hexamersKelkkanen, Kari André; Lundqvist, Bengt; Nørskov, Jens KehletPublished in:Journal of Chemical PhysicsLink to article, DOI:10.1063/1.3193462Publication date:2009Document VersionPublisher's PDF, also known as Version of recordLink back to DTU OrbitCitation (APA):Kelkkanen, K. A., Lundqvist, B., & Nørskov, J. K. (2009). Density functional for van der Waals forces accountsfor hydrogen bond in benchmark set of water hexamers. Journal of Chemical Physics, 131(4), 046102. DOI:10.1063/1.3193462Density functional for van der Waals forces accounts for hydrogen bondin benchmark set of water hexamersAndré K. Kelkkanen,1 Bengt I. Lundqvist,1,2,a and Jens K. Nørskov11Department of Physics, Center for Atomic-Scale Materials Design, Technical University of Denmark,DK-2800 Kgs. Lyngby, Denmark2Department of Applied Physics, Chalmers University of Technology, SE-41296 Göteborg, SwedenReceived 30 May 2009; accepted 11 July 2009; published online 29 July 2009DOI: 10.1063/1.3193462A recent extensive study1 investigates how variousexchange-correlation XC functionals treat hydrogen bondsHBs in water hexamers, a critical HB benchmark set. Ac-curate wave-function studies including perturbative MP2,1quantum-Monte Carlo DQMC,1 and coupled-clusterCCSDT Ref. 2 calculations agree on the relative ener-getics of the low-lying isomers:1 The prism has lowest en-ergy followed by in order cage, book, and cyclic isomersFig. 1. The study1 shows that traditional generalized gradi-ent approximation GGA and hybrid functionals used indensity-functional theory DFT give the wrong dissociation-energy trend of the four isomers Fig. 1 and that van derWaals vdW dispersion forces give key contributions to thedissociation energy and asks whether functionals that incor-porate vdW forces implicitly into the XC functional predictthe correct trend and yield accurate total dissociation-energyvalues.1 Here an affirmative answer is given for the vdW-DFfunctional.3Typically, a HB is an intermolecular bond between anintramolecular bond of an H atom on a donor molecule andan acceptor molecule. The directionality is the angle betweenthese bonds. Studies on various HB-ed dimers suggest thatvdW forces can have a significant effect on the strength ofthe HB, including an indicated directionality effect.4 TheDFT-local-density approximation LDA and DFT-GGAsalso fail to describe highly bent HBs, another effect blamedon their lack of vdW account.5For calculation of electronic structure and total energy,DFT offers an alternative to wave-function methods that isparticularly powerful for extended systems, a well-provenexcellent tool for strongly bound systems. For also abundantsparse systems that are bound by weak nonbonding forces,including HBs, nonlocal correlation functionals have beenproposed recently. One such, the vdW-DF Ref. 3 includesvdW forces in a seamless fashion with a derived XC func-tional,EvdW-DF = EXrevPBE + ECLDA + ECnl, 1whereECnl=12 d3rd3rnrr,rnr 2depends nonlocally on the density nr with a general kernel derived from first principles.3 Already used successfullyfor a wide spectrum of systems,6 its virtues, e.g., biologicalmolecules, are highlighted by its account of stacking and HBinteractions between nucleobases7 and DNA intercalation.8The vdW-DF describes vdW effects approximately3,9 but dif-fers significantly from another method doing so, DFT-D,10being derived from first principles and thus nonempirical andinforming about the electron structure.All calculations are made with the GPAW software.11 ThevdW-DF Ref. 3 implementation is the same real-spacemethod as in Ref. 14, which adds vdW forces