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.

# 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.

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

## Access options

\$32.00

All prices are NET prices.

## 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).

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

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).

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

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).

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).

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

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).

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).

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

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

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).

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).

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

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).

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

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).

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).

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).

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).

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

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

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

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).

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

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

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

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).

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

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).

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).

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).

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).

## 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.

## Author information

Authors

### Contributions

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.

### Corresponding authors

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

## Ethics declarations

### Competing interests

The authors declare no competing interests.

## Peer review

### Peer review information

Nature Chemistry thanks the anonymous reviewers for their contribution to the peer review of this work.

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

## Supplementary information

### Supplementary Information

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

## Rights and permissions

Reprints and Permissions

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

• Accepted:

• Published:

• Issue Date:

• DOI: https://doi.org/10.1038/s41557-022-00907-2