Foudhil Bouakline

Seemingly Anomalous Angular Distributions in H + D2 Reactive Scattering

Spinning Backwards When atoms and molecules collide, the energy embedded in the reaction products gets distributed among translations, vibrations, and rotations. Decades of meticulous experiments have mapped out the quantum mechanical rules underlying this distribution process, particularly in simple systems comprising just three light atoms. Now, Jankunas et al. (p. 1687; see the Perspective by Yang et al.) describe a previously unappreciated wrinkle in the elementary reaction of an H atom with deuterium. Typically, products with low vibrational and rotational excitation tend to scatter backwards from the collision, whereas the spinning products scatter sideways. Above a certain vibrational threshold, however, spinning HD products were observed to scatter backwards. An elementary chemical reaction manifests unexpectedly complex rotational dynamics. When a hydrogen (H) atom approaches a deuterium (D2) molecule, the minimum-energy path is for the three nuclei to line up. Consequently, nearly collinear collisions cause HD reaction products to be backscattered with low rotational excitation, whereas more glancing collisions yield sideways-scattered HD products with higher rotational excitation. Here we report that measured cross sections for the H + D2 → HD(v′ = 4, j′) + D reaction at a collision energy of 1.97 electron volts contradict this behavior. The anomalous angular distributions match closely fully quantum mechanical calculations, and for the most part quasiclassical trajectory calculations. As the energy available in product recoil is reduced, a rotational barrier to reaction cuts off contributions from glancing collisions, causing high-j′ HD products to become backward scattered.

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

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.

Effect of the geometric phase on nuclear dynamics at a conical intersection: Extension of a recent topological approach from one to two coupled surfaces

A recent approach [S. C. Althorpe, J. Chem. Phys. 124, 084105 (2006)] for interpreting geometric phase (GP) effects in a nuclear wave function confined to the lower of two conically intersecting potential energy surfaces is extended to treat coupled dynamics on both surfaces. The approach is exact, and uses simple topology to separate the wave function into contributions from Feynman paths that wind different numbers of times, and in different senses, around the conical intersection. We derive the approach first, by mapping the time-dependent wave packet describing the coupled dynamics onto a double space, and second, by classifying the Feynman paths within a time-ordered expansion of the path integral. The approach is demonstrated numerically for a simple Exe Jahn-Teller system and for a model of the (1)B(1)-S(0) intersection in pyrrole. The approach allows one to investigate and interpret the effect of the GP on population transfer between the surfaces, and also to extract contributions to the coupled nuclear wave function from different reaction paths.

Is the simplest chemical reaction really so simple

Modern computational methods have become so powerful for predicting the outcome for the H + H2 → H2 + H bimolecular exchange reaction that it might seem further experiments are not needed. Nevertheless, experiments have led the way to cause theorists to look more deeply into this simplest of all chemical reactions. The findings are less simple.

Vibrationally inelastic H + D2 collisions are forward-scattered

We have measured differential cross sections (DCSs) for the vibrationally inelastic scattering process H + o-D2(v = 0, j = 0,2) → H + o-D2(v′ = 1–4, j′ even). Several different collision energies and nearly the entire range of populated product quantum states are studied. The products are dominantly forward-scattered in all cases. This behavior is the opposite of what is predicted by the conventional textbook mechanism, in which collisions at small impact parameters compress the bond and cause the products to recoil in the backward direction. Recent quasiclassical trajectory (QCT) calculations examining only the o-D2(v′ = 3, j′) products suggest that vibrationally inelastic scattering is the result of a frustrated reaction in which the D—D bond is stretched, but not broken, during the collision. These QCT calculations provide a qualitative explanation for the observed forward-scattering, but they do not agree with experiments at the lowest values of j′. The present work shows that quantum mechanical calculations agree closely with experiments and expands upon previous results to show that forward-scattering is universally observed in vibrationally inelastic H + D2 collisions over a broad range of conditions.

Strong geometric-phase effects in the hydrogen-exchange reaction at high collision energies: II. Quasiclassical trajectory analysis

Recent calculations on the hydrogen-exchange reaction [Bouakline et al., J. Chem. Phys. 128, 124322 (2008)], have found strong geometric phase (GP) effects in the state-to-state differential cross-sections (DCS), at energies above the energetic minimum of the conical intersection (CI) seam, which cancel out in the integral cross-sections (ICS). In this article, we explain the origin of this cancellation and make other predictions about the nature of the reaction mechanisms at these high energies by carrying out quasiclassical trajectory (QCT) calculations. Detailed comparisons are made with the quantum results by splitting the quantum and the QCT cross-sections into contributions from reaction paths that wind in different senses around the CI and that scatter the products in the nearside and farside directions. Reaction paths that traverse one transition state (1-TS) scatter their products in just the nearside direction, whereas paths that traverse two transition states (2-TS) scatter in both the nearside and farside directions. However, the nearside 2-TS products scatter into a different region of angular phase-space than the 1-TS products, which explains why the GP effects cancel out in the ICS. Analysis of the QCT results also suggests that two separate reaction mechanisms may be responsible for the 2-TS scattering at high energies.

Influence of the Geometric Phase and Non-Adiabatic Couplings on the Dynamics of the H+H(2) Molecular System

The effects of the geometric phase and non-adiabatic coupling induced by the conical intersection between the two lowest electronic potential energy surfaces are investigated for the H + H2 collision and H3 predissociation. The strongest effect of the geometric phase at all collision energies is a significant change in the ortho → ortho and para → para differential cross-sections, which is due to a sign change in the interference between reactive and non reactive contributions. This is caused by the indistinguishability of the three interacting atoms. At high energies (3.5 eV above collision threshold and more), a significant dynamical effect appears in the differential cross-sections. This effect is related to a sign change in the interference between two dynamical paths (direct and looping contributions) connecting reagents to products. Both these symmetry and dynamical effects almost completely disappear in the integral cross-sections. Electronic non-adiabatic couplings are efficient in turning the bound states supported by the cone of the first excited electronic adiabatic potential into resonances which have significant effects only on transitions between excited reagents and products. The study of the decay of these resonances provides clues for the understanding of the experimental results in the predissociation of Rydberg states of H3.

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

Abstract The H + HD → HD(ν′, j′) + H reaction has been studied experimentally and theoretically. Differential cross sections of HD(ν′, j′) products have been measured by means of a Photoloc technique and calculated using a time-independent quantum mechanical theory. Three product states: HD(ν′ = 1, j′ = 8) at a collision energy (Ecoll) of 1.97 eV; HD(ν′ = 2, j′ = 3) at Ecoll = 1.46 eV; and HD(ν′ = 2, j′ = 5) at Ecoll = 1.44 eV, show very good agreement between theory and experiment. The other two, highly rotationally excited states studied, HD(ν′ = 1, j′ = 12) and HD(ν′ = 1, j′ = 13) at Ecoll = 1.97 eV, exhibit a noticeable disagreement between experiment and theory. This is consistent with our most recent findings on the H + D2 → HD(ν′, j′) + D reaction, wherein the differential cross sections of HD(ν′ = 1, high j′) product states showed similar disagreement between the experiment and theory [J. Jankunas, M. Sneha, R. N. Zare, F. Bouakline, and S. C. Althorpe, J. Chem. Phys. 138 (2013) 094310]. In all five cases, however, we find overwhelming support that the experimental signal is a sum of reactive and inelastic scattering events. The interference term escapes detection, frustrating our attempt to observe geometric phase effects. Nevertheless, this work constitutes a first experimental example in which the indistinguishability of reactive and inelastic channels must be taken into account explicitly when constructing differential cross sections.