Ultrafast energy flow in the wake of solution-phase bimolecular reactions


Vibrational energy flow into reactants, and out of products, plays a key role in chemical reactivity, so understanding the microscopic detail of the pathways and rates associated with this phenomenon is of considerable interest. Here, we use molecular dynamics simulations to model the vibrational relaxation that occurs during the reaction CN + c-C6H12 → HCN + c-C6H11 in CH2Cl2, which produces vibrationally hot HCN. The calculations reproduce the observed energy distribution, and show that HCN relaxation follows multiple timescales. Initial rapid decay occurs through energy transfer to the cyclohexyl co-product within the solvent cage, and slower relaxation follows once the products diffuse apart. Re-analysis of the ultrafast experimental data also provides evidence for the dual timescales. These results, which represent a formal violation of conventional linear response theory, provide a detailed picture of the interplay between fluctuations in organic solvent structure and thermal solution-phase chemistry.

Figure 1: MD snapshot of the products from reaction (R1).
Figure 2: Simple kinetic model used to rationalize experimentally measured time profiles.
Figure 3: Time-dependence of the HCN C–H stretching energy obtained from averaging over 250 non-equilibrium MD simulations.
Figure 4: Comparison of the total vibrational energy of the nascent c-C6H11 in both gas-phase and solution-phase reactive dynamics simulations.
Figure 5: Kinetic model demonstrating improved agreement with experiments.


  1. 1

    Gruebele, M. & Wolynes, P. G. Vibrational energy flow and chemical reactions. Acc. Chem. Res. 37, 261–267 (2004).

    CAS  Article  Google Scholar 

  2. 2

    Stratt, R. M. Chemistry—nonlinear thinking about molecular energy transfer. Science 321, 1789–1790 (2008).

    CAS  Article  Google Scholar 

  3. 3

    Chandler, D. Introduction to Modern Statistical Mechanics (Oxford Univ. Press, 1987).

  4. 4

    Turi, L., Minary, P. & Rossky, P. J. Non-linear response and hydrogen bond dynamics for electron solvation in methanol. Chem. Phys. Lett. 316, 465–470 (2000).

    CAS  Article  Google Scholar 

  5. 5

    Moskun, A. C., Jailaubekov, A. E., Bradforth, S. E., Tao, G. H. & Stratt, R. M. Rotational coherence and a sudden breakdown in linear response seen in room-temperature liquids. Science 311, 1907–1911 (2006).

    CAS  Article  Google Scholar 

  6. 6

    Bragg, A. E., Cavanagh, M. C. & Schwartz, B. J. Linear response breakdown in solvation dynamics induced by atomic electron-transfer reactions. Science 321, 1817–1822 (2008).

    CAS  Article  Google Scholar 

  7. 7

    Fonseca, T. & Ladanyi, B. M. Breakdown of linear response for solvation dynamics in methanol. J. Phys. Chem. 95, 2116–2119 (1991).

    CAS  Article  Google Scholar 

  8. 8

    Smallwood, C. J., Bosma, W. B., Larsen, R. E. & Schwartz, B. J. The role of electronic symmetry in charge-transfer-to-solvent reactions: quantum nonadiabatic computer simulation of photoexcited sodium anions. J. Chem. Phys. 119, 11263–11277 (2003).

    CAS  Article  Google Scholar 

  9. 9

    Geissler, P. L. & Chandler, D. Importance sampling and theory of nonequilibrium solvation dynamics in water. J. Chem. Phys. 113, 9759–9765 (2000).

    CAS  Article  Google Scholar 

  10. 10

    Tao, G. H. & Stratt, R. M. The molecular origins of nonlinear response in solute energy relaxation: the example of high-energy rotational relaxation. J. Chem. Phys. http://dx.doi.org/10.1063/1.2336780 (2006).

  11. 11

    Bethardy, G. A., Northrup, F. J. & Macdonald, R. G. The initial vibrational level distribution and relaxation of HCN[ X1Σ+(v1,0,v3)] in the CN (X 2Σ+) + CH4 → HCN + CH3 reaction system. J. Chem. Phys. 105, 4533–4549 (1996).

    CAS  Article  Google Scholar 

  12. 12

    Bethardy, G. A., Northrup, F. J., He, G., Tokue, I. & Macdonald, R. G. Initial vibrational level distribution of HCN[X 1Σ+(v10v3)] from the CN(X2Σ+) + H2 → HCN + H reaction. J. Chem. Phys. 109, 4224–4236 (1998).

    CAS  Article  Google Scholar 

  13. 13

    Bethardy, G. A., Northrup, F. J. & Macdonald, R. G. The initial vibrational state distribution of HCN X 1Σ+(v1,0,v3) from the reaction CN(2Σ+) + C2H6 → HCN + C2H5 . J. Chem. Phys. 102, 7966–7982 (1995).

    CAS  Article  Google Scholar 

  14. 14

    Bethardy, G. A., Wagner, A. F., Schatz, G. C. & terHorst, M. A. A quasiclassical trajectory study of product state distributions from the CN + H2 → HCN + H reaction. J. Chem. Phys. 106, 6001–6015 (1997).

    CAS  Article  Google Scholar 

  15. 15

    Glowacki, D. R., Orr-Ewing, A. J. & Harvey, J. N. Product energy deposition of CN + alkane H abstraction reactions in gas and solution phases. J. Chem. Phys. 134, 214508 (2011).

