A benchmark for the non-covalent interaction (NCI) index or… is it really all in the geometry?

  • Julia Contreras-GarcíaEmail author
  • Roberto A. Boto
  • Fernando Izquierdo-Ruiz
  • Igor Reva
  • Tatiana Woller
  • Mercedes Alonso
Regular Article
Part of the following topical collections:
  1. Festschrift in honour of A. Vela


Describing non-covalent interactions (NCIs) has shown to be of paramount importance in many areas of theoretical chemistry and related disciplines, such as biochemistry and material science. However, non-covalent interactions are subtle effects, very difficult to reproduce from most common computational approaches. Electron density studies have shown to provide a good semiquantitative visual approach to such interactions, which are much less prone to method dependency. But to which extent? This is the question addressed in this contribution. The NCI approach based on the reduced density gradient is given the third degree so as to provide the user with a benchmark on how it is affected by the computational method and the basis set of choice. We have assessed the dependence of the NCI results on the geometry. This last question is addressed in detail to dissect how, why and when the NCI method can be used to understand dispersion interactions. Along various examples, we will show that the NCI index is very little dependent on the method and basis set used in the calculation of the electron density as long as the geometry is kept fixed. Indeed, the biggest variations in NCI come from changes in the geometry. Thus, methods which provide descriptions of a given interaction type of different accuracies will yield different electron density organizations. This gives no qualitative variations in the NCI 3D picture. But it is reflected in quantitative NCI measures even in very subtle cases. Moreover, in the case of a failure of the calculation method, NCI can also reveal the sources of its error. NCI volumes are able to locate the energetic ordering in various conformational situations, but always in a relative manner. Absolute values should not be used in comparisons, nor between compounds that do not belong to the same family.


Non-covalent interactions Benchmark NCI Electron density 



We want to thank Prof. Rzepa for useful discussions and his always present metadata which make research so much easier. This work was supported partially by the framework of CALSIMLAB under the public Grant ANR-11-LABX-0037-01 overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (Reference: ANR-11-IDEX-0004-02). FIR thanks to FPU program from MECD for a Ph.D. Grant and financial support from Spanish Ministerio de Economia y Competitividad and FEDER programs under Projects No. CTQ2012-35899-C02 and No. CTQ2015-67755-C2. M. A. thanks the Fund for Scientific Research−Flanders (FWO-12F4416N) for a postdoctoral fellowship and the Free University of Brussels (VUB) for financial support. The Coimbra Chemistry Centre (CQC) is supported by the Portuguese Fundação para a Ciência e a Tecnologia (FCT), through the Project UI0313/QUI/2013, co-funded by COMPETE-UE. I. R. acknowledges FCT for the Investigador FCT Grant.

Supplementary material

214_2016_1977_MOESM1_ESM.pdf (2.4 mb)
Supplementary material 1 (pdf 2503 KB)


