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.

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.

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.

When a hydrogen (H) atom approaches a deuterium (D(2)) 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 + D(2) → 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.

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We have measured differential cross sections (DCSs) for the HD (v(')=1,j(')=2,6,10) products of the H+D(2) exchange reaction at five different collision energies in the range 1.48< or =E(coll)< or =1.94 eV. The contribution from the less energetic H atoms formed upon spin-orbit excitation of Br in the photolysis of the HBr precursor is taken into account for two collision energies, E(coll)=1.84 and 1.94 eV, allowing us to disentangle the two different channels. The measured DCSs agree well with new time-dependent quantum-mechanical calculations. As the product rotational excitation increases, the DCSs shift from backward to sideward scattering, as expected. We also find that the shapes of the DCSs show only a small overall dependence on the collision energy, with a notable exception occurring for HD (v(')=1,j(')=2), which appears bimodal at high collision energies. We suggest that this feature results from both direct recoil and indirect scattering from the conical intersection.

We investigate methods for filtering reaction mechanisms in the angular scattering of the state-to-state reaction, H + D(2)(v(i) = 0, j(i) = 0, m(i) = 0) --> HD(v(f) = 3, j(f) = 0, m(f) = 0) + D, where v(i), j(i), and m(i) and v(f), j(f), and m(f) are initial and final vibrational, rotational, and helicity quantum numbers, respectively. The input to our filtrations is a new set of accurate quantum scattering matrix elements for total energies in the range 1.52-2.50 eV (in steps of 0.01 eV) and for total angular momentum quantum numbers in the range, 0-40, in steps of unity. We filter reaction mechanisms in both the energy domain and the time domain. The time-domain calculations employ the plane wave packet formulation of time-dependent scattering. The theoretical tools used are nearside-farside (NF) analysis of partial wave series for scattering amplitudes, together with NF local angular momentum (LAM) theory. An energy-domain LAM analysis reveals the existence of an important dynamical feature in the N scattering, a "trench" which bisects the (energy, angle) plane. We use the location of this trench to approximately filter two reaction mechanisms. Transformation to the time domain demonstrates that the two reaction mechanisms correspond to direct and delayed (by about 25 fs) scattering. Further analysis, including filtration in the time domain, shows that the pronounced LAM trench arises from the interference of the energy-domain analogues of the time-direct and time-delayed scattering. Our theory and results provide the first successful demonstration of reaction mechanism filtering carried out directly in the (energy, angle) domain. The calculations and results in this paper extend and complement earlier research reported by Monks, Connor, and Althorpe (Monks, P. D. D.; Connor, J. N. L.; Althorpe, S. C. J. Phys. Chem. A 2006, 110, 741; J. Phys. Chem. A 2007, 111, 10302).

An attempt has been made to measure the theoretically predicted manifestation of a geometric phase in the differential cross section for the H + HD → HD(v' = 2, j' = 5) + H reaction at a center-of-mass collision energy of 1.44 eV (33.2 kcal∕mol). Minute oscillatory differences between calculated differential cross sections that take into account and ignore the effect of geometric phase have proven to be beyond our experimental resolution in spite of the collection of more than 44,000 ions.