    Article  Google Scholar 

  16. 16

    Greaves, S. J. et al. Vibrationally quantum-state-specific reaction dynamics of H atom abstraction by CN radical in solution. Science 331, 1423–1426 (2011).

    CAS  Article  Google Scholar 

  17. 17

    Glowacki, D. R., Paci, E. & Shalashilin, D. V. Boxed molecular dynamics: decorrelation timescales and the kinetic master equation. J. Chem. Theory Comput. 7, 1244–1252 (2011).

    CAS  Article  Google Scholar 

  18. 18

    Glowacki, D. R., Paci, E. & Shalashilin, D. V. Boxed molecular dynamics: a simple and general technique for accelerating rare event kinetics and mapping free energy in large molecular systems. J. Phys. Chem. B 113, 16603–16611 (2009).

    CAS  Article  Google Scholar 

  19. 19

    Owrutsky, J. C., Raftery, D. & Hochstrasser, R. M. Vibrational relaxation dynamics in solutions. Annu. Rev. Phys. Chem. 45, 519–555 (1994).

    CAS  Article  Google Scholar 

  20. 20

    Elles, C. G. & Crim, F. F. Connecting chemical dynamics in gases and liquids. Annu. Rev. Phys. Chem. 57, 273–302 (2006).

    CAS  Article  Google Scholar 

  21. 21

    Dang, L. X. Intermolecular interactions of liquid dichloromethane and equilibrium properties of liquid–vapor and liquid–liquid interfaces: a molecular dynamics study. J. Chem. Phys. 110, 10113–10122 (1999).

    CAS  Article  Google Scholar 

  22. 22

    Laird, B. B. & Thompson, W. H. On the connection between Gaussian statistics and excited-state linear response for time-dependent fluorescence. J. Chem. Phys. http://dx.doi.org/10.1063/1.2747237 (2007).

  23. 23

    Harris, A. L., Brown, J. K. & Harris, C. B. The nature of simple photodissociation reactions in liquids on ultrafast timescales. Annu. Rev. Phys. Chem. 39, 341–366 (1988).

    CAS  Article  Google Scholar 

  24. 24

    Nandi, N., Bhattacharyya, K. & Bagchi, B. Dielectric relaxation and solvation dynamics of water in complex chemical and biological systems. Chem. Rev. 100, 2013–2045 (2000).

    CAS  Article  Google Scholar 

  25. 25

    Voth, G. A. & Hochstrasser, R. M. Transition state dynamics and relaxation processes in solutions: a frontier of physical chemistry. J. Phys. Chem. 100, 13034–13049 (1996).

    CAS  Article  Google Scholar 

  26. 26

    Crim, F. F. Chemical dynamics of vibrationally excited molecules: controlling reactions in gases and on surfaces. Proc. Natl Acad. Sci. USA 105, 12654–12661 (2008).

    CAS  Article  Google Scholar 

  27. 27

    Noé, F. et al. Dynamical fingerprints for probing individual relaxation processes in biomolecular dynamics with simulations and kinetic experiments. Proc. Natl Acad. Sci. USA http://dx.doi.org/10.1073/pnas.1004646108 (2011).

  28. 28

    Franco, M. I., Turina, L., Mershin, A. & Skoulakisa, E. M. C. Molecular vibration-sensing component in Drosophila melanogaster olfaction. Proc. Natl Acad. Sci. USA http://dx.doi.org/10.1073/pnas.1012293108 (2011).

  29. 29

    Glowacki, D. R., Liang, C. H., Marsden, S. P., Harvey, J. N. & Pilling, M. J. Alkene hydroboration: hot intermediates that react while they are cooling. J. Am. Chem. Soc. 132, 13621–13623 (2010).

    CAS  Article  Google Scholar 

  30. 30

    Goldman, L. M., Glowacki, D. R. & Carpenter, B. K. Nonstatistical dynamics in unlikely places: [1,5] hydrogen migration in chemically activated cyclopentadiene. J. Am. Chem. Soc. http://dx.doi.org/10.1021/ja1095717 (2011).

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T.A.A. Oliver, M.N.R. Ashfold, I.P. Clark, G.P. Greetham, A.W. Parker and M. Towrie are thanked for their contributions to the experimental work. Funding was provided by the Engineering and Physical Sciences Research Council Programme (grant EP/G00224X). The authors thank the Leverhulme Trust for an Early Career Research Fellowship (S.J.G.) and the Royal Society and the Wolfson Foundation for a Research Merit Award (A.J.O.E).

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D.R.G. and J.N.H. conceived and designed the simulations. D.R.G. wrote the simulation code, performed the simulations and analysed data. A.J.O.E. conceived the experimental study, and R.A.R, S.J.G. and A.J.O.E. obtained and analysed the experimental data and performed the initial kinetic modelling. D.R.G. wrote the manuscript, with comments and discussions from all the authors.

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Correspondence to David R. Glowacki or Jeremy N. Harvey.

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The authors declare no competing financial interests.

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Glowacki, D., Rose, R., Greaves, S. et al. Ultrafast energy flow in the wake of solution-phase bimolecular reactions. Nature Chem 3, 850–855 (2011). https://doi.org/10.1038/nchem.1154

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