  1. 1.
    Hobza P, Rezac J (2016) Chem Rev 116:4911CrossRefGoogle Scholar
  2. 2.
    Umadevi D, Panigrahi S, Sastry GN (2014) Chem Res 47:2574CrossRefGoogle Scholar
  3. 3.
    Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, OxfordGoogle Scholar
  4. 4.
    Silvi B, Savin A (1994) Nature 371:683CrossRefGoogle Scholar
  5. 5.
    Johnson ER, Keinan S, Mori-Sánchez P, Contreras-García J, Cohen AJ, Yang W (2010) J Am Chem Soc 132:6498CrossRefGoogle Scholar
  6. 6.
    Andres J, Berski S, Contreras-García J, Gonzalez-Navarrete P (2014) J Phys Chem 118:1663CrossRefGoogle Scholar
  7. 7.
    Boto RA, Contreras-García J, Tierny J, Piquemal JP (2015) Mol Phys 114:1Google Scholar
  8. 8.
    Lane JR, Contreras-García J, Piquemal JP, Miller BJ, Kjaergaard HG (2013) J Chem Theory Comput 9:3263CrossRefGoogle Scholar
  9. 9.
    Boto RA, Guenther D, Contreras-García J, Piquemal JP, Tierny J (2014) IEEE Trans Vis Comput Graph 20:2476CrossRefGoogle Scholar
  10. 10.
    Hunter G (1986) Phys Rev Lett 29:197Google Scholar
  11. 11.
    Sagar RP, Ku A, Vedene H (1988) Can J Chem 66:1005CrossRefGoogle Scholar
  12. 12.
    Contreras-García J, Johnson ER, Yang W (2011) J Phys Chem A 115:12983CrossRefGoogle Scholar
  13. 13.
    Gráfová L, Pitoňák M, Řezáč J, Hobza P (2010) J Chem Theory Comput 6:2365CrossRefGoogle Scholar
  14. 14.
    Frisch MJ, Trucks GW, Schlegel HB, Scuseria GE, Robb MA, Cheeseman JR, Scalmani G, Barone V, Mennucci B, Petersson GA, Nakatsuji H, Caricato M, Li X, Hratchian HP, Izmaylov AF, Bloino J, Zheng G, Sonnenberg JL, Hada M, Ehara M, Toyota K, Fukuda R, Hasegawa J, Ishida M, Nakajima T, Honda Y, Kitao O, Nakai H, Vreven T, Jr. Montgomery JA, Peralta JE, Ogliaro F, Bearpark M, Heyd JJ, Brothers E, Kudin KN, Staroverov VN, Kobayashi R, Normand J, Raghavachari K, Rendell A, Burant JC, Iyengar SS, Tomasi J, Cossi M, Rega N, Millam JM, Klene M, Knox JE, Cross JB, Bakken V, Adamo C, Jaramillo J, Gomperts R, Stratmann RE, Yazyev O, Austin AJ, Cammi R, Pomelli C, Ochterski JW, Martin RL, Morokuma K, Zakrzewski VG, Voth GA, Salvador P, Dannenberg JJ, Dapprich S, Daniels AD, Farkas Ö, Foresman JB, Ortiz JV, Cioslowski J, Fox DJ (2010) Gaussian 09. Gaussian Inc, Wallingford. Revision B. 01Google Scholar
  15. 15.
    Becke AD (1993) J Chem Phys 98:5648CrossRefGoogle Scholar
  16. 16.
    Lee C, Yang W, Parr RG (1998) Phys Rev B 37:785CrossRefGoogle Scholar
  17. 17.
    Grimme S (2006) J Comput Chem 27:1787CrossRefGoogle Scholar
  18. 18.
    Cohen A, Mori P, Yang W (2012) Chem Rev 112:289CrossRefGoogle Scholar
  19. 19.
    Izquierdo-Ruiz F, Otero-de-la-Roza A, Contreras-García J, Menéndez JM, Prieto-Ballesteros O, Recio JM (2015) High Press Res 35:49CrossRefGoogle Scholar
  20. 20.
    Giannozzi P, Baroni S, Bonini N, Calandra M, Car R, Cavazzoni C, Ceresoli D, Chiarotti GL, Cococcioni M, Dabo I, Dal Corso A, de Gironcoli S, Fabris S, Fratesi G, Gebauer R, Gerstmann U, Gougoussis C, Kokalj A, Lazzeri M, Martin-Samos L, Marzari N, Mauri F, Mazzarello R, Paolini S, Pasquarello A, Paulatto L, Sbraccia C, Scandolo S, Sclauzero G, Seitsonen AP, Smogunov A, Umari P, Wentzcovitch RM (2009) QUANTUM ESPRESSO: a modular and open-source software project for quantum simulations of materials. J Phys Condens Matter 21:395502/1-19CrossRefGoogle Scholar
  21. 21.
