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The Journal of Chemical Physics

Ultracold D + H2 ( v = 4, j = 0) reaction dynamics: Long-range interactions, diagonal Born–Oppenheimer correction, and a diabatic geometric phase treatment

Y. D. Fang, Jiayu Huang, Dong Hui Zhang

Published Jan 8, 2026• 2 citations
Publisher

Abstract

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.

DOI
10.1063/5.0304342

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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.
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.
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.
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.
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.
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.