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.

Quantum interference between H + D2 quasiclassical reaction mechanisms

Abstract

Interferences are genuine quantum phenomena that appear whenever two seemingly distinct classical trajectories lead to the same outcome. They are common in elastic scattering but are seldom observable in chemical reactions. Here we report experimental measurements of the state-to-state angular distribution for the H + D2 reaction using the ‘photoloc’ technique. For products in low rotational and vibrational states, a characteristic oscillation pattern governs backward scattering. The comparison between the experiments, rigorous quantum calculations and classical trajectories on an accurate potential energy surface allows us to trace the origin of that structure to the quantum interference between different quasiclassical mechanisms, a phenomenon analogous to that observed in the double-slit experiment.

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 theoretically simulated angular distributions for H + D2 HD(v′ = 1, j′) + D at a mean collision energy of 1.97 eV.
Figure 2: Comparison between experimental and theoretically simulated angular distributions for H + D2 HD(v′ = 3, j′) + D at an average collision energy of 1.97 eV.
Figure 3: Interpretation of the classical deflection function for the H + D2(v = 0, j = 0) HD(v′ = 1, j′ = 0) + D reaction at Ecoll = 1.97 eV.
Figure 4: Origin of multiple peaks in backward scattering of HD(v′ = 1, j′ = 0, 3, 5) products.
Figure 5: The interference between different classical mechanisms that scatter at the same angle causes the multiple peaks observed in the experimental DCSs for HD(v′ = 1, j′ = 0).
Figure 6: Coherences between different groups of partial waves for HD(v′ = 3, j′ = 0, 1) products.

References

  1. Aoiz, F. J., Bañares, 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 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  5. Aoiz, F. J. et al. The O(1D) + H2 reaction at 56 meV collision energy: a comparison between quantum mechanical, quasiclassical trajectory, and crossed beam results. J. Chem. Phys. 116, 10692–10703 (2002).

    Article  CAS  Google Scholar 

  6. Skodje, R. T. et al. Resonance-mediated chemical reaction: F + HD → HF + D. Phys. Rev. Lett. 85, 1206–1209 (2000).

    Article  CAS  Google Scholar 

  7. Bernstein, R. B. Extrema in velocity dependence of total elastic cross sections for atomic beam scattering: relation to di-atom bound states. J. Chem. Phys. 37, 1880–1881 (1962).

    Article  CAS  Google Scholar 

  8. Da Silveira, R. Rainbow interference effects in heavy ion elastic scattering. Phys. Lett. B 45, 211–213 (1973).

    Article  CAS  Google Scholar 

  9. Ford, K. W. & Wheeler, J. A. Semiclassical description of scattering. Ann. Phys. 7, 259–286 (1959).

    Article  Google Scholar 

  10. Levine, R. D. & Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reactivity (Oxford Univ. Press, 1987).

    Google Scholar 

  11. Gijsbertsen, A., Linnartz, H., Taatjes, C. A. & Stolte, S. Quantum interference as the source of steric asymmetry and parity propensity rules in NO−rare gas inelastic scattering. J. Am. Chem. Soc. 128, 8777–8789 (2006).

    Article  CAS  Google Scholar 

  12. Eyles, C. J. et al. Interference structures in the differential cross-sections for inelastic scattering of NO by Ar. Nature Chem. 3, 597–602 (2011).

    Article  CAS  Google Scholar 

  13. Nichols, B. et al. Steric effects and quantum interference in the inelastic scattering of NO(X) + Ar. Chem. Sci. 6, 2202–2210 (2015).

    Article  CAS  Google Scholar 

  14. McCurdy, C. W. & Miller, W. H. Interference effects in rotational state distributions: propensity and inverse propensity. J. Chem. Phys. 67, 463–468 (1977).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  16. 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  Google Scholar 

  17. Dong, W. et al. Transition-state spectroscopy of partial wave resonances in the F + HD reaction. Science 327, 1501–1502 (2010).

    Article  CAS  Google Scholar 

  18. 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) + D reaction. J. Phys. Chem. A 111, 10302–10312 (2007).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  20. 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 

  21. Greaves, S. J., Murdock, D., Wrede, E. & Althorpe, S. C. New, unexpected, and dominant mechanisms in the hydrogen exchange reaction. J. Chem. Phys. 128, 164306 (2008).

    Article  Google Scholar 

  22. 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  Google Scholar 

  23. Dobbyn, A. J., McCabe, P., Connor, J. N. L. & Castillo, J. F. Nearside–farside analysis of state-selected differential cross sections for reactive molecular collisions. Phys. Chem. Chem. Phys. 1, 1115–1124 (1999).

    Article  CAS  Google Scholar 

  24. Rackham, E. J., Gonzalez-Lezana, T. & Manolopoulos, D. E. A rigorous test of the statistical model for atom–diatom insertion reactions. J. Chem. Phys. 119, 12895–12907 (2003).

    Article  CAS  Google Scholar 

  25. Panda, A. N. et al. A state-to-state dynamical study of the Br + H2 reaction: comparison of quantum and classical trajectory results. Phys. Chem. Chem. Phys. 14, 13067–13075 (2012).

    Article  CAS  Google Scholar 

  26. Koszinowski, K., Goldberg, N. T., Pomerantz, A. E. & Zare, R. N. Construction and calibration of an instrument for three-dimensional ion imaging. J. Chem. Phys. 125, 133503 (2006).

    Article  Google Scholar 

  27. 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  Google Scholar 

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

    Article  CAS  Google Scholar 

  29. 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).

    Article  CAS  Google Scholar 

  30. Bonnet, L. & Rayez, J. C. Quasiclassical trajectory method for molecular scattering processes: necessity of a weighted binning approach. Chem. Phys. Lett. 277, 183–190 (1997).

    Article  CAS  Google Scholar 

  31. Bañares, L., Aoiz, F. J., Honvault, P., Bussery-Honvault, B. & Launay, J.-M. Quantum mechanical and quasi-classical trajectory study of the C(1D) + H2 reaction dynamics. J. Chem. Phys. 118, 565–568 (2003).

    Article  Google Scholar 

Download references

Acknowledgements

The authors acknowledge funding by the Spanish Ministry of Economy and Competitiveness (grants CTQ2012-37404-C02 and Consolider Ingenio 2010 CSD2009–00038) and the US National Science Foundation (CHE-1151428).

Author information

Authors and Affiliations

Authors

Contributions

R.N.Z. and F.J.A. conceived and designed the research. M.S. and J.J. conducted the photoloc technique experiments, and P.G.J. and D.H.A. carried out the QM and QCT calculations. P.G.J., F.J.A. and R.N.Z. wrote the paper, with contributions from all co-authors.

Corresponding authors

Correspondence to F. Javier Aoiz or Richard N. Zare.

Ethics declarations

Competing interests

The authors declare no competing financial interests.

Supplementary information

Supplementary information

Supplementary information (PDF 989 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Jambrina, P., Herráez-Aguilar, D., Aoiz, F. et al. Quantum interference between H + D2 quasiclassical reaction mechanisms. Nature Chem 7, 661–667 (2015). https://doi.org/10.1038/nchem.2295

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/nchem.2295

This article is cited by

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