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.

Observation and interpretation of a time-delayed mechanism in the hydrogen exchange reaction

Abstract

Extensive theoretical1,2,3,4,5,6,7,8,9,10,11,12,13 and experimental2,13,14,15,16,17,18,19,20,21,22 studies have shown the hydrogen exchange reaction H + H2 → H2 + H to occur predominantly through a ‘direct recoil’ mechanism: the H–H bonds break and form concertedly while the system passes straight over a collinear transition state, with recoil from the collision causing the H2 product molecules to scatter backward. Theoretical predictions agree well with experimental observations of this scattering process15,16,17,18,19,20,22. Indirect exchange mechanisms involving H3 intermediates have been suggested to occur as well8,9,10,11,12,13, but these are difficult to test because bimolecular reactions cannot be studied by the femtosecond spectroscopies23 used to monitor unimolecular reactions. Moreover, full quantum simulations of the time evolution of bimolecular reactions have not been performed. For the isotopic variant of the hydrogen exchange reaction, H + D2 → HD + D, forward scattering features21 observed in the product angular distribution have been attributed21,12 to possible scattering resonances associated with a quasibound collision complex. Here we extend these measurements to a wide range of collision energies and interpret the results using a full time-dependent quantum simulation of the reaction, thus showing that two different reaction mechanisms modulate the measured product angular distribution features. One of the mechanisms is direct and leads to backward scattering, the other is indirect and leads to forward scattering after a delay of about 25 femtoseconds.

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

Relevant articles

Open Access articles citing this article.

Access options

Buy article

Get time limited or full article access on ReadCube.

$32.00

All prices are NET prices.

Figure 1: Comparison between experimental and theoretical results for the H + D2 → HD(v′ = 3,j′ = 0) + D reaction.
Figure 2: Calculated HD(v′ = 3,j′ = 0) angular distributions.
Figure 3: Snapshots from the quantum simulation of the H + D2(v = 0,j = 0) → HD(v′ = 3,j′ = 0) + D reaction.

References

  1. Hirshfelder, J. O., Eyring, H. & Topley, B. Reactions involving hydrogen molecules and atoms. J. Chem. Phys. 4, 170–177 (1936).

    ADS  Article  Google Scholar 

  2. Truhlar, D. G. & Wyatt, R. E. History of H3 kinetics. Annu. Rev. Phys. Chem. 27, 1–43 (1976).

    ADS  CAS  Article  Google Scholar 

  3. Neuhauser, D. et al. State-to-state rates for the D + H2(v = 1,j = 1) → HD(v′,j′) + H reaction–predictions and measurements. Science 257, 519–522 (1992).

    ADS  CAS  Article  Google Scholar 

  4. Boothroyd, A. I., Keogh, W. J., Martin, P. G. & Peterson, M. R. A refined H3 potential surface. J. Chem. Phys. 104, 7139–7152 (1996).

    ADS  CAS  Article  Google Scholar 

  5. Zhang, J. Z. H. & Miller, W. H. Quantum reactive scattering via the S-matrix version of the Kohn variational principle: integral cross sections for H + H2(v1 = j1 = 0) → H2(v2 = 1,j2 = 1,3) + H in the energy range Etotal = 0.9-1.4 eV. Chem. Phys. Lett. 153, 465–470 (1988).

    ADS  CAS  Article  Google Scholar 

  6. Miller, W. H. Recent advances in quantum mechanical reactive scattering theory. Annu. Rev. Phys. Chem. 41, 245–281 (1990).

    ADS  CAS  Article  Google Scholar 

  7. D'Mello, M., Manolopoulos, D. E. & Wyatt, R. E. Quantum dynamics of the H + D2 → D + HD reaction: comparison with experiment. J. Chem. Phys. 94, 5985–5993 (1991).

    ADS  CAS  Article  Google Scholar 

  8. Aoiz, F. J., Herrero, V. J. & Sáez Rábanos, V. Quasiclassical state to state reaction cross sections for D + H2(v = 0,j = 0) → HD(v′,j′) + H. Formation and characteristics of short-lived collision complexes. J. Chem. Phys. 97, 7423–7436 (1992).

    ADS  CAS  Article  Google Scholar 

  9. Miller, W. H. & Zhang, J. Z. H. How to observe the elusive resonances in H or D + H2 → H2 or HD + H reactive scattering. J. Phys. Chem. 95, 12–19 (1991).

    CAS  Article  Google Scholar 

  10. Schatz, G. C. & Kuppermann, A. Dynamical resonances in collinear, coplanar, and three-dimensional quantum mechanical reactive scattering. Phys. Rev. Lett. 35, 1266–1269 (1973).

    ADS  Article  Google Scholar 

  11. Skodje, R. T., Sadeghi, R., Köppel, H. & Krause, J. L. Spectral quantization of transition state dynamics for the three-dimensional H + H2 reaction. J. Chem. Phys. 101, 1725–1729 (1994).

    ADS  CAS  Article  Google Scholar 

  12. Allison, T. C., Friedman, R. S., Kaufman, D. J. & Truhlar, D. G. Analysis of the resonance in H + D2 → HD(v′ = 3) + D. Chem. Phys. Lett. 327, 439–445 (2000).

    ADS  CAS  Article  Google Scholar 

  13. Fernández-Alonso, F. & Zare, R. N. Scattering resonances in the simplest chemical reaction. Annu. Rev. Phys. Chem. 53, 67–99 (2002).

