Observation of the geometric phase effect in the H + HD → H ₂ + D reaction

Abstract

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 → 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 H2products at specific rovibrational levels. The experimental results agree with adiabatic quantum dynamical calculations only when the GP effect is included.

Observation of the geometric phase effect in the H+HD→H2+D reaction below the conical intersection

“…Very recently, with a high-resolution time-sliced velocity map imaging (VMI) -CMB apparatus, we detected D products of the H+HD reactions by using the near threshold ionization scheme 21,36 . The product ro-vibrational state-resolved DCS with fast oscillatory structures in the forward angular distributions have been observed at the collision energies of 1.35 and 2.77 eV 21,36 . At 1.35 eV, which is far below the CI, the reaction appears to take place via a simple direct abstraction mechanism, where the GP plays a negligible role.…”

“…In previous work 36 , quantum dynamics calculations using accurate diabatic coupled PESs had to be carried out to exclude the role of the adiabatic electronically excited state since the studied energy was above the CI. This follows an intriguing question: at an energy well below the CI, where the role of the adiabatic electronically excited state could be simply excluded, will there be observable effects due to the GP?…”

High resolution crossed molecular beams study of the H+HD→H2+D reaction

“…Furthermore, since the DCS reveals the most detailed information on a chemical reaction, the observation of the fine oscillations in the forward scattering direction of the H+HD(v=0, j=0)→H 2 (v ′ , j ′ )+D reaction clearly demonstrates the ability of the VMI technique in acquiring high angular and energy resolution DCSs. Very recently, with the VMI and the near threshold ionization method, investigations were also carried out on the H+HD→H 2 (v ′ , j ′ )+D at a higher collision energy of 2.77 eV [34]. The observed fast forward scattering oscillations show very good agreement with the adiabatic theoretical results only with the geometric phase included.…”

Numerical convergence of the Sinc discrete variable representation for solving molecular vibrational states with a conical intersection in adiabatic representation

“…Therefore, we may conclude that the Sinc DVR method works well for a molecular system with CIs in a usual coordinate. Correspondingly, it is not surprising to see that the Sinc DVR method could give accurate state-to-state results for H+H 2 and H+O 2 reaction and its isotopologues in adiabatic representation including the GP and the DBOC terms [34,35,54,59,60]. Finally, we want to emphasise that the GP influences the states of a molecular quantum system much, regardless of the energy of the CI.…”

“…An understanding of the GP effects in a chemical reaction has developed only recently, owing mainly to a series of theoretical investigations and experiments on the hydrogenexchange H+H 2 →H 2 +H reaction and its isotopologues [26, 27, 34, 35, 46, 48, 49, 52−54]. Very recently, using the high-resolution velocity map imaging (VMI) apparatus, in combination with a newly developed stateto-state quantum wavepacket reactive scattering theory using only the reactant Jacobi coordinate including the GP, the GP effect in the H+HD→H 2 +D reaction at a collision energy of 2.77 eV was clearly identified [54]. It was found that the experimentally measured fast angular oscillations around forward scattering of some specific product ro-vibrational states only agree with the theoretical predictions with inclusion of the GP, but is out-of-phase with the theoretical predictions without inclusion of the GP.…”