Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies

Abstract

We report quantum wave packet calculations of state-to-state reaction probabilities and cross sections for the reaction H+H(2)(v(0)=0,j(0)=0)-->H(2)(v,j)+H, at total energies up to 4.5 eV above the ground state potential minimum. The calculations are repeated using (i) the ground electronic state only, (ii) the ground state plus the diagonal non-Born-Oppenheimer correction, (iii) the ground state, diagonal non-Born-Oppenheimer correction and geometric phase (GP), and (iv) both electronic states including all nonadiabatic couplings, using the diabatic potential approach of Mahapatra et al. [J. Phys. Chem. A 105, 2321 (2001)]. The results for calculations (iii) and (iv) are in very close agreement, showing that the upper electronic state makes only a very small contribution to the state-to-state dynamics, even at energies much higher than the conical intersection minimum (at 2.74 eV). At total energies above 3.5 eV, many of the state-to-state reaction probabilities show strong GP effects, indicating that they are dominated by interference between one- and two-transition-state (1-TS and 2-TS) reaction paths. These effects survive the coherent sum over partial waves to produce features in the state-to-state differential cross sections which could be detected in an experiment with an angular resolution of approximately 20 degrees . Efficient dephasing of the interference between the 1-TS and 2-TS contributions causes almost complete cancellation of the GP in the integral cross sections, thus continuing a trend observed at lower energies in earlier work.

Nonadiabatic effects in the H+H2 exchange reaction: Accurate quantum dynamics calculations at a state-to-state level

“…We therefore say that neither the GP effect nor the couplings to the upper electronic state can influence the state-to-state distinguishable-atom ICSs below the total energy of 3.0 eV. Thus, these results confirmed many previous studies of the GP effect in the title reaction, especially a very recent quantum wave packet state-to-state study, 25 where the converged state-to-state integral and DCSs up to a total energy of 4.5 eV were obtained from calculations with and without GP/nonadiabatic effects.…”

“…Given that the present real wave packet calculation employs a different potential matrix from the DMBE potential matrix used in the recent quantum studies, 22,24,25 the agreement with those previous studies in predicting an insignificant role of the GP effect and the upper electronic state in calculating the state-resolved and the non-state-resolved dynamical quantities with total energies up to 3.0 eV, has presented here a useful confirmation of the previous studies, since there was always a lingering doubt that the nonparticipation of the upper state might be an artifact of the DMBE potential.…”

“…Despite the different methodologies employed in those previous calculations to get the dynamics information at a quantum state-to-state level, the strategies to include the nonadiabatic GP effect are quite similar in that either the vector potential [13][14][15]17 of Mead and Truhlar 26 is introduced into the nuclear Hamiltonian followed by the solution of a generalized Born-Oppenheimer equation, or GP basis functions 1,2 are used in the solution of a standard BornOppenheimer equation. In recent works, 22,24,25 a completely different approach has been applied for studying the nonadiabatic effects in the H + D 2 ͑v =0, j =0͒ → HD͑vЈ =3, jЈ͒ +D and H+H 2 ͑v =0, j =0͒ → H 2 ͑vЈ , jЈ͒ + H reactions at either a quantum state-to-state level or a non-state-resolved level. The product rotational distributions over a collision energy range of 1.49-1.85 eV in H + D 2 ͑Ref.…”

“…24͒ have been computed on the adiabatic sheet and the two-coupled sheets of the double many-body expansion ͑DMBE͒ surface of Varandas et al 21 The fully converged state-to-state integral and differential reactive cross sections up to a total energy of 4.5 eV in H + H 2 have also been obtained. 25 In these works, 22,24,25 the Schrödinger equation, formulated using an electronically diabatic representation, is solved numerically by propagating the wave function directly on the two-coupled-electronic states, combining with a reactant-product decoupling method 27,25 for extracting the state-to-state dynamical quantities. Within this kind of dynamics method, the nonadiabatic GP effects are implicitly included through the diabatization angle in the electronically diabatic representation and the nonadiabatic effects such as the couplings to the upper sheet are also included in the reaction mechanism.…”

Simultaneous Measurement of Reactive and Inelastic Scattering: Differential Cross Section of the H + HD → HD(v′, j′) + H Reaction

“…From previous work [30][31][32][33][34][35][36][37][38], we know that the non-exchange-symmetrised nuclear wavefunction does not encircle the CI at the collision energies considered here, which are far below the energetic minimum of the conical intersection (CI) at 2.74 eV. Hence geometric phase (GP) effects did not need to be taken into account in the calculations of f NR and f R .…”