Abstract
Van der Waals (vdW) interactions stem from electronic zero-point fluctuations and are often critical for the correct description of structure, stability, and response properties of molecules and materials, including biomolecules, nanomaterials, and material interfaces. Here, we give a conceptual as well as mathematical overview of the current state of modeling vdW interactions, focusing in particular on the consequences of different approximations for practical applications. We present a systematic classification of approximate first-principles models based on the adiabatic-connection fluctuation-dissipation theorem, namely the nonlocal density functionals, interatomic methods, and methods based on the random-phase approximation. The applicability of these methods to different types of materials and material properties is discussed in connection with availability of theoretical and experimental benchmarks. We conclude with a roadmap of the open problems that remain to be solved to construct a universal, efficient, and accurate vdW model for realistic material modeling.
This is a preview of subscription content, log in via an institution to check access.
References
Ambrosetti A, Alfè D, DiStasio RA Jr, Tkatchenko A (2014a) Hard numbers for large molecules: toward exact energetics for supramolecular systems. J Phys Chem Lett 5(5):849–855. https://doi.org/10.1021/jz402663k
Ambrosetti A, Reilly AM, DiStasio RA Jr, Tkatchenko A (2014b) Long-range correlation energy calculated from coupled atomic response functions. J Chem Phys 140(18):18A508. https://doi.org/10.1063/1.4865104
Andersson Y, Langreth DC, Lundqvist BI (1996) Van der Waals interactions in density-functional theory. Phys Rev Lett 76(1):102–105. https://doi.org/10.1103/PhysRevLett.76.102
Ángyán JG (2007) On the exchange-hole model of London dispersion forces. J Chem Phys 127(2):024,108. https://doi.org/10.1063/1.2749512
Ángyán JG, Liu RF, Toulouse J, Jansen G (2011) Correlation energy expressions from the adiabatic-connection fluctuation–dissipation theorem approach. J Chem Theory Comput 7(10):3116–3130. https://doi.org/10.1021/ct200501r
Axilrod BM, Teller E (1943) Interaction of the van der Waals type between three atoms. J Chem Phys 11(6):299–300. https://doi.org/10.1063/1.1723844
Ayers PW (2009) A perspective on the link between the exchange(-correlation) hole and dispersion forces. J Math Chem 46(1):86–96. https://doi.org/10.1007/s10910-008-9451-y
Bade WL (1957) Drude-model calculation of dispersion forces. I. General theory. J Chem Phys 27(6):1280–1284. https://doi.org/10.1063/1.1743991
Bade WL, Kirkwood JG (1957) Drude-model calculation of dispersion forces. II. The linear lattice. J Chem Phys 27(6):1284–1288. https://doi.org/10.1063/1.1743992
Becke AD (1988) A multicenter numerical integration scheme for polyatomic molecules. J Chem Phys 88(4):2547–2553. https://doi.org/10.1063/1.454033
Becke AD, Johnson ER (2005a) A density-functional model of the dispersion interaction. J Chem Phys 123(15):154,101. https://doi.org/10.1063/1.2065267
Becke AD, Johnson ER (2005b) Exchange-hole dipole moment and the dispersion interaction. J Chem Phys 122(15):154,104. https://doi.org/10.1063/1.1884601
Becke AD, Johnson ER (2006) Exchange-hole dipole moment and the dispersion interaction: high-order dispersion coefficients. J Chem Phys 124(1):014,104. https://doi.org/10.1063/1.2139668
Becke AD, Roussel MR (1989) Exchange holes in inhomogeneous systems: a coordinate-space model. Phys Rev A 39(8):3761–3767. https://doi.org/10.1103/PhysRevA.39.3761
Björkman T (2012) Van der Waals density functional for solids. Phys Rev B 86(16):165,109. https://doi.org/10.1103/PhysRevB.86.165109
