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Pinpointing the role of geometric phaseDuring chemical reactions, electrons usually rearrange more quickly than nuclei. Thus, theorists often adopt an adiabatic framework that considers vibrational and rotational dynamics within single electronic states. Near the regime where two electronic states intersect, the dynamics get more complicated, and a geometric phase factor is introduced to maintain the simplifying power of the adiabatic treatment. Yuan et al. conducted precise experimental measurements that validate this approach. They studied the elementary H + HD reaction at energies just above the intersection of electronic states and observed angular oscillations in the product-state cross sections that are well reproduced by simulations that include the geometric phase.Science, this issue p. 1289Theory has established the importance of geometric phase (GP) effects in the adiabatic dynamics of molecular systems with a conical intersection connecting the ground- and excited-state potential energy surfaces, but direct observation of their manifestation in chemical reactions remains a major challenge. Here, we report a high-resolution crossed molecular beams study of the H + HD → H2 + D reaction at a collision energy slightly above the conical intersection. Velocity map ion imaging revealed fast angular oscillations in product quantum state–resolved differential cross sections in the forward scattering direction for H2 products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.

It has long been known that there is a conical intersection (CI) between the ground and first excited electronic state in the H 3 system. Its associated geometric phase (GP) effect has been theoretically predicted to exist below the CI since a long time. However, the experimental evidence has not been established yet and its dynamical origin is waiting to be elucidated. Here we report a combined crossed molecular beam and quantum reactive scattering dynamics study of the H+HD → H 2 +D reaction at 2.28 eV, which is well below the CI. The GP effect is clearly identified by the observation of distinct oscillations in the differential cross section around the forward direction. Quantum dynamics theory reveals that the GP effect arises from the phase alteration of a small part of the wave function, which corresponds to an unusual roaming-like abstraction pathway, as revealed by quasi-classical trajectory calculations. The geometric phase effect associated with a conical intersection between the ground and first excited electronic state has been predicted in the H 3 system below the conical intersection energy. The authors, by a crossed molecular beam technique and quantum dynamic calculations, provide experimental evidence and insight into its origin.

Quantum interference between reaction pathways around a conical intersection (CI) is an ultrasensitive probe of detailed chemical reaction dynamics. Yet, for the hydrogen exchange reaction, the difference between contributions of the two reaction pathways increases substantially as the energy decreases, making the experimental observation of interference features at low energy exceedingly challenging. We report in this paper a combined experimental and theoretical study on the H + HD → H 2  + D reaction at the collision energy of 1.72 eV. Although the roaming insertion pathway constitutes only a small fraction (0.088%) of the overall contribution, angular oscillatory patterns arising from the interference of reaction pathways were clearly observed in the backward scattering direction, providing direct evidence of the geometric phase effect at an energy of 0.81 eV below the CI. Furthermore, theoretical analysis reveals that the backward interference patterns are mainly contributed by two distinct groups of partial waves ( J  ~ 10 and J  ~ 19). The well-separated partial waves and the geometric phase collectively influence the quantum reaction dynamics. In a combined experimental and theoretical study of the H + HD → H 2  + D reaction at low collision energy (1.72 eV), the authors obtain detailed information on the quantum reaction dynamics surrounding a conical intersection.

Quantum interference between reaction pathways plays a crucial role in understanding the microscopic mechanisms of chemical reactions. The hydrogen exchange reaction, involving a well-characterized conical intersection, exhibits rich dynamics arising from interference between multiple reactive pathways. Here, we report high-resolution scattering measurements at a collision energy of 2.38 eV, which reveal pronounced sideways angular oscillations in the HD product distribution. Together with exact quantum theoretical calculations, these results provide unambiguous evidence of geometric phase-induced quantum interference in the H + D 2 reaction. Detailed analysis reveals that the observed sideways scattering oscillations, hallmarks of quantum interference, are strongly influenced by transient D–D bond elongation in D 2 reactants. This behavior, in contrast to the reaction with HD, highlights a pronounced isotopic effect and reflects the unique dynamic competition along the roaming insertion pathway. Collectively, these findings underscore the critical role of pathway interference and provide new mechanistic insights into how the isotopic effect modulated the geometric phase in an elementary chemical reaction. When a wave packet traces a conical intersection, its phase must change a sign. The authors show direct experimental and computational evidence of this geometric phase effect for the hydrogen exchange reaction H + D 2  → HD + D.

How the non-reacting moiety of a molecule influences a polyatomic reaction has been a topic of much research interest. Here we present a comprehensive investigation of the D + CH 4  → HD + CH 3 reaction, a benchmark polyatomic elementary reaction with CH 3 as the non-reacting moiety, employing a high-resolution crossed molecular beams apparatus and an accurate seven-dimensional wave packet method. An interesting angular distribution of the CH 3 ( v’  = 1) product umbrella bending vibrational state is observed to scatter more in the sideways direction than the CH 3 ( v’  = 0) one. By monitoring the wave functions on a dividing surface in the transition state region, the CH 3 umbrella bending mode is established as a reporter mode that faithfully reveals how the D atom dynamically approaches CH 4 at different total angular momenta or impact parameters. This discovery of the reporter mode provides an opportunity for the detailed study of polyatomic reaction dynamics. The effects of non-reacting components on polyatomic reactions are still largely unclear. Here, the authors show through a combined experimental and theoretical study of the D + CH 4 reaction that the CH 3 umbrella bending mode serves as a reporter mode, revealing how the D atom dynamically approaches CH 4 .

