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Evaluation of methods for obtaining dispersion energies used in density functional calculations of intermolecular interactions

  • Muhammad Shahbaz
  • Krzysztof Szalewicz
Regular Article
  • 11 Downloads
Part of the following topical collections:
  1. In Memoriam of János Ángyán

Abstract

Since semilocal density functional theory (DFT) approximations cannot recover the dispersion components of interaction energies at intermonomer separations near van der Waals minima and larger, dispersion energies computed by methods other than semilocal DFTs are often added to DFT interaction energies such dispersion energies are assessed here by comparing them to accurate dispersion energies obtained from symmetry-adapted perturbation theory on a set of molecular dimers, including variations of intermonomer separations. The evaluated methods include nonlocal DFT correlation functionals, parameterized atom–atom dispersion functions originating from the asymptotic expansion, and methods based on models of atoms in molecules. In contrast to many published comparisons of such methods focused on total interaction energies, our comparisons evaluate the performance on the actual physical quantity for which these methods have been designed. This performance is discussed in the context of the physical soundness of the methods. Our results show that atom–atom functions reproduce dispersion energies best, with a mean absolute percentage error of the order of 10%. The nonlocal correlation functionals perform much worse, with errors in the range 24–49%, far from what could be called quantitative reproduction of this quantity. The only exception is the recently proposed damped asymptotic dispersion energy functional which gave an error of 12%. The atom-in-molecule methods also gave large errors, above 29%.

Keywords

Density functional theory Dispersion energy Nonlocal correlation functional D3 vdW-DF VV09 VV10 MBD XDM DADE DFT+D 

Notes

Acknowledgements

We thank Dr. Marcin Modrzejewski for providing his code for the MBD calculations. This work was supported by the U.S. Army Research Laboratory and the Army Research Office under Grant W911NF-13-1-0387, as well as by the National Science Foundation Grant CHE-1566036. Computer resources were provided by the University of Delaware Computing Center.

Supplementary material

214_2019_2414_MOESM1_ESM.xlsx (157 kb)
Supplementary material 1 (xlsx 157 KB)