Björkman T (2014) Testing several recent van der Waals density functionals for layered structures. J Chem Phys 141(7):074,708. https://doi.org/10.1063/1.4893329
Björkman T, Gulans A, Krasheninnikov AV, Nieminen RM (2012) Are we van der Waals ready? J Phys Condens Matter 24(42):424,218. https://doi.org/10.1088/0953-8984/24/42/424218
Brandenburg JG, Grimme S (2014) Accurate modeling of organic molecular crystals by dispersion-corrected density functional tight binding (DFTB). J Phys Chem Lett 5(11):1785–1789. https://doi.org/10.1021/jz500755u
Bučko T, Lebègue S, Hafner J, Ángyán JG (2013) Improved density dependent correction for the description of London dispersion forces. J Chem Theory Comput 9(10):4293–4299. https://doi.org/10.1021/ct400694h
Bučko T, Lebègue S, Ángyán JG, Hafner J (2014) Extending the applicability of the Tkatchenko-Scheffler dispersion correction via iterative Hirshfeld partitioning. J Chem Phys 141(3):034,114. https://doi.org/10.1063/1.4890003
Bultinck P, Alsenoy CV, Ayers PW, Carbó-Dorca R (2007) Critical analysis and extension of the Hirshfeld atoms in molecules. J Chem Phys 126(14):144,111. https://doi.org/10.1063/1.2715563
Callen HB, Welton TA (1951) Irreversibility and generalized noise. Phys Rev 83(1):34–40. https://doi.org/10.1103/PhysRev.83.34
Dion M, Rydberg H, Schröder E, Langreth DC, Lundqvist BI (2004) Van der Waals density functional for general geometries. Phys Rev Lett 92(24):246,401. https://doi.org/10.1103/PhysRevLett.92.246401
Dobson JF, White A, Rubio A (2006) Asymptotics of the dispersion interaction: analytic benchmarks for van der Waals energy functionals. Phys Rev Lett 96(7):073,201. https://doi.org/10.1103/PhysRevLett.96.073201
Donchev AG (2006) Many-body effects of dispersion interaction. J Chem Phys 125(7):074,713. https://doi.org/10.1063/1.2337283
Elstner M, Hobza P, Frauenheim T, Suhai S, Kaxiras E (2001) Hydrogen bonding and stacking interactions of nucleic acid base pairs: a density-functional-theory based treatment. J Chem Phys 114(12):5149–5155. https://doi.org/10.1063/1.1329889
Freysoldt C, Grabowski B, Hickel T, Neugebauer J, Kresse G, Janotti A, Van de Walle CG (2014) First-principles calculations for point defects in solids. Rev Mod Phys 86(1):253–305. https://doi.org/10.1103/RevModPhys.86.253
Gao W, Tkatchenko A (2013) Electronic structure and van der Waals interactions in the stability and mobility of point defects in semiconductors. Phys Rev Lett 111(4):045,501. https://doi.org/10.1103/PhysRevLett.111.045501
Ge X, Lu D (2015) Local representation of the electronic dielectric response function. Phys Rev B 92(24):241,107. https://doi.org/10.1103/PhysRevB.92.241107
Geim AK, Grigorieva IV (2013) Van der Waals heterostructures. Nature 499(7459):419–425. https://doi.org/10.1038/nature12385
Gell-Mann M, Brueckner KA (1957) Correlation energy of an electron gas at high density. Phys Rev 106(2):364–368. https://doi.org/10.1103/PhysRev.106.364
Gobre VV, Tkatchenko A (2013) Scaling laws for van der Waals interactions in nanostructured materials. Nat Commun 4:2341. https://doi.org/10.1038/ncomms3341
Grimme S (2004) Accurate description of van der Waals complexes by density functional theory including empirical corrections. J Comput Chem 25(12):1463–1473. https://doi.org/10.1002/jcc.20078
Grimme S (2006) Semiempirical GGA-type density functional constructed with a long-range dispersion correction. J Comput Chem 27(15):1787–1799. https://doi.org/10.1002/jcc.20495
Grimme S, Antony J, Ehrlich S, Krieg H (2010) A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J Chem Phys 132(15):154,104. https://doi.org/10.1063/1.3382344
