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Glory scattering in deeply inelastic molecular collisions

Abstract

For molecular collisions, the deflection of a molecule’s trajectory provides one of the most sensitive probes of the interaction potential and there are general rules of thumb that relate the direction of deflection to precollision conditions. Following intuition, forward scattering results from glancing collisions, whereas near head-on collisions result in back scattering. Here we present the observation of forward scattering in inelastic processes that defies this common wisdom. For deeply inelastic collisions between NO radicals and CO or HD molecules, we observed forward scattering in fully resolved pair-correlated differential cross-sections, despite the low impact parameters that are needed to induce a sufficient energy transfer. We rationalized these findings by extending the textbook model of hard-sphere scattering—taking inelastic energy transfer into account—and attribute the forward scattering to glory-type trajectories caused by attractive forces. This phenomenon, which we refer to as hard-collision glory scattering, is predicted to be ubiquitous. We derive under which conditions hard-collision glory scattering occurs and retrospectively identify such behaviour in previously studied systems.

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Fig. 1: Trajectories and deflection functions predicted from hard-sphere models with hard-sphere radius a for the scattering of NO with HD at a collision energy of 133 cm−1.
Fig. 2: Experimental and simulated scattering images for inelastic scattering.
Fig. 3: Inelastic scattering modelled by CC calculations (solid lines) and semiclassical (dot-dashed lines) calculations for selected inelastic channels in NO−CO and NO−HD collisions at a collision energy of 220 and 133 cm−1, respectively.
Fig. 4: HCGS intensity dependence |db/dχ| at a deflection angle of χ(bHCGS) = 0, normalized to the intensity for backscattering, for various combinations of Vmin/E and ΔE/E.

Data availability

The data that support the findings of this study are available from https://doi.org/10.17026/dans-xh6-fpva.

Code availability

The computer codes used in this study are available from the corresponding authors upon reasonable request.

References

  1. Alagia, M. et al. Dynamics of the simplest chlorine atom reaction: an experimental and theoretical study. Science 273, 1519–1522 (1996).

    Article  CAS  Google Scholar 

  2. Brouard, M. et al. Rotational alignment effects in NO(X) + Ar inelastic collisions: an experimental study. J. Chem. Phys. 138, 104310 (2013).

    Article  CAS  Google Scholar 

  3. Onvlee, J., Vogels, S. N., van der Avoird, A., Groenenboom, G. C. & van de Meerakker, S. Y. T. Resolving rainbows with superimposed diffraction oscillations in NO + rare gas scattering: experiment and theory. New J. Phys. 17, 055019 (2015).

    Article  Google Scholar 

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

    Article  Google Scholar 

  5. 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  Google Scholar 

  6. de Jongh, T. et al. Imaging diffraction oscillations for inelastic collisions of NO radicals with He and D2. J. Chem. Phys. 147, 013918 (2017).

    Article  Google Scholar 

  7. Davis, S. L. M-preserving propensities for rotationally inelastic NH3–He collisions. In the kinematic apse frame. Chem. Phys. 95, 411–416 (1985).

    Article  CAS  Google Scholar 

  8. Khare, V., Kouri, D. J. & Hoffman, D. K. On jz-preserving propensities in molecular collisions. I. Quantal coupled states and classical impulsive approximations. J. Chem. Phys. 74, 2275–2286 (1981).

    Article  Google Scholar 

  9. Hoffman, D. K., Evans, J. W. & Kouri, D. J. The kinematic apse and jz-preserving propensities for nonreactive, dissociative, and reactive polyatomic collisions. J. Chem. Phys. 80, 144–148 (1984).

    Article  CAS  Google Scholar 

  10. 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 

  11. Korsch, H. J. & Schinke, R. A uniform semiclassical sudden approximation for rotationally inelastic scattering. J. Chem. Phys. 73, 1222–1232 (1980).

    Article  CAS  Google Scholar 

  12. Korsch, H. J. & Schinke, R. Rotational rainbows: an IOS study of rotational excitation of hard-shell molecules. J. Chem. Phys. 75, 3850–3859 (1981).

    Article  CAS  Google Scholar 

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

    Article  CAS  Google Scholar 

  14. Royer, A. Semiclassical and classical spectrum in the adiabatic theory of pressure broadening. Phys. Rev. A 4, 499 (1971).

    Article  Google Scholar 

  15. Meijer, A. J. H. M., Groenenboom, G. C. & van der Avoird, A. Semiclassical calculations on the energy dependence of the steric effect for the reactions Ca(1D) + CH3X (jkm = 111) → CaX + CH3 with X = F, Cl, Br. J. Phys. Chem. 100, 16072–16801 (1996).

    Article  CAS  Google Scholar 

  16. Heller, E. J. Time-dependent approach to semiclassical dynamics. J. Chem. Phys. 62, 1544 (1975).

    Article  CAS  Google Scholar 

  17. Aoiz, F. J. et al. A quantum mechanical and quasi-classical trajectory study of the Cl + H2 reaction and its isotopic variants: dependence of the integral cross section on the collision energy and reagent rotation. J. Chem. Phys. 115, 2074 (2001).

