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:

Anisotropic dynamics of resonant scattering between a pair of cold aligned diatoms

Nature Chemistry volume 14, pages 658–663 (2022)Cite this article

Subjects

Abstract

The collision dynamics between a pair of aligned molecules in the presence of a partial-wave resonance provide the most sensitive probe of the long-range anisotropic forces important to chemical reactions. Here we control the collision temperature and geometry to probe the dynamics of cold (1–3 K) rotationally inelastic scattering of a pair of optically state-prepared D2 molecules. The collision temperature is manipulated by combining the gating action of laser state preparation and detection with the velocity dispersion of the molecular beam. When the bond axes of both molecules are aligned parallel to the collision velocity, the scattering rate drops by a factor of 3.5 as collision energies >2.1 K are removed, suggesting a geometry-dependent resonance. Partial-wave analysis of the measured angular distribution supports a shape resonance within the centrifugal barrier of the l = 2 incoming orbital. Our experiment illustrates the strong anisotropy of the quadrupole–quadrupole interaction that controls the dynamics of resonant scattering.

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: HSARP and VSARP scattering rates as the probe beam moves along the molecular beam propagation direction.
Fig. 2: Velocity distribution measured within the probe volume as the probe is moved along the direction of molecular beam propagation.
Fig. 3: HSARP (red dots) and VSARP (blue dots) relative integral scattering rates as a function of the collision speed u90 (m s−1).
Fig. 4: Incoming orbitals l contributing to the Δj = 2 inelastic scattering.
Fig. 5: Partial-wave fitting of the measured scattering angular distribution.

Similar content being viewed by others

Data availability

Source data are provided with this paper.

References

  1. 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).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  3. Henson, A. B., Gersten, S., Shagam, Y., Narevicius, J. & Narevicius, E. Observation of resonances in Penning ionization reactions at sub-kelvin temperatures in merged beams. Science 338, 234–239 (2012).

    Article  CAS  PubMed  Google Scholar 

  4. García-Vela, A., Cabanillas-Vidosa, I., Ferrero, J. C. & Pino, G. A. The role of orbiting resonances in the vibrational relaxation of I2 (B,v′ = 21) by collisions with He at very low energies: a theoretical and experimental study. Phys. Chem. Chem. Phys. 14, 5570 (2012).

    Article  PubMed  CAS  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  6. Bergeat, A., Onvlee, J., Naulin, C., Van Der Avoird, A. & Costes, M. Quantum dynamical resonances in low-energy CO(j = 0) + He inelastic collisions. Nat. Chem. 7, 349–353 (2015).

    Article  CAS  PubMed  Google Scholar 

  7. Jankunas, J., Jachymski, K., Hapka, M. & Osterwalder, A. Observation of orbiting resonances in He (3S1) + NH3 Penning ionization. J. Chem. Phys. 142, 164305 (2015).

    Article  PubMed  CAS  Google Scholar 

  8. Costes, M. & Naulin, C. Observation of quantum dynamical resonances in near cold inelastic collisions of astrophysical molecules. Chem. Sci. 7, 2462–2469 (2016).

    Article  CAS  PubMed  PubMed Central  Google Scholar 

  9. Köhler, T., Góral, K. & Julienne, P. S. Production of cold molecules via magnetically tunable Feshbach resonances. Rev. Mod. Phys. 78, 1311–1361 (2006).

    Article  CAS  Google Scholar 

  10. Wang, T. et al. Dynamical resonances accessible only by reagent vibrational excitation in the F + HD → HF + D reaction. Science 342, 1499–1502 (2013).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  12. Yang, T. et al. Extremely short-lived reaction resonances in Cl + HD (v = 1) → DCl + H due to chemical bond softening. Science 347, 60–63 (2015).

    Article  CAS  PubMed  Google Scholar 

  13. Onvlee, J. et al. Imaging quantum stereodynamics through Fraunhofer scattering of NO radicals with rare-gas atoms. Nat. Chem. 9, 226–233 (2016).