Gunnarsson O, Lundqvist BI (1976) Exchange and correlation in atoms, molecules, and solids by the spin-density-functional formalism. Phys Rev B 13(10):4274–4298. https://doi.org/10.1103/PhysRevB.13.4274
Halgren TA (1992) The representation of van der Waals (vdW) interactions in molecular mechanics force fields: potential form, combination rules, and vdW parameters. J Am Chem Soc 114(20):7827–7843. https://doi.org/10.1021/ja00046a032
Harl J, Schimka L, Kresse G (2010) Assessing the quality of the random phase approximation for lattice constants and atomization energies of solids. Phys Rev B 81(11):115,126. https://doi.org/10.1103/PhysRevB.81.115126
Hepburn J, Scoles G, Penco R (1975) A simple but reliable method for the prediction of intermolecular potentials. Chem Phys Lett 36(4):451–456. https://doi.org/10.1016/0009-2614(75)80278-8
Hermann J, DiStasio RA Jr, Tkatchenko A (2017) First-principles models for van der Waals interactions in molecules and materials: concepts, theory, and applications. Chem Rev 117(6):4714–4758. https://doi.org/10.1021/acs.chemrev.6b00446
Heßelmann A (2009) Derivation of the dispersion energy as an explicit density- and exchange-hole functional. J Chem Phys 130(8):084,104. https://doi.org/10.1063/1.3077939
Hirshfeld FL (1977) Bonded-atom fragments for describing molecular charge densities. Theoret Chim Acta 44(2):129–138. https://doi.org/10.1007/BF00549096
Hunt KLC (1983) Nonlocal polarizability densities and van der Waals interactions. J Chem Phys 78(10):6149–6155. https://doi.org/10.1063/1.444577
Jansen G, Liu RF, Ángyán JG (2010) On the equivalence of ring-coupled cluster and adiabatic connection fluctuation-dissipation theorem random phase approximation correlation energy expressions. J Chem Phys 133(15):154,106. https://doi.org/10.1063/1.3481575
Johnson ER, Becke AD (2006) A post-Hartree-Fock model of intermolecular interactions: inclusion of higher-order corrections. J Chem Phys 124(17):174,104. https://doi.org/10.1063/1.2190220
Jurečka P, Šponer J, Černý J, Hobza P (2006) 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. Phys Chem Chem Phys 8(17):1985–1993. https://doi.org/10.1039/B600027D
Kohn W, Meir Y, Makarov DE (1998) Van der Waals energies in density functional theory. Phys Rev Lett 80(19):4153–4156. https://doi.org/10.1103/PhysRevLett.80.4153
Kurth S, Perdew JP (1999) Density-functional correction of random-phase-approximation correlation with results for jellium surface energies. Phys Rev B 59(16):10,461–10,468. https://doi.org/10.1103/PhysRevB.59.10461
Landau LD, Lifschitz EM (1980) Statistical physics, vol 5, 3rd edn. Pergamon Press, Oxford
Langbein D (1974) Theory of Van Der Waals attraction, Springer tracts in modern physics, vol 72. Springer, Berlin/Heidelberg. https://doi.org/10.1007/BFb0042407. URL http://link.springer.com/chapter/10.1007/BFb0042407
Langreth DC, Perdew JP (1977) Exchange-correlation energy of a metallic surface: wave-vector analysis. Phys Rev B 15(6):2884–2901. https://doi.org/10.1103/PhysRevB.15.2884
Lein M, Gross EKU, Perdew JP (2000) Electron correlation energies from scaled exchange-correlation kernels: importance of spatial versus temporal nonlocality. Phys Rev B 61(20):13,431–13,437. https://doi.org/10.1103/PhysRevB.61.13431
Lucas A (1967) Collective contributions to the long-range dipolar interaction in rare-gas crystals. Physica 35(3):353–368. https://doi.org/10.1016/0031-8914(67)90184-X
Mahan GD (1965) Van der Waals forces in solids. J Chem Phys 43(5):1569–1574. https://doi.org/10.1063/1.1696973
Margenau H (1939) Van der Waals forces. Rev Mod Phys 11(1):1–35. https://doi.org/10.1103/RevModPhys.11.1
