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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