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# Molecular hydrogen interacts more strongly when rotationally excited at low temperatures leading to faster reactions

## Abstract

The role of internal molecular degrees of freedom, such as rotation, has scarcely been explored experimentally in low-energy collisions despite their significance to cold and ultracold chemistry. Particularly important to astrochemistry is the case of the most abundant molecule in interstellar space, hydrogen, for which two spin isomers have been detected, one of which exists in its rotational ground state whereas the other is rotationally excited. Here we demonstrate that quantization of molecular rotation plays a key role in cold reaction dynamics, where rotationally excited ortho-hydrogen reacts faster due to a stronger long-range attraction. We observe rotational state-dependent non-Arrhenius universal scaling laws in chemi-ionization reactions of para-H2 and ortho-H2 by He(23P2), spanning three orders of magnitude in temperature. Different scaling laws serve as a sensitive gauge that enables us to directly determine the exact nature of the long-range intermolecular interactions. Our results show that the quantum state of the molecular rotor determines whether or not anisotropic long-range interactions dominate cold collisions.

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## References

1. 1

Dalgarno, A. in Molecular Hydrogen in Space (eds Combes, F. & Pineau des Forêts, G.) 3 (Cambridge Univ. Press, 2000).

2. 2

Brünken, S. et al. H2D+ observations give an age of at least one million years for a cloud core forming Sun-like stars. Nature 516, 219–221 (2014).

3. 3

Herbst, E. Interstellar processes: ortho/para conversion, radiative association, and dissociative recombination. EPJ Web Conf. 84, 06002 (2015).

4. 4

Smith, I. W. M. Reactions at very low temperatures: gas kinetics at a new frontier. Angew. Chem. Int. Ed. 45, 2842–2861 (2006).

5. 5

Clary, D. C. Fast chemical reactions: theory challenges experiment. Annu. Rev. Phys. Chem. 41, 61–90 (1990).

6. 6

Herbst, E. Three milieux for interstellar chemistry: gas, dust, and ice. Phys. Chem. Chem. Phys. 16, 3344–3359 (2014).

7. 7

Groenenboom, G. C. & Janssen, L. M. C. in Tutorials in Molecular Reaction Dynamics (eds Brouard, M. & Vallance, C.) 392–407 (RSC, 2010).

8. 8

Langevin, P. Une formule fondamentale de théorie cinétique. Ann. Chim. Phys. 5, 245 (1905).

9. 9

Troe, J. Advances in Chemical Physics Vol. 82 (eds Baer, M. & Ng, C.-Y.) 485–529 (Wiley, 1992).

10. 10

Dashevskaya, E. I., Litvin, I., Nikitin, E. E. & Troe, J. Rates of complex formation in collisions of rotationally excited homonuclear diatoms with ions at very low temperature: application to hydrogen isotopes and hydrogen-containing. J. Chem. Phys. 122, 184311 (2005).

11. 11

Olkhov, R. V. & Smith, I. W. M. Rate coefficients for reaction and for rotational energy transfer in collisions between CN in selected rotational levels (X2Σ+, v = 2, N = 0, 1, 6, 10, 15, and 20) and C2H2 . J. Chem. Phys. 126, 134314 (2007).

12. 12

Ospelkaus, S. et al. Quantum-state controlled chemical reactions of ultracold potassium–rubidium molecules. Science 327, 853–857 (2010).

13. 13

Chang, Y.-P. et al. Specific chemical reactivities of spatially separated 3-aminophenol conformers with cold Ca+ ions. Science 342, 98–101 (2013).

14. 14

Marquette, J., Rowe, B. R., Dupeyrat, G., Poissant, G. & Rebrion, C. Ion–polar-molecule reactions: a CRESU study of He+, C+, N+H2O, NH3, at 27, 68 and 163 K. Chem. Phys. Lett. 122, 431–435 (1985).

15. 15

Rowe, B. R., Marquette, J. B., Dupeyrat, G. & Ferguson, E. E. Reactions of He+ and N+ ions with several molecules at 8 K. Chem. Phys. Lett. 113, 403–406 (1985).

16. 16

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

17. 17

Hudson, E., Gilfoy, N., Kotochigova, S., Sage, J. & DeMille, D. Inelastic collisions of ultracold heteronuclear molecules in an optical trap. Phys. Rev. Lett. 100, 203201 (2008).

18. 18

Zahzam, N., Vogt, T., Mudrich, M., Comparat, D. & Pillet, P. Atom–molecule collisions in an optically trapped gas. Phys. Rev. Lett. 96, 023202 (2006).