Marzari N, Mostofi AA, Yates JR, Souza I, Vanderbilt D (2012) Maximally localized Wannier functions: theory and applications. Rev Mod Phys 84(4):1419–1475. https://doi.org/10.1103/RevModPhys.84.1419
Mayer A (2007) Formulation in terms of normalized propagators of a charge-dipole model enabling the calculation of the polarization properties of fullerenes and carbon nanotubes. Phys Rev B 75(4):045,407. https://doi.org/10.1103/PhysRevB.75.045407
Mooij WTM, van Duijneveldt FB, van Duijneveldt-van de Rijdt JGCM, van Eijck BP (1999) Transferable ab initio intermolecular potentials. 1. Derivation from methanol dimer and trimer calculations. J Phys Chem A 103(48):9872–9882. https://doi.org/10.1021/jp991641n
Mutō Y (1943) Hikyokusei bunshi no aida ni sayō suru chikara ni tsuite [On forces acting between nonpolar molecules]. Nippon Sugaku Buturigakkwaishi 17:629–631. https://doi.org/10.11429/subutsukaishi1927.17.10-11-12_629
Olsen T, Thygesen KS (2012) Extending the random-phase approximation for electronic correlation energies: the renormalized adiabatic local density approximation. Phys Rev B 86(8):081,103. https://doi.org/10.1103/PhysRevB.86.081103
Olsen T, Thygesen KS (2013a) Beyond the random phase approximation: improved description of short-range correlation by a renormalized adiabatic local density approximation. Phys Rev B 88(11):115,131. https://doi.org/10.1103/PhysRevB.88.115131
Olsen T, Thygesen KS (2013b) Random phase approximation applied to solids, molecules, and graphene-metal interfaces: from van der Waals to covalent bonding. Phys Rev B 87(7):075,111. https://doi.org/10.1103/PhysRevB.87.075111
Olsen T, Thygesen KS (2014) Accurate ground-state energies of solids and molecules from time-dependent density-functional theory. Phys Rev Lett 112(20):203,001. https://doi.org/10.1103/PhysRevLett.112.203001
Otero-de-la-Roza A, Johnson ER (2012) A benchmark for non-covalent interactions in solids. J Chem Phys 137(5):054,103. https://doi.org/10.1063/1.4738961
Parr RG, Yang W (1989) Density-functional theory of atoms and molecules. No. 16 in The international series of monographs on chemistry. Oxford University Press. URL https://global.oup.com/academic/product/density-functional-theory-of-atoms-and-molecules-9780195092769
Parsegian VA (2005) Van der Waals forces: a handbook for biologists, chemists, engineers, and physicists. Cambridge University Press, Cambridge. URL http://ebooks.cambridge.org/ref/id/CBO9780511614606
Reilly AM, Tkatchenko A (2013a) Seamless and accurate modeling of organic molecular materials. J Phys Chem Lett 4(6):1028–1033. https://doi.org/10.1021/jz400226x
Reilly AM, Tkatchenko A (2013b) Understanding the role of vibrations, exact exchange, and many-body van der Waals interactions in the cohesive properties of molecular crystals. J Chem Phys 139(2):024,705. https://doi.org/10.1063/1.4812819
Reilly AM, Cooper RI, Adjiman CS, Bhattacharya S, Boese AD, Brandenburg JG, Bygrave PJ, Bylsma R, Campbell JE, Car R, Case DH, Chadha R, Cole JC, Cosburn K, Cuppen HM, Curtis F, Day GM, DiStasio RA Jr, Dzyabchenko A, van Eijck BP, Elking DM, van den Ende JA, Facelli JC, Ferraro MB, Fusti-Molnar L, Gatsiou CA, Gee TS, de Gelder R, Ghiringhelli LM, Goto H, Grimme S, Guo R, Hofmann DWM, Hoja J, Hylton RK, Iuzzolino L, Jankiewicz W, de Jong DT, Kendrick J, de Klerk NJJ, Ko HY, Kuleshova LN, Li X, Lohani S, Leusen FJJ, Lund AM, Lv J, Ma Y, Marom N, Masunov AE, McCabe P, McMahon DP, Meekes H, Metz MP, Misquitta AJ, Mohamed S, Monserrat B, Needs RJ, Neumann MA, Nyman J, Obata S, Oberhofer H, Oganov AR, Orendt AM, Pagola GI, Pantelides CC, Pickard CJ, Podeszwa R, Price LS, Price SL, Pulido A, Read MG, Reuter K, Schneider E, Schober C, Shields GP, Singh P, Sugden IJ, Szalewicz K, Taylor CR, Tkatchenko A, Tuckerman ME, Vacarro F, Vasileiadis M, Vazquez-Mayagoitia A, Vogt L, Wang Y, Watson RE, de Wijs GA, Yang J, Zhu Q, Groom CR (2016) Report on the sixth blind test of organic crystal structure prediction methods. Acta Cryst B 72(4):439–459. https://doi.org/10.1107/S2052520616007447
