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Symmetry and the Geometric Phase in Ultracold Chemistry

James F. E. Croft, Jisha Hazra, N. Balakrishnan, Brian K. Kendrick

Published Apr 20, 2017• 0 citations
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Abstract

Quantum reactive scattering calculations are reported for the ultracold hydrogen-exchange reaction and its non-reactive atom-exchange isotopic counterparts, proceeding from excited rotational states. It is shown that while the geometric phase (GP) does not necessarily control the reaction to all final states one can always find final states where it does. For the isotopic counterpart reactions these states can be used to make a measurement of the GP effect by separately measuring the even and odd symmetry contributions, which experimentally requires nuclear-spin final-state resolution. This follows from symmetry considerations that make the even and odd identical-particle exchange symmetry wavefunctions which include the GP locally equivalent to the opposite symmetry wavefunctions which do not. This equivalence reflects the important role discrete symmetries play in ultracold chemistry generally and highlights the key role ultracold reactions can play in understanding fundamental aspects of chemical reactivity.

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The Journal of Physical Chemistry A•Oct 24, 2019•19 citations
Quantum reactive scattering calculations are reported for the ultracold hydrogen-exchange reaction and its non-reactive atom-exchange isotopic counterparts, proceeding from excited rotational states. It is shown that while the geometric phase (GP) does not necessarily control the reaction to all final states one can always find final states where it does. For the isotopic counterpart reactions these states can be used to make a measurement of the GP effect by separately measuring the even and odd symmetry contributions, which experimentally requires nuclear-spin final-state resolution. This follows from symmetry considerations that make the even and odd identical-particle exchange symmetry wavefunctions which include the GP locally equivalent to the opposite symmetry wavefunctions which do not. This equivalence reflects the important role discrete symmetries play in ultracold chemistry generally and highlights the key role ultracold reactions can play in understanding fundamental aspects of chemical reactivity.
Quantum reactive scattering calculations are reported for the ultracold hydrogen-exchange reaction and its non-reactive atom-exchange isotopic counterparts, proceeding from excited rotational states. It is shown that while the geometric phase (GP) does not necessarily control the reaction to all final states, one can always find final states where it does. For the isotopic counterpart reactions, these states can be used to make a measurement of the GP effect by separately measuring the even and odd symmetry contributions, which experimentally requires nuclear-spin final-state resolution. This follows from symmetry considerations that make the even and odd identical-particle exchange symmetry wavefunctions which include the GP locally equivalent to the opposite symmetry wavefunctions which do not. It is shown how this equivalence can be used to define a constant which quantifies the GP effect and can be obtained solely from experimentally observable rates. This equivalence reflects the important role that discrete symmetries play in ultracold chemistry and highlights the key role that ultracold reactions can play in understanding fundamental aspects of chemical reactivity more generally.
Quantum reactive scattering calculations for the hydrogen exchange reaction H+H_{2}(v=4,j=0)→H+H_{2}(v^{'}, j^{'}) and its isotopic analogues are reported for ultracold collision energies. Because of the unique properties associated with ultracold collisions, it is shown that the geometric phase effectively controls the reactivity. The rotationally resolved rate coefficients computed with and without the geometric phase are shown to differ by up to 4 orders of magnitude. The effect is also significant in the vibrationally resolved and total rate coefficients. The dynamical origin of the effect is discussed and the large geometric phase effect reported here might be exploited to control the reactivity through the application of external fields or by the selection of a particular nuclear spin state.
The role of the geometric phase effect on chemical reaction dynamics is explored by examining the hydrogen exchange process in the fundamental H+HD reaction. Results are presented for vibrationally excited HD molecules in the v = 4 vibrational level and for collision energies ranging from 1 μ K to 100 K. It is found that, for collision energies below 3 K, inclusion of the geometric phase leads to dramatic enhancement or suppression of the reaction rates depending on the final quantum state of the HD molecule. The effect was found to be the most prominent for rotationally resolved integral and differential cross sections but it persists to a lesser extent in the vibrationally resolved and total reaction rate coefficients. However, no significant GP effect is present in the reactive channel leading to the D+H 2 product or in the D+H 2 HD+H reaction. A simple interference mechanism involving inelastic (nonreactive) and exchange scattering amplitudes is invoked to account for the observed GP effects. The computed results also reveal a shape resonance in the H+HD reaction near 1 K and the GP effect is found to influence the magnitude of the resonant part of the cross section. Experimental detection of the resonance may allow a sensitive probe of the GP effect in the H+HD reaction.
The role of the geometric phase effect in chemical reaction dynamics has long been a topic of active experimental and theoretical investigations. The topic has received renewed interest in recent years in cold and ultracold chemistry where it was shown to play a decisive role in state-to-state chemical dynamics. We provide a brief review of these developments focusing on recent studies of O + OH and hydrogen exchange in the H + H 2 and D + HD reactions at cold and ultracold temperatures. Non-adiabatic effects in ultracold chemical dynamics arising from the conical intersection between two electronic potential energy surfaces are also briefly discussed. By taking the hydrogen exchange reaction as an illustrative example it is shown that the inclusion of the geometric phase effect captures the essential features of non-adiabatic dynamics at collision energies below the conical intersection.
It is demonstrated that the inclusion of the geometric phase has an important effect on ultracold chemical reaction rates. The effect appears in rotationally and vibrationally resolved integral cross sections as well as cross sections summed over all product quantum states. The effect arises from interference between scattering amplitudes of two reaction pathways: a direct path and a looping path that encircle the conical intersection between the two lowest adiabatic electronic potential energy surfaces. It is magnified when the two scattering amplitudes have comparable magnitude and they scatter into the same angular region which occurs in the isotropic scattering characteristic of the ultracold regime (s-wave scattering). Results are presented for the O + OH → H + O2 reaction for total angular momentum quantum number J = 0-5. Large geometric phase effects occur for collision energies below 0.1 K, but the effect vanishes at higher energies when contributions from different partial waves are included. It is also qualitatively demonstrated that the geometric phase effect can be modulated by applying an external electric field allowing the possibility of quantum control of chemical reactions in the ultracold regime. In this case, the geometric phase plays the role of a "quantum switch" which can turn the reaction "on" or "off".
The results from electronically non-adiabatic and adiabatic quantum reactive scattering calculations are presented for the H + HD( v = 5–9) → H + HD( v ′, j ′) reaction at ultracold collision energies from 10 nK to 60 K. Several experimentally verifiable signatures of the geometric phase are reported in the total and vibrationally and rotationally resolved rate coefficients. Most notable is the predicted 2 orders of magnitude enhancement of the rotationally resolved ultracold rates of odd symmetry relative to those of even symmetry. Prominent shape resonances appear at higher collision energies (100 mK to 20 K), which could be measured experimentally. Significant geometric phase effects are also reported on the resonance energies and lifetimes. In particular, an enhancement (suppression) of the l = 1 ( l = 2) shape resonances for HD( v = 5, 6) is predicted for even symmetry relative to those of odd symmetry.