Skip to main content

Thank you for visiting nature.com. You are using a browser version with limited support for CSS. To obtain the best experience, we recommend you use a more up to date browser (or turn off compatibility mode in Internet Explorer). In the meantime, to ensure continued support, we are displaying the site without styles and JavaScript.

Understanding chemical reactivity using the activation strain model

Nature Protocols volume 15, pages 649–667 (2020)Cite this article

Subjects

Abstract

Understanding chemical reactivity through the use of state-of-the-art computational techniques enables chemists to both predict reactivity and rationally design novel reactions. This protocol aims to provide chemists with the tools to implement a powerful and robust method for analyzing and understanding any chemical reaction using PyFrag 2019. The approach is based on the so-called activation strain model (ASM) of reactivity, which relates the relative energy of a molecular system to the sum of the energies required to distort the reactants into the geometries required to react plus the strength of their mutual interactions. Other available methods analyze only a stationary point on the potential energy surface, but our methodology analyzes the change in energy along a reaction coordinate. The use of this methodology has been proven to be critical to the understanding of reactions, spanning the realms of the inorganic and organic, as well as the supramolecular and biochemical, fields. This protocol provides step-by-step instructions—starting from the optimization of the stationary points and extending through calculation of the potential energy surface and analysis of the trend-decisive energy terms—that can serve as a guide for carrying out the analysis of any given reaction of interest within hours to days, depending on the size of the molecular system.

This is a preview of subscription content, access via your institution

Access options

Rent or buy this article

Get just this article for as long as you need it

$39.95

Learn more

Prices may be subject to local taxes which are calculated during checkout

Fig. 1: General workflow of the procedure.
Fig. 2: Examples of systems for which the ASM has been successfully applied.
Fig. 3: Activation strain diagram.
Fig. 4: Analysis of the oxidative insertion of palladium into the C–Cl bond of chloromethane.
Fig. 5: Comparison of the strain-promoted azide–alkyne cycloaddition reactivity between methyl azide and two different cycloalkynes.

Data availability

The data that support this study are available from the corresponding author upon reasonable request.

Code availability

The open-source PyFrag 2019 code that was used to generate all the data shown in the protocol can be found at https://github.com/sunxb05/PyFrag.

References

  1. Albright, T. A., Burdett, J. K. & Wangbo, W. H. Orbital Interactions in Chemistry 2nd edn (Wiley, New York, 2013).

  2. Piela, L. Ideas of Quantum Chemistry 2nd edn (Elsevier, Amsterdam, 2013).

  3. Becke, A. D. Perspective: fifty years of density-functional theory in chemical physics. J. Chem. Phys. 140, 18A301 (2014).

    Article  PubMed  CAS  Google Scholar 

  4. Goerigk, L. & Grimme, S. Efficient and accurate double-hybrid-meta-GGA density functionals—evaluation with the extended GMTKN30 database for general main group thermochemistry, kinetics, and noncovalent interactions. J. Chem. Theory Comput. 7, 291–309 (2011).

    Article  CAS  PubMed  Google Scholar 

  5. Zhao, Y. & Truhlar, D. G. The M06 suite of density functionals for main group thermochemistry, thermochemical kinetics, noncovalent interactions, excited states, and transition elements: two new functionals and systematic testing of four M06-class functionals and 12 other functionals. Theor. Chem. Acc. 120, 215–241 (2008).

    Article  CAS  Google Scholar 

  6. Perdew, J. P. & Constantin, L. A. Laplacian-level density functionals for the kinetic energy density and exchange-correlation energy. Phys. Rev. B. 75, 155109 (2007).

    Article  CAS  Google Scholar 

  7. Becke, A. D. Density functionals for static, dynamical, and strong correlation. J. Chem. Phys. 138, 074109 (2013).

    Article  PubMed  CAS  Google Scholar 

  8. Zhao, Y., Schultz, N. E. & Truhlar, D. G. Exchange-correlation functional with broad accuracy for metallic and nonmetallic compounds, kinetics, and noncovalent interactions. J. Chem. Phys. 123, 16110 (2005).

    Google Scholar 

  9. Zhao, Y. & Truhlar, D. G. Density functionals with broad applicability in chemistry. Acc. Chem. Res. 41, 157–167 (2008).

    Article  CAS  PubMed  Google Scholar 

  10. Hoffmann, R. Building bridges between inorganic and organic chemistry. Angew. Chem. Int. Ed. Engl. 21, 711–724 (1982). Angew. Chem. 94, 725–739 (1982)..

    Article  Google Scholar 

  11. Fukui, K. The role of frontier molecular orbitals in chemical reactions. Angew. Chem. Int. Ed. Engl. 21, 801–809 (1982). Angew. Chem. 94, 852–861 (1982).

