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Journal of Physics B Atomic Molecular and Optical Physics

Geometric phase effects in ultracold hydrogen exchange reaction

Jisha Hazra, Brian K. Kendrick, N. Balakrishnan

Published Sep 22, 2016• 24 citations
Publisher

Abstract

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.

DOI
10.1088/0953-4075/49/19/194004

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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 H3 system has served as a prototype for geometric phase (GP) effects in bimolecular chemical reactions for over three decades. Despite a large number of theoretical and experimental efforts, no conclusive evidence of GP effects in the integral cross section or reaction rate has been presented until recently [B. Kendrick et al., Phys. Rev. Lett. 115, 153201 (2015)]. Here we report a more detailed account of GP effects in the H + H2(v = 4, j = 0) → H + H2(v′, j′) (para-para) reaction rate coefficients for temperatures between 1 μK (8.6 × 10−11 eV) and 100 K (8.6 × 10−3 eV). The GP effect is found to persist in both vibrationally resolved and total rate coefficients for collision energies up to about 10 K. The GP effect also appears in rotationally resolved differential cross sections leading to a very different oscillatory structure in both energy and scattering angle. It is shown to suppress a prominent shape resonance near 1 K and enhance a shape resonance near 8 K, providing new experimentally verifiable signatures of the GP effect in the fundamental hydrogen exchange reaction. The GP effect in the D + D2 and T + T2 reactions is also examined in the ultracold limit and its sensitivity to the potential energy surface is explored.
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 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.
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".
A non-adiabatic quantum dynamics methodology based on a time-independent coupled-channel approach is applied to the fully symmetric H + H2(v=4-8,j=0) → H + H2(v′,j′) reaction for the first time. A two-state diabatic representation is used which includes the effects of the geometric phase (GP) and other non-adiabatic couplings. Ultracold rate coefficients are reported as a function of collision energy between 1μK and 100K. A second set of adiabatic calculations are also performed both with and without the GP. The results for v>4 are reported here for the first time and a new experimentally detectable signature of the GP is discovered associated with the dramatic appearance of an l=1 shape resonance near 1K in the total rate coefficient for v=6 which is absent for v=4 and 5.
Ultracold hydrogen-exchange reactions have long provided a key platform for identifying subtle quantum mechanical effects in triatomic systems. The long-range interactions, diagonal Born-Oppenheimer correction (DBOC), and geometric phase (GP) have been predicted to influence such reactions, yet their individual effects have not been investigated. Here, we investigate the D + H2(v = 4, j = 0) → H + HD reaction using time-dependent wave packet calculations that incorporate a newly constructed long-range potential, DBOC, and a diabatic GP treatment. The inclusion of the accurate long-range interactions substantially alters the cold reaction dynamics by removing spurious short-range barriers and strongly modifying partial-wave resonances, including a pronounced shift and nearly 70% enhancement of the J = 2 resonance. The DBOC produces a modest overall reduction in the reaction rate, whereas the GP introduces the dominant suppression and governs the interference pattern in both total and state-resolved rates. These results demonstrate that the accurate inclusion of long-range interactions, DBOC, and GP is essential for reliably describing ultracold hydrogen-deuterium exchange reactions, clarifying the distinct roles each contribution plays in the reaction dynamics.