Accurate measurements of product state-resolved angular distributions are central to fundamental studies of chemical reaction dynamics. Yet, fine quantum-mechanical structures in product angular distributions of a reactive scattering process, such as the fast oscillations in the forward-scattering direction, have never been observed experimentally and the nature of these oscillations has not been fully explored. Here we report the crossed-molecular-beam experimental observation of these fast forward-scattering oscillations in the product angular distribution of the benchmark chemical reaction, H + HD → H2 + D. Clear oscillatory structures are observed for the H2(v′ = 0, j′ = 1, 3) product states at a collision energy of 1.35 eV, in excellent agreement with the quantum-mechanical dynamics calculations. Our analysis reveals that the oscillatory forward-scattering components are mainly contributed by the total angular momentum J around 28. The partial waves and impact parameters responsible for the forward scatterings are also determined from these observed oscillations, providing crucial dynamics information on the transient reaction process.

Quantum interference between reaction pathways plays a crucial role in understanding the microscopic mechanisms of chemical reactions. The hydrogen exchange reaction, involving a well-characterized conical intersection, exhibits rich dynamics arising from interference between multiple reactive pathways. Here, we report high-resolution scattering measurements at a collision energy of 2.38 eV, which reveal pronounced sideways angular oscillations in the HD product distribution. Together with exact quantum theoretical calculations, these results provide unambiguous evidence of geometric phase-induced quantum interference in the H + D reaction. Detailed analysis reveals that the observed sideways scattering oscillations, hallmarks of quantum interference, are strongly influenced by transient D-D bond elongation in D reactants. This behavior, in contrast to the reaction with HD, highlights a pronounced isotopic effect and reflects the unique dynamic competition along the roaming insertion pathway. Collectively, these findings underscore the critical role of pathway interference and provide new mechanistic insights into how the isotopic effect modulated the geometric phase in an elementary chemical reaction.

During chemical reactions, electrons usually rearrange more quickly than nuclei. Thus, theorists often adopt an adiabatic framework that considers vibrational and rotational dynamics within single electronic states. Near the regime where two electronic states intersect, the dynamics get more complicated, and a geometric phase factor is introduced to maintain the simplifying power of the adiabatic treatment. Yuan et al. conducted precise experimental measurements that validate this approach. They studied the elementary H + HD reaction at energies just above the intersection of electronic states and observed angular oscillations in the product-state cross sections that are well reproduced by simulations that include the geometric phase. Science , this issue p. 1289 Precise experiments on an elementary reaction validate inclusion of a phase factor in adiabatic quantum mechanical simulations. Theory has established the importance of geometric phase (GP) effects in the adiabatic dynamics of molecular systems with a conical intersection connecting the ground- and excited-state potential energy surfaces, but direct observation of their manifestation in chemical reactions remains a major challenge. Here, we report a high-resolution crossed molecular beams study of the H + HD → H 2 + D reaction at a collision energy slightly above the conical intersection. Velocity map ion imaging revealed fast angular oscillations in product quantum state–resolved differential cross sections in the forward scattering direction for H 2 products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.

How the non-reacting moiety of a molecule influences a polyatomic reaction has been a topic of much research interest. Here we present a comprehensive investigation of the D + CH  → HD + CH reaction, a benchmark polyatomic elementary reaction with CH as the non-reacting moiety, employing a high-resolution crossed molecular beams apparatus and an accurate seven-dimensional wave packet method. An interesting angular distribution of the CH (v' = 1) product umbrella bending vibrational state is observed to scatter more in the sideways direction than the CH (v' = 0) one. By monitoring the wave functions on a dividing surface in the transition state region, the CH umbrella bending mode is established as a reporter mode that faithfully reveals how the D atom dynamically approaches CH at different total angular momenta or impact parameters. This discovery of the reporter mode provides an opportunity for the detailed study of polyatomic reaction dynamics.

Quantum interference between reaction pathways around a conical intersection (CI) is an ultrasensitive probe of detailed chemical reaction dynamics. Yet, for the hydrogen exchange reaction, the difference between contributions of the two reaction pathways increases substantially as the energy decreases, making the experimental observation of interference features at low energy exceedingly challenging. We report in this paper a combined experimental and theoretical study on the H + HD → H  + D reaction at the collision energy of 1.72 eV. Although the roaming insertion pathway constitutes only a small fraction (0.088%) of the overall contribution, angular oscillatory patterns arising from the interference of reaction pathways were clearly observed in the backward scattering direction, providing direct evidence of the geometric phase effect at an energy of 0.81 eV below the CI. Furthermore, theoretical analysis reveals that the backward interference patterns are mainly contributed by two distinct groups of partial waves (J ~ 10 and J ~ 19). The well-separated partial waves and the geometric phase collectively influence the quantum reaction dynamics.