Rex T. Skodje

Observation of Feshbach resonances in the F + H2 --> HF + H reaction.

Reaction resonances, or transiently stabilized transition-state structures, have proven highly challenging to capture experimentally. Here, we used the highly sensitive H atom Rydberg tagging time-of-flight method to conduct a crossed molecular beam scattering study of the F + H2 → HF + H reaction with full quantum-state resolution. Pronounced forward-scattered HF products in the v′ = 2 vibrational state were clearly observed at a collision energy of 0.52 kcal/mol; this was attributed to both the ground and the first excited Feshbach resonances trapped in the peculiar HF(v′ = 3)-H′ vibrationally adiabatic potential, with substantial enhancement by constructive interference between the two resonances.

Observation of a transition state resonance in the integral cross section of the F+HD reaction

We have studied the reaction F+HD at low collision energies using a combination of experimental and theoretical methods. Clear evidence for a reactive resonance is found in the integral cross section for the reactive channel F+HD→HF+D. Using a crossed molecular beam apparatus, the total reactive cross sections for the HF+D and DF+H channels were obtained in the collision energy range of 0.2–5 kcal/mol. In addition, Doppler profiles were obtained over this range of energies, which provide information about the angularly resolved distribution of final vibrational states. The cross section shows a distinctive steplike feature near 0.5 kcal/mol. Furthermore, the Doppler profiles reveal a dramatic change in the angular distribution of products over a narrow energy range centered at 0.5 kcal/mol. This feature is shown to arise from a reactive resonance localized near the transition state. Theoretical scattering calculations have been carried out using the Stark–Werner potential energy surface, which accurately ...

Vibrationally adiabatic models for reactive tunneling

The approximation of vibrational adiabaticity in curvilinear natural collision coordinates is investigated for tunneling in three‐atom collinear reactions. A validity criterion is derived which limits the adiabatic approximation to systems with small reaction‐path curvature. A general formalism is developed for systems which satisfy this criterion. A one‐dimensional Schrodinger equation is proposed which is sufficiently flexible so as to be adaptable to many different models of tunneling. We present three new methods for including reaction‐path curvature effects on multidimensional tunneling in reactive systems: a method based on a quantum mechanical vibrational average (VA) over degrees of freedom transverse to the minimum‐energy path; a method (called DA for dynamical‐path vibrational‐ average) that includes internal centrifugal effects in the description of the transverse vibrational motion (in this method the vibrational average is approximated as a quantal vibrational average about the dynamical path...

Forward scattering due to slow-down of the intermediate in the H + HD --> D + H(2) reaction.

Quantum dynamical processes near the energy barrier that separates reactants from products influence the detailed mechanism by which elementary chemical reactions occur. In fact, these processes can change the product scattering behaviour from that expected from simple collision considerations, as seen in the two classical reactions F + H2 → HF + H and H + H2 → H2 + H and their isotopic variants. In the case of the F + HD reaction, the role of a quantized trapped Feshbach resonance state had been directly determined, confirming previous conclusions that Feshbach resonances cause state-specific forward scattering of product molecules. Forward scattering has also been observed in the H + D2 → HD + D reaction and attributed to a time-delayed mechanism. But despite extensive experimental and theoretical investigations, the details of the mechanism remain unclear. Here we present crossed-beam scattering experiments and quantum calculations on the H + HD → H2 + D reaction. We find that the motion of the system along the reaction coordinate slows down as it approaches the top of the reaction barrier, thereby allowing vibrations perpendicular to the reaction coordinate and forward scattering. The reaction thus proceeds, as previously suggested, through a well-defined ‘quantized bottleneck state’ different from the trapped Feshbach resonance states observed before.

The semiclassical quantization of nonseparable systems using the method of adiabatic switching

A method for the semiclassical quantization of multidimensional bound systems based on the adiabatic hypothesis is examined. The validity criteria for multidimensional adiabaticity is discussed. It is demonstrated that the quantizing orbits for nonseparable systems can often be obtained by propagating a single trajectory from well defined initial conditions with a time‐dependent Hamiltonian for ∼100 periods. Numerical examples using systems with up to five degrees of freedom are presented and show generally excellent results. It is shown that this method can be used to quantize some states using chaotic trajectories.

Geometric investigation of low-dimensional manifolds in systems approaching equilibrium

Many systems approach equilibrium slowly along surfaces of dimension smaller than the original dimensionality. Such systems include coupled chemical kinetics and master equations. In the past the steady state approximation has been used to estimate these lower dimensional surfaces, commonly referred to as “manifolds,” and thus reduce the dimensionality of the system which needs to be studied. However, the steady state approximation is often inaccurate and sometimes difficult to define unambiguously. In recent years two methods have been proposed to go beyond the steady state approximation to improve the accuracy of dimension reduction. We investigate these methods and suggest significant modifications to one of them to allow it to be used for the generation of low-dimensional manifolds in large systems. Based on the geometric investigations, two other approaches are suggested which have some advantages over these two methods for the cases studied here. All four approaches are geometric and offer advantage...

Phase change between separatrix crossings

Abstract The change of the crossing parameter (essentially the phase) between separatrix crossings is calculated for Hamiltonian systems with one degree of freedom and slow time dependence. This completes the calculation of the map for an arbitrary sequence of separatrix crossings. The change of the crossing parameter is used to calculate the retrapping probability. It is found that, even in the limit of infinitely slow time dependence, correlations persist between the separatrix crossings, and corrections to the usual zero-order adiabatic approximation must be included. Comparison with numerical experiments show that the result derived here is accurate for quite large values of the slowness parameter.

Localized Gaussian wave packet methods for inelastic collisions involving anharmonic oscillators

We examine several methods of implementing the time‐dependent Gaussian wave packet method of Heller for collinear atom–molecule collisions involving anharmonic vibrators. We show that reasonably accurate results can be obtained with a procedure involving uncoupled frozen Gaussians with phases evaluated along classical trajectories. Although this method is much more accurate than the standard quasiclassical trajectory method, it involves about the same computational effort.

Spectral quantization of transition state dynamics for the three-dimensional H+H2 reaction

Applying a spectral quantization method, we find the positions and widths of 32 transition state resonances in the three‐dimensional reaction H+H2 with J=0. The assignment of many of the resonances appears to follow asymmetric stretch and bend progressions for a linear triatomic molecule.

A globally smooth ab initio potential surface of the 1 A′ state for the reaction S(1D)+H2

A procedure based on the reproducing kernel Hilbert space (RKHS) interpolation method has been implemented to produce a globally smooth potential energy surface (PES) for the 1 A′ state of the S(1D)+H2 reaction from a set of accurate ab initio data, calculated at the multireference configuration interaction level with augmented polarized quadruple-zeta basis sets and arranged on a three-dimensional regular full grid in the Jacobi coordinates. The procedure includes removing a small number of questionable ab initio data points, implementing a recently developed technique for efficiently handling a partially filled grid, and adopting a sequence of regularizations for attaining additional smoothness. The resulting RKHS PES is analytic, first-order differentiable, and fast to evaluate. Quasiclassical trajectory calculations have been performed and compared with the results based on a recent hybrid PES obtained from a combination of the RKHS interpolation in the entrance channel and Murrell–Carter (MC)-type fi...