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.

  • Article
  • Published:

Direct observation of forward-scattering oscillations in the H+HD→H2+D reaction

Nature Chemistry volume 10, pages 653–658 (2018)Cite this article

Subjects

Abstract

Accurate measurements of product state-resolved angular distributions are central to fundamental studies of chemical reaction dynamics. Yet, fine quantum-mechanical structures in product angular distributions of a reactive scattering process, such as the fast oscillations in the forward-scattering direction, have never been observed experimentally and the nature of these oscillations has not been fully explored. Here we report the crossed-molecular-beam experimental observation of these fast forward-scattering oscillations in the product angular distribution of the benchmark chemical reaction, H + HD → H2 + D. Clear oscillatory structures are observed for the H2(v′ = 0, j′ = 1, 3) product states at a collision energy of 1.35 eV, in excellent agreement with the quantum-mechanical dynamics calculations. Our analysis reveals that the oscillatory forward-scattering components are mainly contributed by the total angular momentum J around 28. The partial waves and impact parameters responsible for the forward scatterings are also determined from these observed oscillations, providing crucial dynamics information on the transient reaction process.

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

Access options

Buy this article

  • Purchase on Springer Link
  • Instant access to full article PDF
Buy now

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

Fig. 1: Schematic of the experimental set-up.
Fig. 2: Experimental and theoretical images of the D-atom product from the H + HD → H2 + D reaction at a collision energy of 1.35 eV with crossing angle of the two beams of 150°.
Fig. 3: Total translational energy of the reaction products in the forward (θ = 0°), sideways (θ = 90°) and backward (θ = 180°) directions in the centre-of-mass frame.
Fig. 4: Experimental and calculated DCSs of the H2(v′,j′) product from the H + HD(v = 0, j = 0) → H2(v′,j′) + D reaction at a collision energy of 1.35 eV.
Fig. 5: Theoretical analysis of fast angular oscillations in the forward-scattering direction.
Fig. 6: Comparison of quantum-chemical and classical corona effects.

Similar content being viewed by others

References

  1. Airy, G. B. On the intensity of light in the neighborhood of a caustic. Trans. Camb. Philos. Soc. 6, 379–403 (1838).

    Google Scholar 

  2. Nussenzveig, H. M. The theory of the rainbow. Atmospheric Phenomena 60–71 (Freeman, San Francisco, CA, 1980).

    Google Scholar 

  3. Neumark, D. M., Wodtke, A. M., Robinson, G. N., Hayden, C. C. & Lee, Y. T. Experimental investigation of resonances in reactive scattering: the F+H2 reaction. Phys. Rev. Lett. 53, 226–229 (1984).

    Article  CAS  Google Scholar 

  4. Dai, D. X. et al. Interference of quantized transition-state pathways in the H+D2→D+HD chemical reaction. Science 300, 1730–1734 (2003).

    Article  CAS  PubMed  Google Scholar 

  5. Berteloite, C. et al. Kinetics and dynamics of the S(1D2) + H2 → SH + H reaction at very low temperatures and collision energies. Phys. Rev. Lett. 105, 203201 (2010).

    Article  CAS  PubMed  Google Scholar 

  6. Dong, W. et al. Transition-state spectroscopy of partial wave resonances in the F + HD reaction. Science 357, 1501–1502 (2010).

    Article  CAS  Google Scholar 

  7. Jambrina, P. G. et al. Quantum interference between H + D2 quasiclassical reaction mechanisms. Nat. Chem. 7, 661–647 (2015).

    Article  CAS  PubMed  Google Scholar 

  8. Harich, S. A. et al. Forward scattering due to slowdown of the intermediate in the H + HD → D + H2 reaction. Nature 419, 281–284 (2002).

    Article  CAS  PubMed  Google Scholar 

  9. Aoiz, F. J., Herrero, V. J. & Rábanos, V. S. 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).

    Article  CAS  Google Scholar 

  10. 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. A 91, 12–19 (1991).