References

  1. 1.
    Hohenberg P, Kohn W (1964) Phys Rev 136:B864CrossRefGoogle Scholar
  2. 2.
    Kohn W, Sham LJ (1965) Phys Rev 140:1133CrossRefGoogle Scholar
  3. 3.
    Jones RO, Gunnarsson O (1989) Rev Mod Phys 61:689CrossRefGoogle Scholar
  4. 4.
    Perdew JP, Wang Y (1992) Phys Rev B 45:13244CrossRefGoogle Scholar
  5. 5.
    Langreth DC, Mehl MJ (1983) Phys Rev A 26:1809Google Scholar
  6. 6.
    Perdew JP, Wang Y (1986) Phys Rev B 33:8800CrossRefGoogle Scholar
  7. 7.
    Becke AD (1988) Phys Rev A 38:3098CrossRefGoogle Scholar
  8. 8.
    Perdew JP, Chevary JA, Vosko SH, Jackson KA, Pederson MR, Singh DJ, Fiolhais C (1992) Phys Rev B 46:6671CrossRefGoogle Scholar
  9. 9.
    Perdew JP, Burke K, Ernzerhof M (1996) Phys Rev Lett 77:3865CrossRefGoogle Scholar
  10. 10.
    Tao J, Perdew JP, Staroverov VN, Scuseria GE (2003) Phys Rev Lett 91:146401PubMedCrossRefGoogle Scholar
  11. 11.
    Sun J, Ruzsinszky A, Perdew JP (2015) Phys Rev Lett 115:036402PubMedCrossRefGoogle Scholar
  12. 12.
    Kristyán S, Pulay P (1994) Chem Phys Lett 229:175CrossRefGoogle Scholar
  13. 13.
    Gunnarsson O, Jonson M, Lundqvist B (1979) Phys Rev B 20:3136CrossRefGoogle Scholar
  14. 14.
    Shahbaz M, Szalewicz K (2018) Phys Rev Lett 121:113402PubMedCrossRefGoogle Scholar
  15. 15.
    Eisenschitz R, London F (1930) Z Phys 60:491CrossRefGoogle Scholar
  16. 16.
    Jeziorski B, Moszyński R, Szalewicz K (1994) Chem Rev 94:1887CrossRefGoogle Scholar
  17. 17.
    Szalewicz K (2012) Wiley Interdiscip Rev Comput Mol Sci 2:254CrossRefGoogle Scholar
  18. 18.
    Kochanski E (1971) Chem Phys Lett 10:543CrossRefGoogle Scholar
  19. 19.
    Jeziorski B, van Hemert M (1976) Mol Phys 31:713CrossRefGoogle Scholar
  20. 20.
    Chalasinski G, Jeziorski B, Andzelm J, Szalewicz K (1977) Mol Phys 33:971CrossRefGoogle Scholar
  21. 21.
    Szalewicz K, Jeziorski B (1979) Mol Phys 38:191CrossRefGoogle Scholar
  22. 22.
    Rybak S, Jeziorski B, Szalewicz K (1991) J Chem Phys 95:6576CrossRefGoogle Scholar
  23. 23.
    Williams HL, Szalewicz K, Moszyński R, Jeziorski B (1995) J Chem Phys 103:4586CrossRefGoogle Scholar
  24. 24.
    Moszyński R, Jeziorski B, Szalewicz K (1993) Int J Quantum Chem 45:409CrossRefGoogle Scholar
  25. 25.
    Korona T, Jeziorski B (2008) J Chem Phys 128:144107PubMedCrossRefGoogle Scholar
  26. 26.
    Misquitta AJ, Szalewicz K (2002) Chem Phys Lett 357:301CrossRefGoogle Scholar
  27. 27.
    Misquitta AJ, Jeziorski B, Szalewicz K (2003) Phys Rev Lett 91:033201PubMedCrossRefGoogle Scholar
  28. 28.
    Hesselmann A, Jansen G (2003) Chem Phys Lett 367:778CrossRefGoogle Scholar
  29. 29.
    Misquitta AJ, Szalewicz K (2005) J Chem Phys 122:214109PubMedCrossRefGoogle Scholar
  30. 30.
    Misquitta AJ, Podeszwa R, Jeziorski B, Szalewicz K (2005) J Chem Phys 123:214103PubMedCrossRefGoogle Scholar
  31. 31.
    Hesselmann A, Jansen G, Schütz M (2005) J Chem Phys 122:014103CrossRefGoogle Scholar
  32. 32.
    Bukowski R, Podeszwa R, Szalewicz K (2005) Chem Phys Lett 414:111CrossRefGoogle Scholar
  33. 33.
    Podeszwa R, Cencek W, Szalewicz K (2012) J Chem Theory Comput 8:1963PubMedCrossRefGoogle Scholar
  34. 34.
    Podeszwa R, Bukowski R, Szalewicz K (2006) J Chem Theory Comput 2:400PubMedCrossRefGoogle Scholar
  35. 35.
    Dion M, Rydberg H, Schröder E, Langreth DC, Lundqvist BI (2004) Phys Rev Lett 92:246401PubMedCrossRefGoogle Scholar
