Centrifugal-sudden hyperspherical study of Cl + HCl → ClH + Cl reaction dynamics on ‘tight-bend’ and ‘loose-bend’ potential energy surfaces

Competing Dynamical Mechanisms in Inelastic Collisions of H + HF

The dynamics of inelastic collisions between HF and H has been investigated in detail by means of time-independent quantum mechanical calculations on the LWA-78 potential energy surface ( Li , G. ; et al. J. Chem. Phys. 2007 , 127 , 174302 ). Reaction probabilities, differential cross sections, and three-vector correlations have been calculated and analyzed. Our results show that there are two competing collision mechanisms that correlate with low and high impact parameters and show very different stereodynamical preferences. The mechanism promoted by high impact parameters is the only one present at low collision energies. We also observe the presence of an apparent threshold in the inelastic cross section for relatively high initial HF rotational quantum numbers, which is associated with the larger energy difference between adjacent rotational quantum states with increasing rotation.

Angular Scattering Dynamics of the CH4 + Cl → CH3 + HCl Reaction Using Nearside-Farside, Local Angular Momentum, and Resummation Theories

The differential cross section (DCS) for the CH4 + Cl → CH3 + HCl reaction is studied at six total energies where all of the species are in their ground states. The scattering (S) matrix elements have been calculated by the rotating line umbrella method for a dual-level ab initio analytic potential energy surface. We make the first application to this reaction of nearside-farside (NF) and local angular momentum (LAM) techniques, including resummation orders (r) of 0, 1, 2, and 3 for the partial-wave series representation of the full scattering amplitude. We find that resummation usually cleans the NF r = 0 DCSs of unphysical oscillations, especially at small angles. This cleaning effect is typically most pronounced when changing from no resummation (r = 0) to r = 1; further resummations from r = 1 to r = 2 and from r = 2 to r = 3 have smaller effects. The NF DCS analyses show that the reaction is N-dominated at sideward and large angles, whereas at small angles there are oscillations caused by NF interference. The NF LAM analysis provides consistent and complementary information, in particular for the total angular momenta that contribute to the reaction at different scattering angles. The NF analyses also provide justification for simpler N-dominant dynamical theories such as the semiclassical optical model, which provides an explanation for the distorted mirror image effect for the moduli of the S matrix elements and the DCSs, as well as the use of a hard-sphere DCS over limited angular ranges.

State-to-state quantum reactive scattering for four-atom chemical reactions: Differential cross section for the H+H2O→H2+OH abstraction reaction

The time-dependent wave packet method was extended to calculate the state-to-state differential cross section for the title four-atom abstraction reaction with H2O in the ground rovibrational state. One spectator OH bond length was fixed in the study, but the remaining five degrees of freedom were treated exactly. It was found that (a) the differential cross section changes from being strongly backward peaked at low collision energy to sideward scattering at E = 1.4 eV, and (b) the rotational state-resolved differential cross section for H2 differs substantially from that for OH.

Theories of reactive scattering

This paper is an overview of the theory of reactive scattering, with emphasis on fully quantum mechanical theories that have been developed to describe simple chemical reactions, especially atom-diatom reactions. We also describe related quasiclassical trajectory applications, and in all of this review the emphasis is on methods and applications concerned with state-resolved reaction dynamics. The review first provides an overview of the development of the theory, including a discussion of computational methods based on coupled channel calculations, variational methods, and wave packet methods. Choices of coordinates, including the use of hyperspherical coordinates are discussed, as are basis set and discrete variational representations. The review also summarizes a number of applications that have been performed, especially the two most comprehensively studied systems, H+H2 and F+H2, along with brief discussions of a large number of other systems, including other hydrogen atom transfer reactions, insertion reactions, electronically nonadiabatic reactions, and reactions involving four or more atoms. For each reaction we describe the method used and important new physical insight extracted from the results.

Local angular momentum-local impact parameter analysis: derivation and properties of the fundamental identity, with applications to the F+H2, H+D2, and Cl+HCl chemical reactions

The technique of local angular momentum-local impact parameter (LAM-LIP) analysis has recently been shown to provide valuable dynamical information on the angular scattering of chemical reactions under semiclassical conditions. The LAM-LIP technique exploits a nearside-farside (NF) decomposition of the scattering amplitude, which is assumed to be a Legendre partial wave series. In this paper, we derive the "fundamental NF LAM identity," which relates the full LAM to the NF LAMs (there is a similar identity for the LIP case). Two derivations are presented. The first uses complex variable techniques, while the second exploits an analogy between the motion of the scattering amplitude in the Argand plane with changing angle and the classical mechanical motion of a particle in a plane with changing time. Alternative forms of the fundamental LAM-LIP identity are described, one of which gives rise to a CLAM-CLIP plot, where CLAM denotes (Cross section) x LAM and CLIP denotes (Cross section) x LIP. Applications of the NF LAM theory, together with CLAM plots, are reported for state-to-state transitions of the benchmark reactions F+H2-->FH+H, H+D2-->HD+D, and Cl+HCl-->ClH+Cl, using as input both numerical and parametrized scattering matrix elements. We use the fundamental LAM identity to explain the important empirical observation that a NF cross section analysis and a NF LAM analysis provide consistent (and complementary) information on the dynamics of chemical reactions.

Theory of Time-Dependent Reactive Scattering: Cumulative Time-Evolving Differential Cross Sections and Nearside−Farside Analyses of Time-Dependent Scattering Amplitudes for the H + D2 → HD + D Reaction

Nearside-farside (NF) theory, originally developed in the energy domain for the time-independent description of molecular collisions and chemical reactions, is applied to the plane wave packet (PWP) formulation of time-dependent scattering. The NF theory decomposes the partial wave series representation for the time-dependent PWP scattering amplitude into two time-dependent subamplitudes: one N, the other F. In addition, NF local angular momentum (LAM) theory is applied to the PWP scattering amplitude. The novel concept of a cumulative time-evolving differential cross section is introduced, in which the upper infinite time limit of a half-Fourier transform is replaced by a finite time. In a similar way, a cumulative energy-evolving angular distribution is defined. Application is made to the state-to-state reaction, H + D2(v(i) = 0, j(i) = 0) --> HD(v(f) = 3, j(f) = 0) + D, where v(i), j(i) and v(f), j(f) are vibrational and rotational quantum numbers for the initial and final states, respectively. This reaction exhibits time-direct and time-delayed (by about 25 fs) collision mechanisms. It is shown that the direct-time mechanism is N dominant scattering, whereas the time-delayed mechanism exhibits characteristics of NF interference. The NF and LAM theories provide valuable insights into the time-dependent properties of a reaction, as do snapshots from a movie of the cumulative time-evolving differential cross section.