    Article  PubMed  CAS  Google Scholar 

  14. Vogels, S. N. et al. Scattering resonances in bimolecular collisions between NO radicals and H2 challenge the theoretical gold standard. Nat. Chem. 10, 435–440 (2018).

    Article  CAS  PubMed  Google Scholar 

  15. Paliwal, P. et al. Determining the nature of quantum resonances by probing elastic and reactive scattering in cold collisions. Nat. Chem. 13, 94–98 (2021).

    Article  CAS  PubMed  Google Scholar 

  16. Klein, A. et al. Directly probing anisotropy in atom–molecule collisions through quantum scattering resonances. Nat. Phys. 13, 35–38 (2017).

    Article  CAS  Google Scholar 

  17. de Jongh, T. et al. Imaging the onset of the resonance regime in low-energy NO–He collisions. Science 368, 626–630 (2020).

    Article  PubMed  CAS  Google Scholar 

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

    Article  CAS  PubMed  Google Scholar 

  19. Schaefer, J. & Meyer, W. Theoretical studies of H2–H2 collisions. I. Elastic scattering of ground state para- and ortho-H2 in the rigid rotor approximation. J. Chem. Phys. 70, 344–360 (1979).

    Article  CAS  Google Scholar 

  20. 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).

    Article  CAS  Google Scholar 

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

    Article  PubMed  CAS  Google Scholar 

  22. Quéméner, G. & Balakrishnan, N. Quantum calculations of H2–H2 collisions: from ultracold to thermal energies. J. Chem. Phys. 130, 11430 (2009).

    Article  CAS  Google Scholar 

  23. Balakrishnan, N., Quéméner, G., Forrey, R. C., Hinde, R. J. & Stancil, P. C. Full-dimensional quantum dynamics calculations of H2–H2 collisions. J. Chem. Phys. 134, 014301 (2011).

    Article  CAS  PubMed  Google Scholar 

  24. Sultanov, R. A., Guster, D. & Adhikari, S. K. Low temperature HD + ortho-/para-H2 inelastic scattering of astrophysical interest. J. Phys. B 49, 015203 (2016).

    Article  CAS  Google Scholar 

  25. Jambrina, P. G. et al. Stereodynamical control of a quantum scattering resonance in cold molecular collisions. Phys. Rev. Lett. 123, 43401 (2019).

    Article  CAS  Google Scholar 

  26. Croft, J. F. E. & Balakrishnan, N. Controlling rotational quenching rates in cold molecular collisions. J. Chem. Phys. 150, 044116 (2019).

    Article  CAS  Google Scholar 

  27. Yang, B. et al. Quantum dynamics of CO–H2 in full dimensionality. Nat. Commun. 6, 6629 (2015).

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

    Article  CAS  PubMed  Google Scholar 

  29. Perreault, W. E., Mukherjee, N. & Zare, R. N. Quantum controlled rotationally inelastic scattering of HD with H2 and D2 near 1 kelvin reveals collisional partner reorientation. Nat. Chem. 10, 561–567 (2018).

    Article  CAS  PubMed  Google Scholar 

  30. Perreault, W. E., Mukherjee, N. & Zare, R. N. HD (v = 1, j = 2, m) orientation controls HD–He rotationally inelastic scattering near 1 K. J. Chem. Phys. 150, 174301 (2019).

    Article  PubMed  CAS  Google Scholar 

  31. Ketterle, W. & van Druten, N. J. Evaporative cooling of trapped atoms. Adv. At. Mol. Opt. Phys. 37, 181–236 (1996).

    Article  CAS  Google Scholar 

  32. Ni, K. K. et al. Dipolar collisions of polar molecules in the quantum regime. Nature 464, 1324–1328 (2010).

    Article  CAS  PubMed  Google Scholar 

  33. Perreault, W. E., Mukherjee, N. & Zare, R. N. Stark-induced adiabatic Raman passage examined through the preparation of D2 (v = 2, j = 0) and D2 (v = 2, j = 2, m = 0). J. Chem. Phys. 150, 234201 (2019).

    Article  PubMed  CAS  Google Scholar 

  34. Mukherjee, N. & Zare, R. N. Stark-induced adiabatic Raman passage for preparing polarized molecules. J. Chem. Phys. 135, 024201 (2011).