  36. 36.
    Lee K, Murray ED, Kong L, Lundqvist BI, Langreth DC (2010) Phys Rev B 82:081101CrossRefGoogle Scholar
  37. 37.
    Vydrov OA, Van Voorhis T (2009) Phys Rev Lett 103:063004PubMedCrossRefGoogle Scholar
  38. 38.
    Vydrov OA, Van Voorhis T (2010) J Chem Phys 133:244103PubMedCrossRefPubMedCentralGoogle Scholar
  39. 39.
    Shahbaz M, Szalewicz K (2018) Dispersion energy from local polarizability density (submitted)Google Scholar
  40. 40.
    Thonhauser T, Cooper VR, Li S, Puzder A, Hyldgaard P, Langreth DC (2007) Phys Rev B 76:125112CrossRefGoogle Scholar
  41. 41.
    Berland K, Cooper VR, Lee K, Schröder E, Thonhauser T, Hyldgaard P, Lundqvist BI (2015) Rep Prog Phys 78:066501PubMedCrossRefGoogle Scholar
  42. 42.
    Stone AJ (2013) The theory of intermolecular forces, 2nd edn. Clarendon Press, OxfordCrossRefGoogle Scholar
  43. 43.
    Ángyán JG, Jansen G, Loos M, Hattig C, Hess BA (1994) Chem Phys Lett 219:267CrossRefGoogle Scholar
  44. 44.
    Hättig C, Jansen G, Hess BA, Ángyán JG (1997) Mol Phys 91:145CrossRefGoogle Scholar
  45. 45.
    Rob F, Szalewicz K (2013) Chem Phys Lett 572:146CrossRefGoogle Scholar
  46. 46.
    Rob F, Szalewicz K (2013) Mol Phys 111:1430CrossRefGoogle Scholar
  47. 47.
    Wu Q, Yang W (2002) J Chem Phys 116:515CrossRefGoogle Scholar
  48. 48.
    Grimme S (2004) J Comput Chem 25:1463PubMedCrossRefGoogle Scholar
  49. 49.
    Grimme S (2006) J Comput Chem 27:1787PubMedCrossRefGoogle Scholar
  50. 50.
    Grimme S, Antony J, Elrich S, Krieg H (2010) J Chem Phys 132:154104PubMedCrossRefGoogle Scholar
  51. 51.
    Caldeweyher E, Bannwarth C, Grimme S (2017) J Chem Phys 147:034112PubMedCrossRefGoogle Scholar
  52. 52.
    Pernal K, Podeszwa R, Patkowski K, Szalewicz K (2009) Phys Rev Lett 103:263201PubMedCrossRefGoogle Scholar
  53. 53.
    Podeszwa R, Pernal K, Patkowski K, Szalewicz K (2010) J Phys Chem Lett 1:550CrossRefGoogle Scholar
  54. 54.
    Bucko T, Hafner J, Lebegue S, Ángyán JG (2010) J Phys Chem A 114:11814PubMedCrossRefGoogle Scholar
  55. 55.
    Becke AD, Johnson ER (2005) J Chem Phys 122:154104PubMedCrossRefGoogle Scholar
  56. 56.
    Becke AD, Johnson ER (2005) J Chem Phys 123:154101PubMedCrossRefGoogle Scholar
  57. 57.
    Ángyán JG (2007) J Chem Phys 127:024108PubMedCrossRefGoogle Scholar
  58. 58.
    Tkatchenko A, Scheffler M (2009) Phys Rev Lett 102:073005PubMedCrossRefGoogle Scholar
  59. 59.
    Tkatchenko A, DiStasio RA, Car R, Scheffler M (2012) Phys Rev Lett 108:236402PubMedCrossRefGoogle Scholar
  60. 60.
    Bucko T, Lebegue S, Hafner J, Ángyán JG (2013) Phys Rev B 87:064110CrossRefGoogle Scholar
  61. 61.
    Bucko T, Lebegue S, Hafner J, Ángyán JG (2013) J Chem Theory Comput 9:4293PubMedCrossRefGoogle Scholar
  62. 62.
    Bucko T, Lebegue S, Ángyán JG, Hafner J (2014) J Chem Phys 141:034114PubMedCrossRefGoogle Scholar
  63. 63.
    Bucko T, Lebegue S, Gould T, Ángyán JG (2016) J Phys Condens Matter 28:045201PubMedCrossRefGoogle Scholar
  64. 64.
    Murray ED, Lee K, Langreth DC (2009) J Chem Theory Comput 5:2754PubMedCrossRefGoogle Scholar
  65. 65.
    Austin A, Petersson GA, Frisch MJ, Dobek FJ, Scalmani G, Throssell K (2012) J Chem Theory Comput 8:4989PubMedCrossRefGoogle Scholar
  66. 66.
    Ángyán JG, Gerber IC, Toulouse J, Savin A (2005) Phys Rev A 72:012510CrossRefGoogle Scholar
