No abstract

Quantum mechanical integral and differential cross sections have been calculated for the title reaction at the three collision energies studied in the 1985 molecular beam experiment of Lee and co-workers, using the new ab initio potential energy surface of Stark and Werner (preceding paper). Although the overall agreement between the calculated and experimental center-of-mass frame angular distributions is satisfactory, there are still some noticeable differences. In particular, the forward scattering of HF(v′=3) is more pronounced in the present calculations than it is in the experiment and the calculations also predict some forward scattering of HF(v′=2). A comparison with the quasiclassical trajectory results of Aoiz and co-workers on the same potential energy surface shows that the forward scattering is largely a quantum mechanical effect in both cases, being dominated by high orbital angular momenta in the tunneling region where the combined centrifugal and potential energy barrier prevents classical trajectories from reacting. The possible role of a reactive scattering resonance in contributing to the quantum mechanical forward scattering is also discussed in some detail.

The inclusion of Quantum Mechanical (QM) effects such as zero point energy (ZPE) and tunneling in simulations of chemical reactions, especially in the case of light atom transfer, is an important problem in computational chemistry. In this respect, the hydrogen exchange reaction and its isotopic variants constitute an excellent benchmark for the assessment of approximate QM methods. In particular, the recently developed ring polymer molecular dynamics (RPMD) technique has been demonstrated to give very good results for bimolecular chemical reactions in the gas phase. In this work, we have performed a detailed RPMD study of the H + H(2) reaction and its isotopologues Mu + H(2), D + H(2) and Heμ + H(2), at temperatures ranging from 200 to 1000 K. Thermal rate coefficients and kinetic isotope effects have been computed and compared with exact QM calculations as well as with quasiclassical trajectories and experiment. The agreement with the QM results is good for the heaviest isotopologues, with errors ranging from 15% to 45%, and excellent for Mu + H(2), with errors below 15%. We have seen that RPMD is able to capture the ZPE effect very accurately, a desirable feature of any method based on molecular dynamics. We have also verified Richardson and Althorpe's prediction [J. O. Richardson and S. C. Althorpe, J. Chem. Phys., 2009, 131, 214106] that RPMD will overestimate thermal rates for asymmetric reactions and underestimate them for symmetric reactions in the deep tunneling regime. The ZPE effect along the reaction coordinate must be taken into account when assigning the reaction symmetry in the multidimensional case.

A general quantum-mechanical method for computing kinetic isotope effects is presented. The method is based on the quantum-instanton approximation for the rate constant and on the path-integral Metropolis-Monte Carlo evaluation of the Boltzmann operator matrix elements. It computes the kinetic isotope effect directly, using a thermodynamic integration with respect to the mass of the isotope, thus avoiding the more computationally expensive process of computing the individual rate constants. The method should be more accurate than variational transition-state theories or the semiclassical instanton method since it does not assume a single tunneling path and does not use a semiclassical approximation of the Boltzmann operator. While the general Monte Carlo implementation makes the method accessible to systems with a large number of atoms, we present numerical results for the Eckart barrier and for the collinear and full three-dimensional isotope variants of the hydrogen exchange reaction H + H 2 → H 2 + H. In all seven test cases, for temperatures between 250 and 600 K, the error of the quantum instanton approximation for the kinetic isotope effects is less than ϳ10%.

The usual theoretical procedure for evaluating the di †erential cross section (DCS) of a molecular collision consists of numerically summing a partial wave series (PWS) for the scattering amplitude. The PWS typically has many numerically signiÐcant terms making it difficult (or impossible) to gain physical insight into the origin of structure in a DCS. A nearsideÈfarside (NF) analysis of a DCS decomposes the PWS scattering amplitude into two subamplitudes : one nearside, the other farside. This decomposition is successful if the magnitudes of the two subamplitudes are never much greater than that of the scattering amplitude itself. It is then often possible to gain a clear physical picture of the origin of structure in a DCS, and hence obtain information on the collision dynamics. A new NF theory called the restricted NF decomposition is described. We present the Ðrst application of this NF decomposition to reactive molecular collisions whose PWS are expanded in a basis set of reduced rotation matrix elements. The reactions whose DCSs we NF analyze are :] HD ] D. matrix elements are employed as input to the NF analyses. DCSs are also computed using a simple semiclassical optical model. We demonstrate that the restricted NF decomposition provides valuable physical insights into the structured angular distributions of these three chemical reactions. Applications of NF methods to elastic and inelastic molecular angular scattering are also described.