    ADS  Article  Google Scholar 

  14. Nieh, J.-C. & Valentini, J. J. Experimental observation of dynamical resonances in the H + H2 reaction. Phys. Rev. Lett. 60, 519–522 (1988).

    ADS  CAS  Article  Google Scholar 

  15. Schnieder, L., Seekamp-Rahn, K., Wrede, E. & Welge, K. H. Experimental determination of quantum state resolved differential cross sections for the hydrogen exchange reaction H + D2 → HD + D. J. Chem. Phys. 107, 6175–6195 (1997).

    ADS  CAS  Article  Google Scholar 

  16. Wrede, E. et al. The dynamics of the hydrogen exchange reaction at 2.20 eV collision energy: comparison of experimental and theoretical differential cross sections. J. Chem. Phys. 110, 9971–9981 (1999).

    ADS  CAS  Article  Google Scholar 

  17. Fernández-Alonso, F., Bean, B. D. & Zare, R. N. Differential cross sections for H + D2 → HD(v′ = 1,J′ = 1,5,8) + D at 1.7 eV. J. Chem. Phys. 111, 1035–1042 (1999).

    ADS  Article  Google Scholar 

  18. Fernández-Alonso, F., Bean, B. D. & Zare, R. N. Differential cross sections for H + D2 → HD(v′ = 2,J′ = 0,3,5) + D at 1.55 eV. J. Chem. Phys. 111, 2490–2498 (1999).

    ADS  Article  Google Scholar 

  19. Liu, K. Crossed-beam studies of neutral reactions: state-specific differential cross sections. Annu. Rev. Phys. Chem. 52, 139–164 (2001).

    ADS  CAS  Article  Google Scholar 

  20. Casavecchia, P. Chemical reaction dynamics with molecular beams. Rep. Prog. Phys. 63, 355–414 (2000).

    ADS  CAS  Article  Google Scholar 

  21. Fernández-Alonso, F. et al. Evidence for scattering resonances in the H + D2 reaction. Angew. Chem. Int. Edn Engl. 39, 2748–2752 (2000).

    Article  Google Scholar 

  22. Fernández-Alonso, F. et al. Forward scattering in the H + D2 → HD + D reaction: comparison between experiment and theoretical predictions. J. Chem. Phys. 115, 4534–4545 (2001).

    ADS  Article  Google Scholar 

  23. Zewail, A. H. Femtochemistry: atomic-scale dynamics of the chemical bond. J. Phys. Chem. 104, 5660–5694 (2000).

    CAS  Article  Google Scholar 

  24. Rinnen, K.-D., Buntine, M. A., Kliner, D. A. V., Zare, R. N. & Huo, W. M. Quantitative determination of H2, HD, and D2 internal-state distributions by (2+1) resonance-enhanced multiphoton ionization. J. Chem. Phys. 95, 214–225 (1991).

    ADS  CAS  Article  Google Scholar 

  25. Althorpe, S. C. Quantum wavepacket method for state-to-state reactive cross sections. J. Chem. Phys. 114, 1601–1616 (2001).

    ADS  CAS  Article  Google Scholar 

  26. Skouteris, D., Castillo, J. F. & Manolopoulos, D. E. ABC: a quantum reactive scattering program. Comput. Phys. Commun. 133, 128–135 (2000).

    ADS  CAS  Article  Google Scholar 

  27. Althorpe, S. C., Kouri, D. J. & Hoffman, D. K. Further partitioning of the reactant-product decoupling equations of state-to-state reactive scattering and their solution by the time-independent wavepacket method. J. Chem. Phys. 107, 7816–7824 (1997).

    ADS  CAS  Article  Google Scholar 

  28. Judson, R. S., Kouri, D. J., Neuhauser, D. & Baer, M. Time-dependent wavepacket method for the complete determination of S-matrix elements for reactive molecular collisions in 3 dimensions. Phys. Rev. A 42, 351–366 (1990).

    ADS  CAS  Article  Google Scholar 

  29. Balint-Kurti, G. G., González, A. I., Goldfield, E. M. & Gray, S. K. Quantum reactive scattering of O(1D) + H2 and O(1D) + HD. Faraday Discuss. 110, 169–183 (1998).

    ADS  CAS  Article  Google Scholar 

  30. Huang, Y., Zhu, W., Kouri, D. J. & Hoffman, D. K. Distributed approximating function approach to atom-diatom reactive scattering: Time-dependent and time-independent wavepacket treatments. J. Phys. Chem. 98, 1868–1874 (1994).

    CAS  Article  Google Scholar 

Download references

Acknowledgements

We thank L. Bañares and J. F. Castillo for discussions on the H + D2 reaction, and D. C. Clary, D. E. Manolopoulos and J. M. Hutson for reading the manuscript. S.C.A. thanks the Royal Society for a University Research Fellowship. F.F.A. acknowledges partial support by a European Union Marie Curie fellowship. The experimental part of this work was supported at Stanford by the US National Science Foundation.

Author information

Authors and Affiliations

Authors

Corresponding author

Correspondence to Stuart C. Althorpe.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Rights and permissions

Reprints and Permissions

About this article

Cite this article

Althorpe, S., Fernández-Alonso, F., Bean, B. et al. Observation and interpretation of a time-delayed mechanism in the hydrogen exchange reaction. Nature 416, 67–70 (2002). https://doi.org/10.1038/416067a

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1038/416067a

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

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