  67. 67.
    Gerber IC, Ángyán JG (2005) Chem Phys Lett 416:370CrossRefGoogle Scholar
  68. 68.
    Gerber IC, Ángyán JG (2007) J Chem Phys 126:044103PubMedCrossRefGoogle Scholar
  69. 69.
    Toulouse J, Gerber IC, Jansen G, Savin A, Ángyán JG (2009) Phys Rev Lett 102:096404PubMedCrossRefGoogle Scholar
  70. 70.
    Lebegue S, Harl J, Gould T, Ángyán JG, Kresse G, Dobson JF (2010) Phys Rev Lett 105:196401PubMedCrossRefGoogle Scholar
  71. 71.
    Zhu WM, Toulouse J, Savin A, Ángyán JG (2010) J Chem Phys 132:244108PubMedCrossRefGoogle Scholar
  72. 72.
    Toulouse J, Zhu W, Savin A, Jansen G, Ángyán JG (2011) J Chem Phys 135:084119PubMedCrossRefGoogle Scholar
  73. 73.
    Lebegue S, Harl J, Gould T, Ángyán JG, Kresse G, Dobson JF (2012) Phys Rev Lett 105:196401CrossRefGoogle Scholar
  74. 74.
    Ángyán JG, Liu R-F, Toulouse J, Jansen G (2011) J Chem Theory Comput 7:3116PubMedCrossRefGoogle Scholar
  75. 75.
    Mussard B, Szalay PG, Ángyán JG (2014) J Chem Theory Comput 10:1968PubMedCrossRefGoogle Scholar
  76. 76.
    Taylor DC, Ángyán JG, Galli G, Zhang C, Gygi F, Hirao K, Song JW, Rahul K, von Lilienfeld OA, Podeszwa R, Bulik IW, Henderson TM, Scuseria GE, Toulouse J, Truhlar DG, Peverati R, Szalewicz K (2016) J Chem Phys 145:124105PubMedCrossRefGoogle Scholar
  77. 77.
    Claudot J, Kim WJ, Dixit A, Kim H, Gould T, Rocca D, Lebègue S (2018) J Chem Phys 148:064112PubMedCrossRefGoogle Scholar
  78. 78.
    Patkowski K, Szalewicz K, Jeziorski B (2006) J Chem Phys 125:154107PubMedCrossRefGoogle Scholar
  79. 79.
    Patkowski K, Szalewicz K, Jeziorski B (2010) Theor Chem Acc 127:211CrossRefGoogle Scholar
  80. 80.
    Langreth DC, Perdew JP (1975) Solid State Commun 17:1425CrossRefGoogle Scholar
  81. 81.
    Langreth DC, Perdew JP (1977) Phys Rev B 15:2884CrossRefGoogle Scholar
  82. 82.
    Gunnarsson O, Lundqvist BI (1976) Phys Rev B 13:4274CrossRefGoogle Scholar
  83. 83.
    Lindhard J (1954) Kgl Danske Videnskab Selskab Mat-Fys Medd 28(8):1–57Google Scholar
  84. 84.
    Bohr N, Lindhard J (1954) Mat Fys Medd Dan Vid Selsk 28(7):1–31Google Scholar
  85. 85.
    Nozieres P, Pines D (1958) Phys Rev 111:442CrossRefGoogle Scholar
  86. 86.
    Rapcewicz K, Ashcroft N (1991) Phys Rev B 44:4032CrossRefGoogle Scholar
  87. 87.
    Andersson Y, Langreth DC, Lundqvist BI (1996) Phys Rev Lett 76:102PubMedCrossRefGoogle Scholar
  88. 88.
    Lundqvist BI, Andersson Y, Shao H, Chan S, Langreth D (1995) Int J Quantum Chem 56:247CrossRefGoogle Scholar
  89. 89.
    Hult E, Andersson Y, Lundqvist BI, Langreth DC (1996) Phys Rev Lett 77:2029PubMedCrossRefGoogle Scholar
  90. 90.
    Dobson JF, Dinte BP (1996) Phys Rev Lett 76:1780PubMedCrossRefGoogle Scholar
  91. 91.
    Andersson Y, Hult E, Apell P, Langreth DC, Lundqvist BI (1998) Solid Stat Commun 106:235CrossRefGoogle Scholar
  92. 92.
    Andersson Y, Rydberg H (1999) Phys Scr 60:211CrossRefGoogle Scholar
  93. 93.
    Vydrov OA, Van Voorhis T (2009) J Chem Phys 130:104105PubMedCrossRefGoogle Scholar
  94. 94.
    Zhang Y, Yang W (1998) Phys Rev Lett 80:890CrossRefGoogle Scholar
  95. 95.
    Cooper VR, Kong L, Langreth DC (2010) Phys Proc 3:1417CrossRefGoogle Scholar
  96. 96.
    Berland K, Hyldgaard P (2014) Phys Rev B 89:035412CrossRefGoogle Scholar
  97. 97.