perturbatively3to a self-consistent revPBE15 calculation. The latter uses awell converged grid spacing of 0.13 Å and Eq. 2 is evalu-ated on a grid twice as dense a grid spacing of 0.15 Å resultsin binding-energy differences smaller than 1%. The hex-amer is in a cubic cell with side 18 Å and 35 electronic bandsare used. The dissociation energy is calculated as in Ref. 1but with the vdW-DF.Figure 1 shows trends in dissociation-energy values ofthe water-hexamer isomers relative to the prism configura-tion. Even within the narrow energy scale, the trends in theresults from wave-function methods MP2 Ref. 1, DQMCRef. 1, and CCSDT Ref. 2 are very distinct and close toeach other and to earlier CCSDT results.16 These trendscannot be accounted for by DFT with traditional GGA PBERef. 17, RPBE Ref. 18, and revPBE Ref. 15 and hybridPBE0 Ref. 13 XC functionals.1 Clearly, the vdW-DF andDFT-D methods give both the right stable configuration andthe proper energetic order of the lowest isomers.To follow a trend is not a sufficient criterion for a goodXC functional. For instance, LDA gives trend but is ignoreddue to lack of basic nonlocal interactions and its known over-estimate of dissociation of water clusters by more than50%.1,19 The vdW-DF dissociation-energy values of the low-lying isomers show an underbinding of about 50 meV/H2OTable I. At typical vdW separations about 3–5 Å theaccuracy of vdW-DF might be about 0.01 eV,14 but it isexpected to be worse at the short separations of HBsO–H separations being 1.9 Å in the water dimer20 and, e.g.,1.7–2.0 Å in the water hexamer cage,1 with vdW-DF andMP2 numbers given in Table I. The revPBE exchangefunctional15 used in vdW-DF lies close to exact exchangeHartree–Fock HF results for, e.g., argon, krypton,3 andbenzene dimers21 but gets repulsive at shorter separations,THE JOURNAL OF CHEMICAL PHYSICS 131, 046102 20090021-9606/2009/1314/046102/2/$25.00 © 2009 American Institute of Physics131, 046102-1Downloaded 23 Jun 2010 to 192.38.67.112. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jspwhere other flavors of GGA might be closer as for the waterdimer Fig. 2. The relatively small underbinding by use ofother less repulsive exchange functionals such as PBE,17 HF,and a hopefully soon developed systematically improved ex-change functional. The latter should be accurate in regionswhere the HB applies and where vdW and covalent bondshave comparable strengths. Figure 2 shows that there is roomfor further stabilization for the hexamer. We believe that therelative error found for the water hexamer will translate toother more complex water clusters and that the vdW-DFcould be expected to predict structure and phase diagrams ofliquid water.We thank Angelos Michaelides, Biswajit Santra, andMatthias Scheffler for providing the hexamer structures cal-culated in Ref. 1. The Center for Atomic-Scale MaterialsDesign is funded by the Lundbeck Foundation.aElectronic mail: bengt.lundqvist@chalmers.se.1 B. Santra, A. Michaelides, M. Fuchs, A. Tkatchenko, C. Filippi, and M.Scheffler, J. Chem. Phys. 129, 194111 2008.2 D. Bates and G. Tschumper, J. Phys. Chem. A 113, 3555 2009.3 M. Dion, H. Rydberg, E. Schröder, D. C. Langreth, and B. I. Lundqvist,Phys. Rev. Lett. 92, 246401 2004.4 T. Steiner and G. R. Desiraju, Chem. Commun. Cambridge 8, 8911998.5 J. N. Ireta and M. Scheffler, J. Phys. Chem. A 108, 5692 2004.6 D. C. Langreth, B. I. Lundqvist, S. D. Chakarova-Kack, V. R. Cooper, M.Dion, P. Hyldgaard, A. Kelkkanen, J. Kleis, L. Kong, S. Li, P. G. Moses,E. Murray, A. Puzder, H. Rydberg, E. Schröder, and T. Thonhauser, J.Phys.: Condens. Matter 