    Article  Google Scholar 

  12. Marcus, R. A. On the theory of oxidation-reduction reactions involving electron transfer. I. J. Chem. Phys. 24, 966–978 (1956).

    Article  CAS  Google Scholar 

  13. Marcus, R. A. Electrostatic free energy and other properties of states having nonequilibrium polarization. I. J. Chem. Phys. 24, 979–989 (1956).

    Article  CAS  Google Scholar 

  14. Pross, A. & Shaik, S. S. A qualitative valence-bond approach to organic reactivity. Acc. Chem. Res. 16, 363–370 (1983).

    Article  CAS  Google Scholar 

  15. Usharani, D., Janardanan, D., Li, C. & Shaik, S. A theory for bioinorganic chemical reactivity of oxometal complexes and analogous oxidants: the exchange and orbital-selection rules. Acc. Chem. Res. 46, 471–482 (2013).

    Article  CAS  PubMed  Google Scholar 

  16. Bickelhaupt, F. M. Understanding reactivity with Kohn-Sham molecular orbital theory: E2-SN2 mechanistic spectrum and other concepts. J. Comput. Chem. 20, 114–128 (1999).

    Article  CAS  Google Scholar 

  17. Bickelhaupt, F. M. & Houk, K. N. Analyzing reaction rates with the distortion/interaction-activation strain model. Angew. Chem. Int. Ed. 56, 10070–10086 (2017). Angew. Chem. 129, 10204–10221 (2017).

    Article  CAS  Google Scholar 

  18. Wolters, L. P. & Bickelhaupt, F. M. The activation strain model and molecular orbital theory. WIREs Comput. Mol. Sci. 5, 324–343 (2015).

    Article  CAS  Google Scholar 

  19. Fernández, I. & Bickelhaupt, F. M. The activation strain model and molecular orbital theory: understanding and designing chemical reactions. Chem. Soc. Rev. 43, 4953–4967 (2014).

    Article  PubMed  Google Scholar 

  20. ADF, SCM, Theoretical Chemistry, Vrije Universiteit, Amsterdam, The Netherlands, http://www.scm.com

  21. te Velde, G. et al. Chemistry with ADF. J. Comput. Chem. 22, 931–967 (2001).

    Article  Google Scholar 

  22. Bickelhaupt, F. M. & Baerends, E. J. Kohn-Sham density functional theory: predicting and understanding chemistry. In Reviews in Computational Chemistry, Vol. 15 (eds Lipkowitz, K. B. & Boyd, D. B) 1-86. (Wiley-Blackwell, Hoboken, NJ, 2000)

  23. Sun, X., Soini, T. M., Poater, J., Hamlin, T. A. & Bickelhaupt, F. M. Pyfrag 2019–automating the exploration and analysis of reaction mechanisms. J. Comput. Chem. 40, 2227–2233 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  24. Sun, X., Soini, T. M., Poater, J., Hamlin, T. A. & Bickelhaupt F. M. PyFrag 2019 [tutorial], (https://pyfragdocument.readthedocs.io/en/latest/includeme.html).

  25. Fonseca Guerra, C., Handgraaf, J.-W., Baerends, E. J. & Bickelhaupt, F. M. Voronoi deformation density (VDD) charges. Assessment of the Mulliken, Bader, Hirshfeld, Weinhold and VDD methods for charge analysis. J. Comput. Chem. 25, 189–210 (2004).

    Article  PubMed  CAS  Google Scholar 

  26. Hirshfeld, F. L. Bonded-atom fragments for describing molecular charge densities. Theor. Chim. Acta 44, 129–138 (1977).

    Article  CAS  Google Scholar 

  27. Swart, M., van Duijnen, P. Th & Snijders, J. G. A charge analysis derived from an atomic multipole expansion. J. Comput. Chem. 22, 79–88 (2001).

    Article  CAS  Google Scholar 

  28. Cabrera-Trujillo, J. J. & Fernández, I. Influence of the Lewis acid/base pairs on the reactivity of geminal E-CH2–Eʹ frustrated Lewis pairs. Chem. Eur. J. 24, 17823–17831 (2018).

    Article  CAS  PubMed  Google Scholar 

  29. García-Rodeja, Y., Solà, M. & Fernández, I. Understanding the reactivity of planar polycyclic aromatic hydrocarbons: towards the graphene limit. Chem. Eur. J. 22, 10572–10580 (2016).

    Article  PubMed  CAS  Google Scholar 

  30. García-Rodeja, Y., Solà, M. & Fernández, I. Influence of the charge on the reactivity of azafullerenes. Phys. Chem. Chem. Phys. 20, 28011–28018 (2018).