    Becke AD, Johnson ER (2007) J Chem Phys 127:154108CrossRefGoogle Scholar
  22. 22.
    Otero-de-la-Roza A, Johnson ER (2012) J Chem Phys 136:174109CrossRefGoogle Scholar
  23. 23.
    Kresse G, Joubert D (1999) Phys Rev B 59:1758CrossRefGoogle Scholar
  24. 24.
    Monkhorst HJ, Pack JD (1976) Phys Rev B 13:5188CrossRefGoogle Scholar
  25. 25.
    Fletcher R (1980) Practical methods of optimization. Wiley, New YorkGoogle Scholar
  26. 26.
    Zhao Y, Truhlar DG (2008) Theor Chem Acc 120:215CrossRefGoogle Scholar
  27. 27.
    Armstrong A, Boto RA, Dingwall P, Contreras-García J, Harvey MJ, Mason N, Rzepa HS (2014) Chem Sci 5:2057CrossRefGoogle Scholar
  28. 28.
    Grimme S, Ehrlich S, Goerigk L (2011) J Comput Chem 32:1456CrossRefGoogle Scholar
  29. 29.
    Rzepa HS, Harvey MS, Mason N (2014) Digital data repositories in chemistry and their integration with journals and electronic laboratory notebooks. Am Chem Soc 54:2627Google Scholar
  30. 30.
    Contreras-García J, Johnson ER, Keinan S, Chaudret R, Piquemal J-P, Beratan DN, Yang W (2011) J Chem Theory Comput 7:625CrossRefGoogle Scholar
  31. 31.
    Boto RA, Contreras-García J, Tierny J, Piquemal JP (to be submitted)Google Scholar
  32. 32.
    Martín Pendás A, Francisco E (available upon request)Google Scholar
  33. 33.
    Otero-de-la-Roza A, Johnson ER, Luaña V (2014) Comput Phys Commun 185:1007CrossRefGoogle Scholar
  34. 34.
    Otero-de-la-Roza A, Contreras-García J, Johnson ER (2012) Phys Chem Chem Phys 14:12165CrossRefGoogle Scholar
  35. 35.
    Humphrey W, Dalke A, Schulten K (1996) J Mol Graph 14:33CrossRefGoogle Scholar
  36. 36.
    Jabłoński M, Palusiak M (2010) J Phys Chem A 114:2240CrossRefGoogle Scholar
  37. 37.
    Jabłoński M, Palusiak M (2010) J Phys Chem A 114:12498CrossRefGoogle Scholar
  38. 38.
    Cohen AJ, Mori-Sánchez P, Yang W (2008) Phys Rev B 77:115123CrossRefGoogle Scholar
  39. 39.
    Mori-Sánchez P, Cohen AJ, Yang W (2008) Phys Rev Lett 100:146401CrossRefGoogle Scholar
  40. 40.
    Spackman MA, Maslen EN (1986) J Phys Chem 90:2020CrossRefGoogle Scholar
  41. 41.
    Pendás AM, Luaña V, Pueyo L, Francisco E, Mori-Sánchez P (2002) J Chem Phys 117:1017CrossRefGoogle Scholar
  42. 42.
    Fiedler S, Broecker J, Keller S (2010) Cell Mol Life Sci 67:1779CrossRefGoogle Scholar
  43. 43.
    Alonso M, Woller T, Martin-Martinez FJ, Contreras-García J, Geerlings P, De Proft F (2014) Chem Eur J 20:4931CrossRefGoogle Scholar
  44. 44.
    Contreras-García J, Calatayud M, Piquemal J-P, Recio JM (2012) Comput Theor Chem 998:193CrossRefGoogle Scholar
  45. 45.
    Gatti C (2005) Z Kristallogr 220:399Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2016

Authors and Affiliations

  • Julia Contreras-García
    • 1
    Email author
  • Roberto A. Boto
    • 1
    • 2
  • Fernando Izquierdo-Ruiz
    • 3
  • Igor Reva
    • 4
  • Tatiana Woller
    • 5
  • Mercedes Alonso
    • 5
  1. 1.UMR 7616, Laboratoire de Chimie ThéoriqueSorbonne Universités, UPMC Univ Paris 06 & CNRSParisFrance
  2. 2.ICSSorbonne Universités, UPMC Univ Paris 06ParisFrance
  3. 3.Departamento de Química Física y AnalíticaUniversidad de OviedoOviedoSpain
  4. 4.CQC, Department of ChemistryUniversity of CoimbraCoimbraPortugal
  5. 5.ALGC Research Group General Chemistry (ALGC)Vrije Universiteit Brussel (VUB)BrusselsBelgium

Personalised recommendations