    Berland K, Arter CA, Cooper VR, Lee K, Lundqvist BI, Schröder E, Thonhauser T, Hyldgaard P (2014) J Chem Phys 140:18A539PubMedCrossRefGoogle Scholar
  98. 98.
    Hamada I (2014) Phys Rev B 89:121103CrossRefGoogle Scholar
  99. 99.
    Tang KT, Toennies JP (1984) J Chem Phys 80:3726CrossRefGoogle Scholar
  100. 100.
    Langreth DC, Lundqvist BI (2010) Phys Rev Lett 104:099303PubMedCrossRefGoogle Scholar
  101. 101.
    Hepburn J, Scoles G, Penco R (1975) Chem Phys Lett 36:451CrossRefGoogle Scholar
  102. 102.
    Gianturco FA, Paesani F, Laranjeira MF, Vassilenko V, Cunha MA, Shashkov AG, Zolotoukhina AF (1998) Mol Phys 94:605CrossRefGoogle Scholar
  103. 103.
    Wu X, Vargas MC, Nayak S, Lotrich VL, Scoles G (2001) J Chem Phys 115:8748CrossRefGoogle Scholar
  104. 104.
    Grimme S, Ehrlich S, Goerigk L (2011) J Comput Chem 32:1456PubMedCrossRefGoogle Scholar
  105. 105.
    Smith DG, Burns LA, Patkowski K, Sherrill CD (2016) J Phys Chem Lett 7:2197PubMedCrossRefGoogle Scholar
  106. 106.
    Salem L (1960) Mol Phys 3:441CrossRefGoogle Scholar
  107. 107.
    Tang KT, Karplus M (1968) Phys Rev 171:70CrossRefGoogle Scholar
  108. 108.
    Hirshfeld FL (1977) Theor Chim Acta 44:129CrossRefGoogle Scholar
  109. 109.
    Otero-De-La-Roza A, Johnson ER (2013) J Chem Phys 138:204109PubMedCrossRefGoogle Scholar
  110. 110.
    Donchev A (2006) J Chem Phys 125:074713PubMedCrossRefGoogle Scholar
  111. 111.
    Whitfield TW, Martyna GJ (2006) Chem Phys Lett 424:409CrossRefGoogle Scholar
  112. 112.
    Jones A, Thompson A, Crain J, Müser MH, Martyna GJ (2009) Phys Rev B 79:144119CrossRefGoogle Scholar
  113. 113.
    Szalewicz K, Bukowski R, Jeziorski B (2005) In: Dykstra CE, Frenking G, Kim KS, Scuseria GE (eds) Theory and applications of computational chemistry: the first fourty years, Chap 33. Elsevier, Amsterdam, pp 919–962CrossRefGoogle Scholar
  114. 114.
    Jankiewicz W, Podeszwa R, Witek HA (2018) J Chem Theory Comput 14:5079PubMedCrossRefGoogle Scholar
  115. 115.
    Dunning TH Jr (1989) J Chem Phys 90:1007CrossRefGoogle Scholar
  116. 116.
    Kendall RA, Dunning TH Jr, Harrison RJ (1992) J Chem Phys 96:6796CrossRefGoogle Scholar
  117. 117.
    Woon DE, Dunning TH Jr (1993) J Chem Phys 98:1358CrossRefGoogle Scholar
  118. 118.
    Williams HL, Mas EM, Szalewicz K, Jeziorski B (1995) J Chem Phys 103:7374CrossRefGoogle Scholar
  119. 119.
    Shao Y, Molnar LF, Jung Y, Kussmann J, Ochsenfeld C, Brown ST, Gilbert AT, Slipchenko LV, Levchenko SV et al. (2006) Phys Chem Chem Phys 8:3172PubMedCrossRefGoogle Scholar
  120. 120.
    Neese F (2012) Wiley Interdiscip Rev Comput Mol Sci 2:73CrossRefGoogle Scholar
  121. 121.
    Rohrdanz MA, Martins KM, Herbert JM (2009) J Chem Phys 130:054112PubMedCrossRefGoogle Scholar
  122. 122.
    Modrzejewski M, Chalasinski G, Szczesniak MM (2014) J Chem Theory Comput 10:4297PubMedCrossRefGoogle Scholar
  123. 123.
    Valiev M, Bylaska EJ, Govind N, Kowalski K, Straatsma TP, Van Dam HJ, Wang D, Nieplocha J, Apra E, Windus TL et al (2010) Comput Phys Commun 181:1477CrossRefGoogle Scholar
  124. 124.
    Perdew JP, Yue W (1986) Phys Rev B 33:8800CrossRefGoogle Scholar

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© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Department of Physics and AstronomyUniversity of DelawareNewarkUSA

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