    Article  PubMed  Google Scholar 

  31. García-Rodeja, Y. & Fernández, I. Factors controlling the reactivity of strained-alkyne embedded cycloparaphenylenes. J. Org. Chem. 84, 4330–4337 (2019).

    Article  PubMed  CAS  Google Scholar 

  32. Larrañaga, O. & de Cózar, A. Effect of an α-methyl substituent on the dienophile on Diels‐Alder endo:exo selectivity. ChemistryOpen 8, 49–57 (2019).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  33. Jin, R., Liu, S. & Lan, Y. Distortion–interaction analysis along the reaction pathway to reveal the reactivity of the Alder-ene reaction of enes. RSC Adv. 5, 61426–61435 (2015).

    Article  CAS  Google Scholar 

  34. Liu, S., Lei, Y., Qi, X. & Lan, Y. Reactivity for the Diels–Alder reaction of cumulenes: a distortion-interaction analysis along the reaction pathway. J. Phys. Chem. A 118, 2638–2645 (2014).

    Article  CAS  PubMed  Google Scholar 

  35. Galabov, B., Koleva, G., Schaefer, H. F. III & Allen, W. D. Nucleophilic influences and origin of the SN2 allylic effect. Chem. Eur. J. 24, 11637–11648 (2018).

    Article  CAS  PubMed  Google Scholar 

  36. Fell, J. S., Martin, B. N. & Houk, K. N. Origins of the unfavorable activation and reaction energies of 1-azadiene heterocycles compared to 2-azadiene heterocycles in Diels-Alder reactions. J. Org. Chem. 82, 1912–1919 (2017).

    Article  CAS  PubMed  Google Scholar 

  37. Champagne, P. A. & Houk, K. N. Influence of endo- and exocyclic heteroatoms on stabilities and 1,3-dipolar cycloaddition reactivities of mesoionic azomethine ylides and imines. J. Org. Chem. 82, 10980–10988 (2017).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  38. Svatunek, D. & Houk, K. N. autoDIAS: a Python tool for an automated distortion/interaction activation strain analysis. J. Comput. Chem. 40, 2509–2515 (2019).

    Article  CAS  PubMed  Google Scholar 

  39. Laloo, J. Z. A., Savoo, N., Laloo, N., Rhyman, L. & Ramasami, P. ExcelAutomat 1.3: fragment analysis based on the distortion/interaction-activation strain model. J. Comput. Chem. 40, 619–624 (2019).

    Article  CAS  PubMed  Google Scholar 

  40. Liu, Y., Su, B., Dong, W., Li, Z. H. & Wang, H. Structural characterization of a boron (III) η2-σ-silane-complex. J. Am. Chem. Soc. 141, 8358–8363 (2019).

    Article  CAS  PubMed  Google Scholar 

  41. Sun, X., Rocha, M. V. J., Hamlin, T. A., Poater, J. & Bickelhaupt, F. M. Understanding the differences between iron and palladium in cross-coupling reactions. Phys. Chem. Chem. Phys. 21, 9651–9664 (2019).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  42. Hong, X., Chan, K., Tsai, C. & Nørskov, J. K. How doped MoS2 breaks transition-metal scaling relations for CO2 electrochemical reduction. ACS Catal. 6, 4428–4437 (2016).

    Article  CAS  Google Scholar 

  43. Vermeeren, P., Sun, X. & Bickelhaupt, F. M. Arylic C–X bond activation by palladium catalysts: activation-strain analyses of reactivity trends. Sci. Rep. 8, 10729 (2018).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  44. Hamlin, T. A., Levandowski, B. J., Narsaria, A. K., Houk, K. N. & Bickelhaupt, F. M. Structural distortion of cycloalkynes influences cycloaddition rates both by strain and interaction energies. Chem. Eur. J. 25, 6342–6348 (2019).

    Article  CAS  PubMed  Google Scholar 

  45. Hamlin, T. A., Fernández, I. & Bickelhaupt, F. M. How dihalogens catalyze Michael addition reactions. Angew. Chem. Int. Ed. 58, 8922–8926 (2019). Angew. Chem. 131, 9015-9020 (2019).

    Article  CAS  Google Scholar 

  46. van der Lubbe, S. C. C. & Fonseca Guerra, C. Hydrogen-bond strength of CC and GG pairs determined by steric repulsion: electrostatics and charge transfer overruled. Chem. Eur. J. 23, 10249–10253 (2017).