19. 19

Staanum, P., Kraft, S. D., Lange, J., Wester, R. & Weidemüller, M. Experimental investigation of ultracold atom–molecule collisions. Phys. Rev. Lett. 96, 023201 (2006).

20. 20

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

21. 21

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, 234–238 (2012).

22. 22

Shagam, Y. & Narevicius, E. Sub-kelvin collision temperatures in merged neutral beams by correlation in phase-space. J. Phys. Chem. C 117, 22454–22461 (2013).

23. 23

Jankunas, J., Bertsche, B. & Osterwalder, A. Study of the Ne(3P2) + CH3F electron-transfer reaction below 1 K. J. Phys. Chem. A 118, 3875–3879 (2014).

24. 24

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

25. 25

Siska, P. E. Molecular-beam studies of Penning ionization. Rev. Mod. Phys. 65, 337–412 (1993).

26. 26

Roberge, W. & Dalgarno, A. The formation and destruction of HeH+ in astrophysical plasmas. Astrophys. J. 255, 489 (1982).

27. 27

Lique, F., Li, G., Werner, H.-J. & Alexander, M. H. Communication: non-adiabatic coupling and resonances in the F + H2 reaction at low energies. J. Chem. Phys. 134, 231101 (2011).

28. 28

Holmgren, S. L., Waldman, M. & Klemperer, W. Internal dynamics of van der Waals complexes. I. Born–Oppenheimer separation of radial and angular motion. J. Chem. Phys. 67, 4414 (1977).

29. 29

Dubernet, M.-L. & Hutson, J. M. Atom–molecule van der Waals complexes containing open-shell atoms. I. General theory and bending levels. J. Chem. Phys. 101, 1939 (1994).

30. 30

Kirste, M. et al. Quantum-state resolved bimolecular collisions of velocity-controlled OH with NO radicals. Science 338, 1060–1063 (2012).

31. 31

Makrides, C. et al. Ultracold chemistry with alkali-metal–rare-earth molecules. Phys. Rev. A 91, 012708 (2015).

32. 32

Buckingham, A. D. Molecular quadrupole moments. Q. Rev. Chem. Soc. 13, 183 (1959).

33. 33

Gorin, E. Photolysis of aldehydes and ketones in the presence of iodine vapor. J. Chem. Phys. 7, 256 (1939).

34. 34

Veatch, G. & Oskam, H. Collision processes occurring in decaying plasmas produced in helium–hydrogen mixtures. Phys. Rev. A 8, 389–396 (1973).

35. 35

Jachymski, K., Krych, M., Julienne, P. S. & Idziaszek, Z. Quantum-defect model of a reactive collision at finite temperature. Phys. Rev. A 90, 042705 (2014).

36. 36

Gribakin, G. & Flambaum, V. Calculation of the scattering length in atomic collisions using the semiclassical approximation. Phys. Rev. A 48, 546–553 (1993).

37. 37

Sadeghpour, H. R. et al. Collisions near threshold in atomic and molecular physics. J. Phys. B 33, R93–R140 (2000).

38. 38

Wigner, E. On the behavior of cross-sections near thresholds. Phys. Rev. 73, 1002–1009 (1948).

39. 39

Gao, B. Universal model for exoergic bimolecular reactions and inelastic processes. Phys. Rev. Lett. 105, 263203 (2010).

40. 40

Nesbitt, D. J. High-resolution infrared spectroscopy of weakly bound molecular complexes. Chem. Rev. 88, 843–870 (1988).

41. 41

Even, U., Jortner, J., Noy, D., Lavie, N. & Cossart-Magos, C. Cooling of large molecules below 1 K and He clusters formation. J. Chem. Phys. 112, 8068 (2000).

42. 42

Wiley, W. C. & McLaren, I. H. Time-of-flight mass spectrometer with improved resolution. Rev. Sci. Instrum. 26, 1150 (1955).

43. 43

Luria, K., Lavie, N. & Even, U. Dielectric barrier discharge source for supersonic beams. Rev. Sci. Instrum. 80, 104102 (2009).

44. 44

Metcalf, H. J. & van der Straten, P. Laser Cooling and Trapping (Springer, 1999).

45. 45

Martin, D. W., Weiser, C., Sperlein, R. F., Bernfeld, D. L. & Siska, P. E. Collision energy dependence of product branching in Penning ionization: He*(21S, 23S) + H2, D2, and HD. J. Chem. Phys. 90, 1564 (1989).