21, 084203 2009.7 V. R. Cooper, T. Thonhauser, A. Puzder, E. Schröder, B. I. Lundqvist,and D. C. Langreth, J. Am. Chem. Soc. 130, 1304 2008; V. R. Cooper,T. Thonhauser, and D. C. Langreth, J. Chem. Phys. 128, 204102 2008.8 S. Li, V. R. Cooper, T. Thonhauser, B. I. Lundqvist, and D. C. Langreth,“Stacking interactions and DNA intercalation,” J. Phys. Chem. B inpress.9 T. Thonhauser, V. R. Cooper, S. Li, A. Puzder, P. Hyldgaard, and D. C.Langreth, Phys. Rev. B 76, 125112 2007.10 S. Grimme, J. Comput. Chem. 25, 1463 2004.11 J. J. Mortensen, L. B. Hansen, and K. W. Jacobsen, Phys. Rev. B 71,035109 2005.12 M. Stadele, M. Moukara, J. Majewski, P. Vogl, and A. Görling, Phys.Rev. B 59, 10031 1999.13 C. Adamo and V. Barone, J. Chem. Phys. 110, 6158 1999.14 P. G. Moses, J. J. Mortensen, B. I. Lundqvist, and J. K. Nørskov, J.Chem. Phys. 130, 104709 2009.15 Y. Zhang and W. Yang, Phys. Rev. Lett. 80, 890 1998.16 R. M. Olson, J. L. Bentz, R. A. Kendall, M. W. Schmidt, and M. S.Gordon, J. Chem. Theory Comput. 3, 1312 2007.17 J. P. Perdew, K. Burke, and M. Ernzerhof, Phys. Rev. Lett. 77, 38651996.18 B. Hammer, L. B. Hansen, and J. K. Nørskov, Phys. Rev. B 59, 74131999.19 C. Lee, H. Chen, and G. Fitzgerald, J. Chem. Phys. 101, 4472 1994.20 T. Taketsugu and D. J. Wales, Mol. Phys. 100, 2793 2002.21 A. Puzder, M. Dion, and D. C. Langreth, J. Chem. Phys. 124, 1641052006.Prism Cage Book Cyclic-20-15-10-5051015BindingenergiesperH2OrelativetoPrism[meV]DMCMP2revPBEvdW-DFPBERPBECCSD(T)DFT-DPBE0MP2vdW-DFDMCPBErevPBERPBECCSD(T)DFT-DPBE0FIG. 1. Dissociation energy per H2O molecule of the water hexamer inlow-lying isomers shown below calculated with wave-function MP2 Ref.1, DQMC Ref. 1, and CCSDT Ref. 2 and DFT methods with XCfunctionals in the PBE, RPBE, and revPBE flavors of GGA and in PBE0Ref. 1, DFT-D Ref. 1, and vdW-DF relative to the prism isomer.TABLE I. Calculated dissociation-energy values in meV/H2O and shortestseparations between hydrogen and oxygen atoms R–O–H of the low-lyingwater-hexamer isomers. Absolute-energy values Ediss calculated with thevdW-DF Ref. 3 allows comparison with MP2 result Ref. 1 numbers inparentheses, and relative energy values Ereldiss with results from a recentCCSDT calculation Ref. 2 numbers in square brackets.Prism Cage Book CyclicEdiss 280332 279332 277330 269324Ereldiss 00 12 47 1113R–O–H Å 1.81.7 1.91.9 1.81.8 1.81.71,5 2 2,5 3 3,5O--H separation [A]-200-1000100Exchangepartofdimerdissociationenergy[meV]revPBE_XRPBE_XPBE0_XEXX(X)LDA_XPBE_XFIG. 2. Exchange part of the dissociation energy for the water dimer atvarying separations defined by inset with exact exchange HF calculatedby the EXXX method Ref. 12 and with DFT using PBE, RPBE, revPBE,and LDA XC functionals, each calculated self-consistently and then sub-tracting the correlation energy. LDA exchange is showed to illustrate itstendency to overbind. The nonself-consistent PBE densities exchange partof PBE0 is also included by mixing of PBE and EXX exchange as inRef. 13.046102-2 Kelkkanen, Lundqvist, and Nørskov J. Chem. Phys. 131, 046102 2009Downloaded 23 Jun 2010 to 192.38.67.112. Redistribution subject to AIP license or copyright; see http://jcp.aip.org/jcp/copyright.jsp

Kelkkanen, AK

Lundqvist, Bengt I.

Norskov, Jens K.

Chalmers Publication Library

Density functional for van der Waals forces accounts for hydrogen bond benchmark set of water hexamers

Lundqvist, Bengt,

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Density functional for van der Waals forces accounts for hydrogen bond in benchmark set of water hexamers

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