    Article  PubMed  CAS  Google Scholar 

  47. van der Lubbe, S. C. C., Zaccaria, F., Sun, X. & Fonseca Guerra, C. Secondary electrostatic interaction model revised: prediction comes mainly from measuring charge accumulation in hydrogen-bonded monomers. J. Am. Chem. Soc. 141, 4878–4885 (2019).

    Article  PubMed  PubMed Central  CAS  Google Scholar 

  48. Hamlin, T. A., van Beek, B., Wolters, L. P. & Bickelhaupt, F. M. Nucleophilic substitution in solution: activation strain analysis of weak and strong solvent effects. Chem. Eur. J. 24, 5927–5938 (2018).

    Article  CAS  PubMed  Google Scholar 

  49. Laloo, J. Z. A., Rhyman, L., Ramasami, P., Bickelhaupt, F. M. & de Cózar, A. Ion-pair SN2 substitution: activation strain analyses of counter-ion and solvent effect. Chem. Eur. J. 22, 4431–4439 (2016).

    Article  CAS  PubMed  Google Scholar 

  50. Zaccaria, F., Paragi, G. & Fonseca Guerra, C. The role of alkali metal cations in the stabilization of guanine quadruplexes: why K+ is the best. Phys. Chem. Chem. Phys. 18, 20895–20904 (2016).

    Article  CAS  PubMed  Google Scholar 

  51. Zaccaria, F. & Fonseca Guerra, C. RNA versus DNA G-quadruplex: the origin of increased stability. Chem. Eur. J. 24, 16315–16322 (2018).

    Article  CAS  PubMed  Google Scholar 

  52. Pollice, R., Bot, M., Kobylianskii, I. J., Shenderovich, I. & Chen, P. Attenuation of London dispersion in dichloromethane solutions. J. Am. Chem. Soc. 139, 13126–13140 (2017).

    Article  CAS  PubMed  Google Scholar 

  53. Ess, D. H. & Houk, H. K. Distortion/interaction energy control of 1,3-dipolar cycloaddition reactivity. J. Am. Chem. Soc. 129, 10646–10647 (2007).

    Article  CAS  PubMed  Google Scholar 

  54. Ess, D. H. & Houk, H. K. Theory of 1,3-dipolar cycloadditions: distortion/interaction and frontier molecular orbital models. J. Am. Chem. Soc. 130, 10187–10198 (2008).

    Article  CAS  PubMed  Google Scholar 

  55. Hamlin, T. A. et al. Elucidating the trends in reactivity of aza-1,3-dipolar cycloadditions. Eur. J. Org. Chem. 2019, 378–386 (2019).

    Article  CAS  Google Scholar 

  56. de Jong, G. Th, Solà, M., Visscher, L. & Bickelhaupt, F. M. Ab initio benchmark study for the oxidative addition of CH4 to Pd: importance of basis-set flexibility and polarization. J. Chem. Phys. 121, 9982–9992 (2004).

    Article  PubMed  CAS  Google Scholar 

  57. de Jong, G. Th, Geerke, D. P., Diefenbach, A. & Bickelhaupt, F. M. DFT benchmark study for the oxidative addition of CH4 to Pd. Performance of various density functionals. Chem. Phys. 313, 261–270 (2005).

    Article  CAS  Google Scholar 

  58. de Jong, G. Th, Geerke, D. P., Diefenbach, A., Solà, M. & Bickelhaupt, F. M. Oxidative addition of the ethane C–C bond to Pd. An ab initio benchmark and DFT validation study. J. Comput. Chem. 26, 1006–1020 (2005).

    Article  PubMed  CAS  Google Scholar 

  59. de Jong, G. Th & Bickelhaupt, F. M. Oxidative addition of fluoromethane C–F bond to Pd. An ab initio benchmark and DFT validation study. J. Phys. Chem. A. 109, 9685–9699 (2005).

    Article  PubMed  CAS  Google Scholar 

  60. de Jong, G. Th & Bickelhaupt, F. M. Oxidative addition of the chloromethane C–Cl bond to Pd, an ab initio benchmark and DFT validation. J. Chem. Theory Comput. 2, 322–335 (2006).

    Article  PubMed  CAS  Google Scholar 

  61. Grimme, S., Antony, J., Ehrlich, S. & Krieg, H. A consistent and accurate ab initio parametrization of density functional dispersion correction (DFT-D) for the 94 elements H-Pu. J. Chem. Phys. 132, 154104 (2010).

    Article  PubMed  CAS  Google Scholar 

  62. Johnson, E. R. & Becke, A. D. A post-Hartree-Fock model of intermolecular interactions. J. Chem. Phys. 123, 024101 (2005).