46. 46

Pratt, S. T., Dehmer, P. M. & Dehmer, J. L. Photoionization of excited molecular states. H2 C 1Πu . Chem. Phys. Lett. 105, 28–33 (1984).

47. 47

Hapka, M., Chałasiński, G., Kłos, J. & Żuchowski, P. S. First-principle interaction potentials for metastable He(3S) and Ne(3P) with closed-shell molecules: application to Penning-ionizing systems. J. Chem. Phys. 139, 014307 (2013).

48. 48

Hapka, M., Żuchowski, P. S., Szczęśniak, M. M. & Chałasiński, G. Symmetry-adapted perturbation theory based on unrestricted Kohn–Sham orbitals for high-spin open-shell van der Waals complexes. J. Chem. Phys. 137, 164104 (2012).

49. 49

Bishop, D. M. & Pipin, J. Dipole, quadrupole, octupole, and dipole–octupole polarizabilities at real and imaginary frequencies for H, He, and H2 and the dispersion-energy coefficients for interactions between them. Int. J. Quantum Chem. 45, 349–361 (1993).

50. 50

Werner, H.-J. et al. MOLPRO, version 2012.1; http://www.molpro.net

51. 51

Aidas, K. et al. The Dalton quantum chemistry program system. Wiley Interdiscip. Rev.: Comput. Mol. Sci. 4, 269 (2014).

52. 52

Averbukh, V. & Cederbaum, L. S. Ab initio calculation of interatomic decay rates by a combination of the Fano ansatz, Green's-function methods, and the Stieltjes imaging technique. J. Chem. Phys. 123, 204107 (2005).

53. 53

Gokhberg, K., Averbukh, V. & Cederbaum, L. S. Decay rates of inner-valence excitations in noble gas atoms. J. Chem. Phys. 126, 154107 (2007).

54. 54

Kopelke, S., Gokhberg, K., Averbukh, V., Tarantelli, F. & Cederbaum, L. S. Ab initio interatomic decay widths of excited states by applying Stieltjes imaging to Lanczos pseudospectra. J. Chem. Phys. 134, 094107 (2011).

55. 55

Extensible Computational Chemistry Environment Basis Set Database, Version 02/25/04 (Molecular Science Computing Facility, Environmental and Molecular Sciences Laboratory, Pacific Northwest Laboratory).

56. 56

Kaufmann, K., Baumeister, W. & Jungen, M. Universal Gaussian basis sets for an optimum representation of Rydberg and continuum wavefunctions. J. Phys. B 22, 2223–2240 (1989).

57. 57

Langhoff, P. in Electron–Molecule and Photon–Molecule Collisions (eds Rescigno, T., McKoy, V. & Schneider, B.) 183 (Plenum, 1979).

58. 58

Aquilante, F. et al. MOLCAS 7: the next generation. J. Comput. Chem. 31, 224–247 (2010).

## Acknowledgements

The authors thank R. Kosloff and R. Moszynski for discussions as well as O. Tal and D. Rakhmilevitch for advice and help in the generation of para-hydrogen. This research was made possible, in part, by the historic generosity of the Harold Perlman family. The authors acknowledge financial support from the European Commission through ERC grant EU-FP7-ERC-CoG 1485 QuCC (Y.S., A.K., E.N.), from the Alexander von Humboldt Foundation (W.S.), from the Lee Family Foundation (R.Y.) and from the UK's Engineering and Physical Sciences Research Council (V.A., R.Y.) through the Career Acceleration Fellowship (award EP/H003657/1) and the Programme Grant on Attosecond Dynamics (award EP/I032517), as well as from the Deutsche Forschungsgemeinschaft through Research Unit 1789 (V.A.).

## Author information

Authors

### Contributions

The experimental work and data analysis were carried out by Y.S., A.K. and E.N. Ab initio potential surfaces and interaction strengths were calculated by W.S. The ionization widths were calculated by R.Y. and V.A. All authors contributed to the discussion of experimental results, derivation of the theoretical model and writing of the manuscript.

### Corresponding author

Correspondence to Edvardas Narevicius.

## Ethics declarations

### Competing interests

The authors declare no competing financial interests.

## Supplementary information

### Supplementary information

Supplementary information (PDF 247 kb)

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Shagam, Y., Klein, A., Skomorowski, W. et al. Molecular hydrogen interacts more strongly when rotationally excited at low temperatures leading to faster reactions. Nature Chem 7, 921–926 (2015). https://doi.org/10.1038/nchem.2359

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