    Article  PubMed  CAS  Google Scholar 

  35. Mukherjee, N., Perreault, W. E. & Zare, R. N. in Frontiers and Advances in Molecular Spectroscopy (ed. Laane, J.) 1–46 (Elsevier, 2018).

  36. Perreault, W. E., Zhou, H., Mukherjee, N. & Zare, R. N. Harnessing the power of adiabatic curve crossing to populate the highly vibrationally excited H2 (v = 7, j = 0) level. Phys. Rev. Lett. 124, 163202 (2020).

    Article  CAS  PubMed  Google Scholar 

  37. 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, 074201 (2014).

    Article  PubMed  CAS  Google Scholar 

  38. Croft, J. F. E., Balakrishnan, N., Huang, M. & Guo, H. Unraveling the stereodynamics of cold controlled HD–H2 collisions. Phys. Rev. Lett. 121, 113401 (2018).

    Article  CAS  PubMed  Google Scholar 

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

    Article  CAS  Google Scholar 

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

    Google Scholar 

  41. Diep, P. & Johnson, J. K. An accurate H2–H2 interaction potential from first principles. J. Chem. Phys. 112, 4465–4473 (2000).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  43. Buck, U., Huisken, F., Kohlhase, A., Otten, D. & Schaefer, J. State resolved rotational excitation in D2 + H2 collisions. J. Chem. Phys. 78, 4439–4450 (1983).

    Article  CAS  Google Scholar 

  44. Chefdeville, S. et al. Appearance of low energy resonances in CO–para-H2 inelastic collisions. Phys. Rev. Lett. 109, 023201 (2012).

    Article  PubMed  CAS  Google Scholar 

  45. Hu, M. G. et al. Direct observation of ultracold bimolecular reactions. Science 366, 1111–1115 (2019).

    Article  CAS  PubMed  Google Scholar 

  46. Even, U. The Even–Lavie valve as a source for high intensity supersonic beam. EPJ Tech. Instrum. 2, 17 (2015).

    Article  Google Scholar 

  47. 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  PubMed  CAS  Google Scholar 

Download references

Acknowledgements

This work was supported by the US Army Research Office through the MURI programme under grant number W911NF-19-1-0283 and the National Science Foundation under grant number PHY- 2110256.

Author information

Authors and Affiliations

  1. Department of Chemistry, Stanford University, Stanford, CA, USA

    Haowen Zhou, William E. Perreault, Nandini Mukherjee & Richard N. Zare

Authors
  1. Haowen Zhou
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. William E. Perreault
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Nandini Mukherjee
    View author publications

    You can also search for this author in PubMed Google Scholar

  4. Richard N. Zare
    View author publications

    You can also search for this author in PubMed Google Scholar

Contributions

Experimental data were taken by H.Z., W.E.P. and N.M., and analysis and calculations were performed by N.M. All authors participated in discussion and writing of the manuscript.

Corresponding authors

Correspondence to Nandini Mukherjee or Richard N. Zare.

Ethics declarations

Competing interests

The authors declare no competing interests.

Peer review

Peer review information

Nature Chemistry thanks Roland Wester and the other, anonymous, reviewer(s) for their contribution to the peer review of this work.

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 Figs. 1 and 2, Tables 1–5 and Discussion.

Source data

Source Data Fig. 1

Normalized, angle-resolved scattering data for both orientations at all delays.

Source Data Fig. 3

Normalized, angle-resolved scattering data for both orientations at all delays.

Source Data Fig. 5

Normalized, angle-resolved scattering data for both orientations at all delays.

Rights and permissions

Reprints and permissions

About this article

Check for updates. Verify currency and authenticity via CrossMark

Cite this article

Zhou, H., Perreault, W.E., Mukherjee, N. et al. Anisotropic dynamics of resonant scattering between a pair of cold aligned diatoms. Nat. Chem. 14, 658–663 (2022). https://doi.org/10.1038/s41557-022-00926-z

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1038/s41557-022-00926-z

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