Ren X, Tkatchenko A, Rinke P, Scheffler M (2011) Beyond the random-phase approximation for the electron correlation energy: the importance of single excitations. Phys Rev Lett 106(15):153,003. https://doi.org/10.1103/PhysRevLett.106.153003
Ren X, Rinke P, Joas C, Scheffler M (2012) Random-phase approximation and its applications in computational chemistry and materials science. J Mater Sci 47(21):7447–7471. https://doi.org/10.1007/s10853-012-6570-4
Ren X, Rinke P, Scuseria GE, Scheffler M (2013) Renormalized second-order perturbation theory for the electron correlation energy: concept, implementation, and benchmarks. Phys Rev B 88(3):035,120. https://doi.org/10.1103/PhysRevB.88.035120
Renne MJ, Nijboer BRA (1967) Microscopic derivation of macroscopic Van der Waals forces. Chem Phys Lett 1(8):317–320. https://doi.org/10.1016/0009-2614(67)80004-6
Řezáč J, Riley KE, Hobza P (2011) S66: a well-balanced database of benchmark interaction energies relevant to biomolecular structures. J Chem Theory Comput 7(8):2427–2438. https://doi.org/10.1021/ct2002946
Ruiz VG, Liu W, Zojer E, Scheffler M, Tkatchenko A (2012) Density-functional theory with screened van der Waals interactions for the modeling of hybrid inorganic-organic systems. Phys Rev Lett 108(14):146,103. https://doi.org/10.1103/PhysRevLett.108.146103
Ruzsinszky A, Perdew JP, Tao J, Csonka GI, Pitarke JM (2012) Van der Waals coefficients for nanostructures: fullerenes defy conventional wisdom. Phys Rev Lett 109(23):233,203. https://doi.org/10.1103/PhysRevLett.109.233203
Sato T, Nakai H (2009) Density functional method including weak interactions: dispersion coefficients based on the local response approximation. J Chem Phys 131(22):224,104. https://doi.org/10.1063/1.3269802
Sato T, Nakai H (2010) Local response dispersion method. II. Generalized multicenter interactions. J Chem Phys 133(19):194,101. https://doi.org/10.1063/1.3503040
Schimka L, Gaudoin R, Klimeš J, Marsman M, Kresse G (2013) Lattice constants and cohesive energies of alkali, alkaline-earth, and transition metals: random phase approximation and density functional theory results. Phys Rev B 87(21):214,102. https://doi.org/10.1103/PhysRevB.87.214102
Scuseria GE, Henderson TM, Sorensen DC (2008) The ground state correlation energy of the random phase approximation from a ring coupled cluster doubles approach. J Chem Phys 129(23):231,101. https://doi.org/10.1063/1.3043729
Silvestrelli PL (2008) Van der Waals interactions in DFT made easy by Wannier functions. Phys Rev Lett 100(5):053,002. https://doi.org/10.1103/PhysRevLett.100.053002
Silvestrelli PL (2013) Van der Waals interactions in density functional theory by combining the quantum harmonic oscillator-model with localized Wannier functions. J Chem Phys 139(5):054,106. https://doi.org/10.1063/1.4816964
Silvestrelli PL, Benyahia K, Grubisiĉ S, Ancilotto F, Toigo F (2009) Van der Waals interactions at surfaces by density functional theory using Wannier functions. J Chem Phys 130(7):074,702. https://doi.org/10.1063/1.3077288
Steinmann SN, Corminboeuf C (2010) A system-dependent density-based dispersion correction. J Chem Theory Comput 6(7):1990–2001. https://doi.org/10.1021/ct1001494
