Skip to main content

Thank you for visiting 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.

Cold quantum-controlled rotationally inelastic scattering of HD with H2 and D2 reveals collisional partner reorientation


Molecular interactions are best probed by scattering experiments. Interpretation of these studies has been limited by lack of control over the quantum states of the incoming collision partners. We report here the rotationally inelastic collisions of quantum-state prepared deuterium hydride (HD) with H2 and D2 using a method that provides an improved control over the input states. HD was coexpanded with its partner in a single supersonic beam, which reduced the collision temperature to 0–5 K, and thereby restricted the involved incoming partial waves to s and p. By preparing HD with its bond axis preferentially aligned parallel and perpendicular to the relative velocity of the colliding partners, we observed that the rotational relaxation of HD depends strongly on the initial bond-axis orientation. We developed a partial-wave analysis that conclusively demonstrates that the scattering mechanism involves the exchange of internal angular momentum between the colliding partners. The striking differences between H2/HD and D2/HD scattering suggest the presence of anisotropically sensitive resonances.

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.


All prices are NET prices.

Fig. 1: Relative-speed and energy distributions.
Fig. 2: Two different collision geometries.
Fig. 3: D2/HD mixed-beam scattering.
Fig. 4: H2/HD mixed-beam scattering.


  1. Blatt, J. M. & Biedenharn, L. C. The angular distribution of scattering and reaction cross sections. Rev. Mod. Phys. 24, 258–272 (1952).

    CAS  Article  Google Scholar 

  2. Arthurs, A. M. & Dalgarno, A. The theory of scattering by a rigid rotator. Proc. R. Soc. A 256, 540–551 (1960).

    Article  Google Scholar 

  3. Warren, W. S., Rabitz, H. & Dahleh, M. Coherent control of quantum dynamics: the dream is alive. Science 259, 1581–1589 (1993).

    CAS  Article  Google Scholar 

  4. Zare, R. N. Laser control of chemical reactions. Science 279, 1875–1879 (1998).

    CAS  Article  Google Scholar 

  5. PanH., Wang, F,. Czakó, G. & Liu, K. Direct mapping of the angle-dependent barrier to reaction for Cl + CHD3 using polarized scattering data. Nat. Chem. 9, 1175–1180 (2017).

    CAS  Article  Google Scholar 

  6. Smith, G. P. & Zare, R. N. Angular distribution of product internal states using laser fluorescence detection: the Ba + KCl reaction. J. Chem. Phys. 64, 2632–2640 (1976).

    CAS  Article  Google Scholar 

  7. Lin, J. J., Zhou, J., Shiu, W. & Liu, K. State-specific correlation of coincident product pairs in the F + CD4 reaction. Science 300, 966–969 (2003).

    CAS  Article  Google Scholar 

  8. Bartlett, N. C.-M. et al. Differential cross sections for H + D2 → HD(v′ = 2, j′ = 0,3,6,9) + D at center-of-mass collision energies of 1.25, 1.61, and 1.97 eV. Phys. Chem. Chem. Phys. 13, 8175–8179 (2011).

    CAS  Article  Google Scholar 

  9. Stuhl, B. K., Hummon, M. T. & Ye, J. Cold state-selected molecular collisions and reactions. Annu. Rev. Phys. Chem. 65, 501–518 (2014).

    CAS  Article  Google Scholar 

  10. Naulin, C. & Costes, M. Experimental search for scattering resonances in near cold molecular collisions. Int. Rev. Phys. Chem. 33, 427–446 (2014).

    CAS  Article  Google Scholar 

  11. Aoiz, F. J. et al. A new perspective: imaging the stereochemistry of molecular collisions. Phys. Chem. Chem. Phys. 17, 30210–30228 (2015).

    CAS  Article  Google Scholar 

  12. Loesch, H. J. Orientation and alignment in reactive beam collisions: recent progress. Annu. Rev. Phys. Chem. 46, 555–594 (1995).

    CAS  Article  Google Scholar 

  13. Jones, E. M. & Brooks, P. R. Focusing and orienting asymmetric-top molecules in molecular beams. J. Chem. Phys. 53, 55–58 (1970).

    CAS  Article  Google Scholar 

  14. Loesch, H. J. & Remscheid, A. Brute force in molecular reaction dynamics: a novel technique for measuring steric effects. J. Chem. Phys. 93, 4779 (1990).

    CAS  Article  Google Scholar 

  15. van Leuken, J. J., van Amerom, F. H. W., Bulthuis, J., Snijders, J. G. & Stolte, S. Parity-resolved rotationally inelastic collisions of hexapole state-selected NO (2Π1/2, J = 0.5) with Ar. J. Phys. Chem. 99, 15573–15579 (1995).

    Article  Google Scholar 

  16. Brouard, M. et al. Fully quantum state-resolved inelastic scattering of NO(X) + Kr: differential cross sections and product rotational alignment. J. Chem. Phys. 141, 164306 (2014).

    CAS  Article  Google Scholar 

  17. Watanabe, D., Ohoyama, H., Matsumura, T. & Kasai, T. Effect of mutual configuration between molecular orientation and atomic orientation in the oriented Ar + oriented CF3H reaction. Phys. Rev. Lett. 99, 1–4 (2007).

    Google Scholar 

  18. Brouard, M., Parker, D. H. & van de Meerakker, S. Y. T. Taming molecular collisions using electric and magnetic fields. Chem. Soc. Rev. 43, 7279–7294 (2014).

    CAS  Article  Google Scholar 

  19. Rohlfing, E. A., Chandler, D. W. & Parker, D. H. Direct measurement of rotational energy transfer rate constants for HCl (v = 1). J. Chem. Phys. 87, 5229–5237 (1987).