    Article  CAS  Google Scholar 

  63. Grimme, S., Ehrlich, S. & Goerigk, L. Effect of the damping function in dispersion corrected density functional theory. J. Comput. Chem. 32, 1456–1465 (2011).

    Article  CAS  PubMed  Google Scholar 

  64. Bento, A. P., Solà, M. & Bickelhaupt, F. M. Ab initio and DFT benchmark study for nucleophilic substitution at carbon (SN2@C) and silicon (SN2@Si). J. Comput. Chem. 26, 1497–1504 (2005).

    Article  CAS  PubMed  Google Scholar 

  65. Bento, A. P., Solà, M. & Bickelhaupt, F. M. E2 and SN2 reactions of X– + CH3CH2X (X = F, Cl). An ab initio and DFT benchmark study. J. Chem. Theory Comput. 4, 929–940 (2008).

    Article  CAS  PubMed  Google Scholar 

  66. Pieniazek, S. N., Clemente, F. R. & Houk, K. N. Sources of error in DFT computations of C–C bond formation thermochemistries: π→σ transformations and error cancellation by DFT methods. Angew. Chem. Int. Ed. 47, 7746–7749 (2008). Angew. Chem. 120, 7860-7863 (2008).

    Article  CAS  Google Scholar 

  67. Bannwarth, C., Ehlert, S. & Grimme, S. GFN2-xTB—an accurate and broadly parametrized self-consistent tight-binding quantum chemical method with multipole electrostatics and density-dependent dispersion contributions. J. Chem. Theory Comput. 15, 1652–1671 (2019).

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

We thank the Netherlands Organization for Scientific Research (NWO) and the Dutch Astrochemistry Network (DAN) for financial support. Furthermore, we thank X. Sun for fruitful discussions and for testing of the complete protocol.

Author information

Authors and Affiliations

  1. Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, Vrije Universiteit Amsterdam, Amsterdam, The Netherlands

    Pascal Vermeeren, Stephanie C. C. van der Lubbe, Célia Fonseca Guerra, F. Matthias Bickelhaupt & Trevor A. Hamlin

  2. Leiden Institute of Chemistry, Gorlaeus Laboratories, Leiden University, Leiden, The Netherlands

    Célia Fonseca Guerra

  3. Institute for Molecules and Materials, Radboud University Nijmegen, Nijmegen, The Netherlands

    F. Matthias Bickelhaupt

Authors
  1. Pascal Vermeeren
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Stephanie C. C. van der Lubbe
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Célia Fonseca Guerra
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. F. Matthias Bickelhaupt
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Trevor A. Hamlin
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

P.V., S.C.C.v.d.L., and T.A.H. participated in the design of the protocol. P.V., S.C.C.v.d.L., C.F.G., F.M.B., and T.A.H. wrote the manuscript.

Corresponding authors

Correspondence to F. Matthias Bickelhaupt or Trevor A. Hamlin.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

Peer review information Nature Protocols thanks Xin Hong and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

Publisher’s note Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Related links

Key references using this protocol

Vermeeren, P., Sun, X. & Bickelhaupt, F. M. Sci. Rep. 8, 10729 (2018): https://doi.org/10.1038/s41598-018-28998-3

Sun, X., Soini, T. M., Poater, J., Hamlin, T. A. & Bickelhaupt, F. M. J. Comput. Chem. 40, 2227–2233 (2019): https://doi.org/10.1002/jcc.25871

Key data used in this protocol

Vermeeren, P., Sun, X. & Bickelhaupt, F. M. Sci. Rep. 8, 10729 (2018): https://doi.org/10.1038/s41598-018-28998-3

Hamlin, T. A., Levandowski, B. J., Narsaria, A. K., Houk, K. N. & F. Bickelhaupt, F. M. Chem. Eur. J. 25, 6342–6348 (2019): https://doi.org/10.1002/chem.201900295

Supplementary information

Supplementary Information

Supplementary Methods 1–17, Supplementary Data 1 and 2

Reporting Summary

Rights and permissions

Reprints and Permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Vermeeren, P., van der Lubbe, S.C.C., Fonseca Guerra, C. et al. Understanding chemical reactivity using the activation strain model. Nat Protoc 15, 649–667 (2020). https://doi.org/10.1038/s41596-019-0265-0

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41596-019-0265-0

This article is cited by

Comments

By submitting a comment you agree to abide by our Terms and Community Guidelines. If you find something abusive or that does not comply with our terms or guidelines please flag it as inappropriate.

Search

Advanced search

Quick links

Nature Briefing

Sign up for the Nature Briefing newsletter — what matters in science, free to your inbox daily.

Get the most important science stories of the day, free in your inbox. Sign up for Nature Briefing