    Article  Google Scholar 

  11. Greaves, S. J., Murdock, D. & Wrede, E. A quasiclassical trajectory study of the time-delayed forward scattering in the hydrogen exchange reaction. J. Chem. Phys. 128, 164307 (2008).

    Article  CAS  PubMed  Google Scholar 

  12. Aoiz, F. J., Bañares, L. & Castillo, J. F. D. Sokolovski energy dependence of forward scattering in the differential cross section of the H + D2 → HD(v′ = 3, j′ = 0) + D reaction. J. Chem. Phys. 117, 2546–2556 (2002).

    Article  CAS  Google Scholar 

  13. Goldberg, N. T., Zhang, J. Y., Miller, D. J. & Zare, R. N. Corroboration of theory for H + D2 → HD(v′ = 3, j′ = 0) + D reactive scattering dynamics. J. Phys. Chem. A 112, 9266–9268 (2008).

    Article  CAS  PubMed  Google Scholar 

  14. Monks, P. D. D., Connor, J. N. L. & Althorpe, S. C. Nearside-farside and local angular momentum analyses of time-independent scattering amplitudes for the H + D2 (v i = 0, j i = 0) → HD(v f = 3, j f = 0) reaction. J. Phys. Chem. A 111, 10302–103112 (2007).

    Article  CAS  PubMed  Google Scholar 

  15. Monks, P. D. D., Connor, J. N. L. & Althorpe, S. C. Theory of time-dependent reactive scattering: cumulative time-evolving differential cross sections and nearside-farside analyses of time-dependent scattering amplitudes for the H + D2 → HD + D reaction. J. Phys. Chem. A 110, 741–748 (2006).

    Article  CAS  PubMed  Google Scholar 

  16. Wang, X. A. et al. HF(v′ = 3) forward scattering in the F + H2 reaction: shape resonance and slow-down mechanism. Proc. Natl Acad. Sci. USA 105, 6227–6231 (2008).

    Article  PubMed  Google Scholar 

  17. Castillo, J. F., Manolopoulos, D. E., Stark, K. & Werner, H. J. Quantum mechanical angular distributions for the F + H2 reaction. J. Chem. Phys. 104, 6531–6546 (1996).

    Article  CAS  Google Scholar 

  18. Sokolovski, D., De Fazio, D., Cavalli, S. & Aquilanti, V. On the origin of the forward peak and backward oscillations in the F + H2(v = 0) → HF(v′ = 2) + H reaction. Phys. Chem. Chem. Phys. 9, 5664–5671 (2007).

    Article  CAS  PubMed  Google Scholar 

  19. Connor, J. N. L. Theory of forward glory scattering for chemical reactions. Phys. Chem. Chem. Phys. 6, 377–390 (2004).

    Article  CAS  Google Scholar 

  20. Xiahou, C. & Connor, J. N. L. Theory of forward glory scattering for chemical reactions: accuracy of semiclassical approximations using a J-shifted Eckart parameterization for the scattering matrix element. Mol. Phys. 104, 159–175 (2006).

    Article  CAS  Google Scholar 

  21. Fleming, D. G. et al. Kinetic isotope effects for the reactions of muonic helium and muonium with H2. Science 331, 448–450 (2011).

    Article  CAS  PubMed  Google Scholar 

  22. Jankunas, J. et al. Seemingly anomalous angular distributions in H + D2 reactive scattering. Science 336, 1687–1690 (2012).

    Article  CAS  PubMed  Google Scholar 

  23. Kitsopoulos, T. N., Baldwin, D. P., Zare, R. N. & Chandler, D. W. Reaction product imaging: the H + D2 reaction. Science 260, 1605–1610 (1993).

    Article  CAS  PubMed  Google Scholar 

  24. 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).