Steinmann SN, Corminboeuf C (2011) Comprehensive benchmarking of a density-dependent dispersion correction. J Chem Theory Comput 7(11):3567–3577. https://doi.org/10.1021/ct200602x
Stone AJ (2013) The theory of intermolecular forces, 2nd edn. Oxford University Press, Oxford URL http://www.oxfordscholarship.com/view/10.1093/acprof:oso/9780199672394.001.0001/acprof-9780199672394
Szabo A, Ostlund NS (1996) Modern quantum chemistry: introduction to advanced electronic structure theory, rev edn. URL http://store.doverpublications.com/0486691861.html
Tao J, Perdew JP, Ruzsinszky A (2010) Long-range van der Waals attraction and alkali-metal lattice constants. Phys Rev B 81(23):233,102. https://doi.org/10.1103/PhysRevB.81.233102
Tkatchenko A, Scheffler M (2009) Accurate molecular Van Der Waals interactions from ground-state electron density and free-atom reference data. Phys Rev Lett 102(7):073,005. https://doi.org/10.1103/PhysRevLett.102.073005
Tkatchenko A, DiStasio RA Jr, Car R, Scheffler M (2012) Accurate and efficient method for many-body van der Waals interactions. Phys Rev Lett 108(23):236,402. https://doi.org/10.1103/PhysRevLett.108.236402
Tkatchenko A, Ambrosetti A, DiStasio RA Jr (2013) Interatomic methods for the dispersion energy derived from the adiabatic connection fluctuation-dissipation theorem. J Chem Phys 138(7):74,106. https://doi.org/10.1063/1.4789814
Toulouse J, Colonna F, Savin A (2004) Long-range–short-range separation of the electron-electron interaction in density-functional theory. Phys Rev A 70(6):062,505. https://doi.org/10.1103/PhysRevA.70.062505
Toulouse J, Gerber IC, Jansen G, Savin A, Ángyán JG (2009) Adiabatic-connection fluctuation-dissipation density-functional theory based on range separation. Phys Rev Lett 102(9):096,404. https://doi.org/10.1103/PhysRevLett.102.096404
Unsöld A (1927) Quantentheorie des Wasserstoffmolekülions und der Born-Landéschen Abstoßungskräfte. Z Physik 43(8):563–574. https://doi.org/10.1007/BF01397633
Verstraelen T, Pauwels E, De Proft F, Van Speybroeck V, Geerlings P, Waroquier M (2012) Assessment of atomic charge models for gas-phase computations on polypeptides. J Chem Theory Comput 8(2):661–676. https://doi.org/10.1021/ct200512e
Vydrov OA, Van Voorhis T (2010) Nonlocal van der Waals density functional: the simpler the better. J Chem Phys 133(24):244,103. https://doi.org/10.1063/1.3521275
Wu Q, Yang W (2002) Empirical correction to density functional theory for van der Waals interactions. J Chem Phys 116(2):515–524. https://doi.org/10.1063/1.1424928
Zhang GX, Tkatchenko A, Paier J, Appel H, Scheffler M (2011) Van der Waals interactions in ionic and semiconductor solids. Phys Rev Lett 107(24):245,501. https://doi.org/10.1103/PhysRevLett.107.245501
Acknowledgments
The authors acknowledge partial financial support by the Luxembourg National Research Fund within the FNR-CORE program (No. FNR-11360857) and the ERC Consolidator Grant “BeStMo.”
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Section Editor information
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this entry
Cite this entry
Hermann, J., Tkatchenko, A. (2018). van der Waals Interactions in Material Modelling. In: Andreoni, W., Yip, S. (eds) Handbook of Materials Modeling . Springer, Cham. https://doi.org/10.1007/978-3-319-42913-7_6-1
Download citation
DOI: https://doi.org/10.1007/978-3-319-42913-7_6-1
Received:
Accepted:
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-42913-7
Online ISBN: 978-3-319-42913-7
eBook Packages: Springer Reference Physics and AstronomyReference Module Physical and Materials ScienceReference Module Chemistry, Materials and Physics