    CAS  Article  Google Scholar 

  20. Dittmann, P. et al. The effect of vibrational excitation (3 ≤ v′ ≤ 19) on the reaction Na2 (v′) + Cl → NaCl + Na. J. Chem. Phys. 97, 9472 (1992).

    CAS  Article  Google Scholar 

  21. Liu, K. Perspective: vibrational-induced steric effects in bimolecular reactions. J. Chem. Phys. 142, 80901 (2015).

    Article  Google Scholar 

  22. Palla, F., Galli, D. & Silk, J. Deuterium in the universe. Astrophys. J. 451, 44–50 (1995).

    CAS  Article  Google Scholar 

  23. Dong, W., Mukherjee, N. & Zare, R. N. Optical preparation of H2 rovibrational levels with almost complete population transfer. J. Chem. Phys. 139, 74204 (2013).

    Article  Google Scholar 

  24. Mukherjee, N., Dong, W. & Zare, R. N. Coherent superposition of M-states in a single rovibrational level of H2 by Stark-induced adiabatic Raman passage. J. Chem. Phys. 140, 74201 (2014).

    Article  Google Scholar 

  25. Weck, P. F. & Balakrishnan, N. Importance of long-range interactions in chemical reactions at cold and ultracold temperatures. Int. Rev. Phys. Chem. 25, 283–311 (2006).

    CAS  Article  Google Scholar 

  26. Quéméner, G, Balakrishnan, N. & Dalgamo, A. in Stwalley, W. C., Krems, R. V. & Friedrich, B. (eds) Cold Molecules: Theory, Experiment, Applications 69–124 (CRC, Boca Raton, 2009)..

  27. Krems, R. V. Cold controlled chemistry. Phys. Chem. Chem. Phys. 10, 4079–4092 (2008).

    CAS  Article  Google Scholar 

  28. de Miranda, M. H. G. et al. Controlling the quantum stereodynamics of ultracold bimolecular reactions. Nat. Phys. 7, 502–507 (2011).

    Article  Google Scholar 

  29. van de Meerakker, S. Y., Bethlem, H. L., Vanhaecke, N. & Meijer, G. Manipulation and control of molecular beams. Chem. Rev. 112, 4828–4878 (2012).

    Article  Google Scholar 

  30. Rowe, B. R. & Marquette, J. B. CRESU studies of ion/molecule reactions. Int. J. Mass Spectrom. Ion. Process 80, 239–254 (1987).

    CAS  Article  Google Scholar 

  31. Shagam, Y. et al. Molecular hydrogen interacts more strongly when rotationally excited at low temperatures leading to faster reactions. Nat. Chem. 7, 921–926 (2015).

    CAS  Article  Google Scholar 

  32. Chefdeville, S. et al. Observation of partial wave resonances in low-energy O2–H2 inelastic collisions. Science 341, 1094–1096 (2013).

    CAS  Article  Google Scholar 

  33. Perreault, W. E., Mukherjee, N. & Zare, R. N. Quantum control of molecular collisions at 1 kelvin. Science 358, 356–359 (2017).

    CAS  Article  Google Scholar 

  34. Amarasinghe, C. & Suits, A. G. Intrabeam scattering for ultracold collisions. J. Phys. Chem. Lett. 8, 5153–5159 (2017).

    CAS  Article  Google Scholar 

  35. Perreault, W. E., Mukherjee, N. & Zare, R. N. Angular and internal state distributions of H2 + generated by (2 + 1) resonance enhanced multiphoton ionization of H2 using time-of-flight mass spectrometry. J. Chem. Phys. 144, 214201 (2016).

    Article  Google Scholar 

  36. Perreault, W. E., Mukherjee, N. & Zare, R. N. Preparation of a selected high vibrational energy level of isolated molecules. J. Chem. Phys. 145, 154203 (2016).

    Article  Google Scholar 

  37. Buck, U., Huisken, F., Maneke, G. & Schaefer, J. State resolved rotational excitation in HD + D2 collisions. I. Angular dependence of 0→2 transitions. J. Chem. Phys. 74, 535–544 (1981).

    CAS  Article  Google Scholar 

  38. Buck, U. Rotationally inelastic scattering of hydrogen molecules and the non-spherical interaction. Faraday Discuss. Chem. Soc. 73, 187–203 (1982).

    Article  Google Scholar 

  39. Schaefer, J. Rotational integral cross sections and rate coeffients of HD scattered by He and H2. Astron. Astrophys. Suppl. Ser. 85, 1101–1125 (1990).

    CAS  Google Scholar 

  40. Lee, T.-G. et al. State-to-state rotational transitions in H2 + H2 collisions at low temperatures. J. Chem. Phys. 125, 114302 (2006).

    Article  Google Scholar 

  41. Lavert-Ofir, E. et al. Observation of the isotope effect in sub-kelvin reactions. Nat. Chem. 6, 332–335 (2014).

    CAS  Article  Google Scholar 

Download references


This work has been supported by the US Army Research Office under ARO Grant No. W911NF-16-1-1061 and MURI Grant No. W911NF-12-1-0476.

Author information

Authors and Affiliations



All authors conceived of this study. W.E.P. and N.M. carried out the experimental work. N.M. developed the partial-wave analysis used to interpret the data. All the authors wrote the paper.

Corresponding authors

Correspondence to Nandini Mukherjee or Richard N. Zare.

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 Results and Analysis, Supplementary Tables 1–9

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Perreault, W.E., Mukherjee, N. & Zare, R.N. Cold quantum-controlled rotationally inelastic scattering of HD with H2 and D2 reveals collisional partner reorientation. Nature Chem 10, 561–567 (2018).

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI:

This article is cited by


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