Interferences are genuine quantum phenomena that appear whenever two seemingly distinct classical trajectories lead to the same outcome. They are common in elastic scattering but are seldom observable in chemical reactions. Here we report experimental measurements of the state-to-state angular distribution for the H + D2 reaction using the ‘photoloc’ technique. For products in low rotational and vibrational states, a characteristic oscillation pattern governs backward scattering. The comparison between the experiments, rigorous quantum calculations and classical trajectories on an accurate potential energy surface allows us to trace the origin of that structure to the quantum interference between different quasiclassical mechanisms, a phenomenon analogous to that observed in the double-slit experiment.
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Aoiz, F. J., Bañares, L. & Herrero, V. J. The H + H2 reactive system. Progress in the study of the dynamics of the simplest reaction. Int. Rev. Phys. Chem. 24, 119–190 (2005).
Jankunas, J. et al. Seemingly anomalous angular distributions in H + D2 reactive scattering. Science 336, 1687–1690 (2012).
Jankunas, J. et al. Is the simplest chemical reaction really so simple? Proc. Natl Acad. Sci. USA 111, 15–20 (2014).
Schnieder, L. et al. Experimental studies and theoretical predictions for the H + D2 → HD + D reaction. Science 269, 207–210 (1995).
Aoiz, F. J. et al. The O(1D) + H2 reaction at 56 meV collision energy: a comparison between quantum mechanical, quasiclassical trajectory, and crossed beam results. J. Chem. Phys. 116, 10692–10703 (2002).
Skodje, R. T. et al. Resonance-mediated chemical reaction: F + HD → HF + D. Phys. Rev. Lett. 85, 1206–1209 (2000).
Bernstein, R. B. Extrema in velocity dependence of total elastic cross sections for atomic beam scattering: relation to di-atom bound states. J. Chem. Phys. 37, 1880–1881 (1962).
Da Silveira, R. Rainbow interference effects in heavy ion elastic scattering. Phys. Lett. B 45, 211–213 (1973).
Ford, K. W. & Wheeler, J. A. Semiclassical description of scattering. Ann. Phys. 7, 259–286 (1959).
Levine, R. D. & Bernstein, R. B. Molecular Reaction Dynamics and Chemical Reactivity (Oxford Univ. Press, 1987).
Gijsbertsen, A., Linnartz, H., Taatjes, C. A. & Stolte, S. Quantum interference as the source of steric asymmetry and parity propensity rules in NO−rare gas inelastic scattering. J. Am. Chem. Soc. 128, 8777–8789 (2006).
Eyles, C. J. et al. Interference structures in the differential cross-sections for inelastic scattering of NO by Ar. Nature Chem. 3, 597–602 (2011).
Nichols, B. et al. Steric effects and quantum interference in the inelastic scattering of NO(X) + Ar. Chem. Sci. 6, 2202–2210 (2015).
McCurdy, C. W. & Miller, W. H. Interference effects in rotational state distributions: propensity and inverse propensity. J. Chem. Phys. 67, 463–468 (1977).
Dai, D. et al. Interference of quantized transition-state pathways in the H + D2 → D + HD chemical reaction. Science 300, 1730–1734 (2003).
Berteloite, C. et al. Kinetics and dynamics of the S(1D2) + H2 → SH + H reaction at very low temperatures and collision energies. Phys. Rev. Lett. 105, 203201 (2010).
Dong, W. et al. Transition-state spectroscopy of partial wave resonances in the F + HD reaction. Science 327, 1501–1502 (2010).
Monks, P. D. D., Connor, J. N. L. & Althorpe, S. C. Nearside−farside and local angular momentum analyses of time-independent scattering amplitudes for the H + D2 (v i = 0, j i = 0) → HD (v f = 3, j f = 0) + D reaction. J. Phys. Chem. A 111, 10302–10312 (2007).
Goldberg, N. T., Zhang, J., Miller, D. J. & Zare, R. N. Corroboration of theory for H + D2 → D + HD (v′ = 3, j′ = 0) reactive scattering dynamics. J. Phys. Chem. A 112, 9266–9268 (2008).
Boothroyd, A. I., Keogh, W. J., Martin, P. G. & Peterson, M. R. A refined H3 potential energy surface. J. Chem. Phys. 104, 7139–7152 (1996).
Greaves, S. J., Murdock, D., Wrede, E. & Althorpe, S. C. New, unexpected, and dominant mechanisms in the hydrogen exchange reaction. J. Chem. Phys. 128, 164306 (2008).
Greaves, S. J., Murdock, D. & Wrede, E. A quasiclassical trajectory study of the time-delayed forward scattering in the hydrogen exchange reaction. J. Chem. Phys. 128, 164307 (2008).
Dobbyn, A. J., McCabe, P., Connor, J. N. L. & Castillo, J. F. Nearside–farside analysis of state-selected differential cross sections for reactive molecular collisions. Phys. Chem. Chem. Phys. 1, 1115–1124 (1999).
Rackham, E. J., Gonzalez-Lezana, T. & Manolopoulos, D. E. A rigorous test of the statistical model for atom–diatom insertion reactions. J. Chem. Phys. 119, 12895–12907 (2003).
Panda, A. N. et al. A state-to-state dynamical study of the Br + H2 reaction: comparison of quantum and classical trajectory results. Phys. Chem. Chem. Phys. 14, 13067–13075 (2012).
Koszinowski, K., Goldberg, N. T., Pomerantz, A. E. & Zare, R. N. Construction and calibration of an instrument for three-dimensional ion imaging. J. Chem. Phys. 125, 133503 (2006).
Jankunas, J., Sneha, M., Zare, R. N., Bouakline, F. & Althorpe, S. C. Disagreement between theory and experiment grows with increasing rotational excitation of HD(v′, j′) product for the H + D2 reaction. J. Chem. Phys. 138, 094310 (2013).
Skouteris, D., Castillo, J. F. & Manolopoulos, D. E. ABC: a quantum reactive scattering program. Comp. Phys. Comm. 133, 128–135 (2000).
Aoiz, F. J., Herrero, V. J. & Sáez Rábanos, V. Quasiclassical state to state reaction cross sections for D + H2(v = 0, j = 0) → HD(v′,j′) + H. Formation and characteristics of short-lived collision complexes. J. Chem. Phys. 97, 7423–7436 (1992).
Bonnet, L. & Rayez, J. C. Quasiclassical trajectory method for molecular scattering processes: necessity of a weighted binning approach. Chem. Phys. Lett. 277, 183–190 (1997).
Bañares, L., Aoiz, F. J., Honvault, P., Bussery-Honvault, B. & Launay, J.-M. Quantum mechanical and quasi-classical trajectory study of the C(1D) + H2 reaction dynamics. J. Chem. Phys. 118, 565–568 (2003).
The authors acknowledge funding by the Spanish Ministry of Economy and Competitiveness (grants CTQ2012-37404-C02 and Consolider Ingenio 2010 CSD2009–00038) and the US National Science Foundation (CHE-1151428).
The authors declare no competing financial interests.
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Jambrina, P., Herráez-Aguilar, D., Aoiz, F. et al. Quantum interference between H + D2 quasiclassical reaction mechanisms. Nature Chem 7, 661–667 (2015). https://doi.org/10.1038/nchem.2295
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