    Article  CAS  PubMed  Google Scholar 

  25. Zare, R. N. The hydrogen games and other adventures in chemistry. Annu. Rev. Phys. Chem. 64, 1–19 (2013).

    Article  CAS  PubMed  Google Scholar 

  26. Aoiz, F. J., Banares, L. & Herrero, V. J. The H + H2 reactive system. Progress in the study of the dynamics of the simplest reaction. Int. Rev. Phys. Chem. 24, 119–190 (2005).

    Article  CAS  Google Scholar 

  27. Althorpe, S. C. et al. Observation and interpretation of a time-delayed mechanism in the hydrogen exchange reaction. Nature 416, 67–70 (2002).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  Google Scholar 

  30. Schnieder, L. et al. Experimental studies and theoretical predictions for the H + D2 → HD + D reaction. Science 269, 207–210 (1995).

    Article  CAS  PubMed  Google Scholar 

  31. Goldberga, N. T. et al. Vibrationally inelastic H + D2 collisions are forward-scattered. Proc. Natl Acad. Sci. USA 105, 18194–18199 (2008).

    Article  Google Scholar 

  32. Jankunas, J. et al. Is the simplest chemical reaction really so simple? Proc. Natl Acad. Sci. USA 111, 15–20 (2014).

    Article  CAS  PubMed  Google Scholar 

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

    Article  Google Scholar 

  34. Vogels, S. N. et al. High-resolution imaging of velocity-controlled molecular collisions using counter propagating beams. Phys. Rev. Lett. 113, 263202 (2014).

    Article  CAS  PubMed  Google Scholar 

  35. von Zastrow, A. et al. State-resolved diffraction oscillations imaged for inelastic collisions of NO radicals with He, Ne and Ar. Nat. Chem. 6, 216–221 (2014).

    Article  CAS  Google Scholar 

  36. Vogels, S. N. et al. Imaging resonances in low-energy NO–He inelastic collisions. Science 350, 787–790 (2015).

    Article  CAS  PubMed  Google Scholar 

  37. Onvlee, J. et al. Imaging quantum stereodynamics through Fraunhofer scattering of NO radicals with rare-gas atoms. Nat. Chem. 9, 226–233 (2017).

    Article  CAS  PubMed  Google Scholar 

  38. Sun, Z., Guo, H. & Zhang, D. H. Extraction of state-to-state reactive scattering attributes from wave packet in reactant Jacobi coordinates. J. Chem. Phys. 132, 084112 (2010).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  Google Scholar 

  40. Bouakline, F., Althorpe, S. C. & Peláez Ruiz, D. Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies. J. Chem. Phys. 128, 124322 (2008).

    Article  CAS  PubMed  Google Scholar 

  41. Juanes-Marcos, J. C., Althorpe, S. C. & Wrede, E. Theoretical study of geometric phase effects in the hydrogen-exchange reaction. Science 309, 1227–1230 (2005).

    Article  CAS  PubMed  Google Scholar 

  42. Jankunas, J., Sneha, M., Zare, R. N., Bouakline, F. & Althorpe, S. C. Disagreement between theory and experiment grows with increasing rotational excitation of HD(v′, j′) product for the H + D2 reaction. J. Chem. Phys. 138, 094310 (2013).

    Article  CAS  PubMed  Google Scholar 

  43. Kendrick, B. K. Geometric phase effects in chemical reaction dynamics and molecular spectra. J. Phys. Chem. A 107, 6739 (2003).

    Article  CAS  Google Scholar 

  44. Chao, S. D. et al. A fully state- and angle-resolved study of the H + HD → D + H2 reaction: comparison of a molecular beam experiment to ab initio quantum reaction dynamics. J. Chem. Phys. 117, 8341–8361 (2002).

    Article  CAS  Google Scholar 

  45. Greaves, S. J., Murdock, D., Wrede, E. & Althorpe, S. C. Fully quantum state-resolved inelastic scattering of NO(X)+Kr: differential cross sections and product rotational alignment. J. Chem. Phys. 128, 164306 (2008).