    Article  CAS  Google Scholar 

  18. Semenov, A. & Babikov, D. Accurate calculations of rotationally inelastic scattering cross sections using mixed quantum/classical theory. J. Phys. Chem. Lett. 5, 275–278 (2014).

    Article  CAS  Google Scholar 

  19. Semenov, A. & Babikov, D. Mixed quantum/classical theory for molecule–molecule inelastic scattering: derivations of equations and application to N2 + H2 system. J. Phys. Chem. A 119, 12329–12338 (2015).

    Article  CAS  Google Scholar 

  20. Billing, G. D. & Fisher, E. R. VV and VT rate coefficients in N2 by a quantum-classical model. Chem. Phys. 43, 395–401 (1979).

    Article  CAS  Google Scholar 

  21. Billing, G. D. On the applicability of the classical trajectory equations in inelastic scattering theory. Chem. Phys. Lett. 30, 391–393 (1975).

    Article  Google Scholar 

  22. Billing, G. D. Semi-classical calculations of rotational/vibrational transitions in He–H2. Chem. Phys. 9, 359–369 (1975).

    Article  CAS  Google Scholar 

  23. Cacciatore, M. & Billing, G. D. Semiclassical calculation of VV and VT rate coefficients in CO. Chem. Phys. Lett. 58, 395–407 (1981).

    CAS  Google Scholar 

  24. Zhang, X. & Stolte, S. A quasi quantum treatment of the spin orbit state changing and conserving rotationally inelastic NO(X)–He collisions. Chem. Phys. 514, 4–19 (2018).

    Article  CAS  Google Scholar 

  25. Clausius, R. Über die Art der Bewegung, welche wir Wärme nennen. Ann. Phys. 176, 353–380 (1857).

    Article  Google Scholar 

  26. Child, M. S. Molecular Collision Theory (Academic, 1974).

    Google Scholar 

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

    Google Scholar 

  28. Griffiths, D. J. & Schroeter, D. F. Introduction to Quantum Mechanics (Cambridge Univ. Press, 2018).

  29. Gao, Z. et al. Observation of correlated excitations in bimolecular collisions. Nat. Chem. 10, 469–473 (2018).

    Article  CAS  Google Scholar 

  30. Sun, Z.-F. et al. Molecular square dancing in CO–CO collisions. Science 369, 307–309 (2020).

    Article  CAS  Google Scholar 

  31. Lester, W. A. The N Coupled-Channel Problem (Plenum, 1976).

  32. Gao, Z. et al. Correlated energy transfer in rotationally and spin–orbit inelastic collisions of NO(X2Π1/2, j = 1/2f) with O2(\({}^{3}{{{\Sigma }}}_{g}^{-}\)). Phys. Chem. Chem. Phys. 20, 12444–12453 (2018).

    Article  CAS  Google Scholar 

  33. Onvlee, J., Vogels, S. N., von Zastrow, A., Parker, D. H. & van de Meerakker, S. Y. T. Molecular collisions coming into focus. Phys. Chem. Chem. Phys. 16, 15768–15779 (2014).

    Article  CAS  Google Scholar 

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

    Article  Google Scholar 

  35. Eppink, A. T. J. B. & Parker, D. H. Velocity map imaging of ions and electrons using electrostatic lenses: application in photoelectron and photofragment ion imaging of molecular oxygen. Rev. Sci. Instrum. 68, 3477–3484 (1997).

    Article  CAS  Google Scholar 

Download references

Acknowledgements

This work is part of the research programme of the Netherlands Organization for Scientific Research (NWO). S.Y.T.v.d.M. acknowledges support from the European Research Council (ERC) under the European Union’s Seventh Framework Program (FP7/2007-2013/ERC grant agreement no. 335646 MOLBIL) and from the ERC under the European Union’s Horizon 2020 Research and Innovation Program (grant agreement no. 817947 FICOMOL). G.T. acknowledges support from the China Scholarship Council. We thank N. Janssen and A. van Roij for expert technical support. We thank S. Vogels for assistance during the NO−HD experiments. We thank M. van Hemert for the quasiclassical calculations of RET in bimolecular systems. We thank M. van Hemert and D. Parker for fruitful discussions and for carefully reading the manuscript.

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The experiments were carried out by G.T. and Z.G. and supervised by S.Y.T.v.d.M. Theoretical calculations were performed by M.B., A.v.d.A., G.C.G. and T.K. Data analysis and simulations were performed by G.T. and Z.G. The manuscript was written by M.B., S.Y.T.v.d.M. and T.K. with contributions from all the authors. All the authors were involved in the interpretation of the data and the preparation of the manuscript.

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Correspondence to Sebastiaan Y. T. van de Meerakker or Tijs Karman.

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Supplemental material including detailed descriptions of numerical calculations, theoretical models, application to several molecules, and Supplementary Figs. 1–32.

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Besemer, M., Tang, G., Gao, Z. et al. Glory scattering in deeply inelastic molecular collisions. Nat. Chem. 14, 664–669 (2022). https://doi.org/10.1038/s41557-022-00907-2

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