    Article  CAS  PubMed  Google Scholar 

  46. Zhang, J. Z. H. & Miller, W. H. Quantum reactive scattering via the S-matrix version of the Kohn variational principle: Differential and integral cross sections for D + H2 → HD + H. J. Chem. Phys. 91, 1528 (1989).

    Article  CAS  Google Scholar 

  47. Jankunas, J., Sneha, M., Zare, R. N., Bouakline, F. & Althorpe, S. C. Hunt for geometric phase effects in H + HD → HD(v′,j′) + H. J. Chem. Phys. 139, 144316 (2013).

    Article  CAS  PubMed  Google Scholar 

Download references

Acknowledgements

This work was supported by the National Natural Science Foundation of China (NSFC Center for Chemical Dynamics), the Strategic Priority Research Program of Chinese Academy of Sciences (grant no. XDB17000000) and the Ministry of Science and Technology. The authors also thank Ting Xie, Siwen Wang, Yuxin Tan and Qiming Qiu for their help with the experiment.

Author information

Author notes

  1. These authors contributed equally: Daofu Yuan, Shengrui Yu.

Authors and Affiliations

  1. Hefei National Laboratory for Physical Sciences at the Microscale, Department of Chemical Physics, iChEM (Collaborative Innovation Center of Chemistry for Energy Materials), University of Science and Technology of China, Hefei, China

    Daofu Yuan, Wentao Chen, Jiwei Sang, Chang Luo, Tao Wang, Xingan Wang & Xueming Yang

  2. Hangzhou Institute of Advanced Studies, Zhejiang Normal University, Hangzhou, China

    Shengrui Yu

  3. State Key Laboratory of Molecular Reaction Dynamics, Dalian Institute of Chemical Physics, Chinese Academy of Sciences, Dalian, China

    Tao Wang, Xin Xu, Zhigang Sun, Dong H. Zhang & Xueming Yang

  4. Dipartimento di Chimica, Biologia e Biotecnologie, Università degli Studi di Perugia, Perugia, Italy

    Piergiorgio Casavecchia

  5. Department of Chemistry, Southern University of Science and Technology, Shenzhen, China

    Xueming Yang

Authors
  1. Daofu Yuan
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Shengrui Yu
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Wentao Chen
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Jiwei Sang
    View author publications

    You can also search for this author in PubMed Google Scholar

  5. Chang Luo
    View author publications

    You can also search for this author in PubMed Google Scholar

  6. Tao Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  7. Xin Xu
    View author publications

    You can also search for this author in PubMed Google Scholar

  8. Piergiorgio Casavecchia
    View author publications

    You can also search for this author in PubMed Google Scholar

  9. Xingan Wang
    View author publications

    You can also search for this author in PubMed Google Scholar

  10. Zhigang Sun
    View author publications

    You can also search for this author in PubMed Google Scholar

  11. Dong H. Zhang
    View author publications

    You can also search for this author in PubMed Google Scholar

  12. Xueming Yang
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

X.Y., D.H.Z., Z.S. and X.W. conceived and supervised the research. The experiments were carried out by D.Y., S.Y., W.C., J.S., C.L., P.C. and X.W. Data analysis and interpretation were performed by D.Y., S.Y., W.C., T. W.,P.C., X.W. and X.Y. Theoretical calculations were performed by X.X., Z.S. and D.H.Z. The manuscript was written by X.Y., D.H.Z., Z.S. and X.W., with contributions from all authors. All authors contributed to discussions about the content of the paper.

Corresponding authors

Correspondence to Xingan Wang, Zhigang Sun, Dong H. Zhang or Xueming Yang.

Ethics declarations

Competing interests

The authors declare no competing interests.

Additional information

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

Supplementary information

Supplementary Information

Supplementary Methods, Results, Fig. 1–9 and Table 1

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Yuan, D., Yu, S., Chen, W. et al. Direct observation of forward-scattering oscillations in the H+HD→H2+D reaction. Nature Chem 10, 653–658 (2018). https://doi.org/10.1038/s41557-018-0032-9

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41557-018-0032-9

This article is cited by

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