Filtering reaction dynamics using nearside-farside theory and local angular momentum theory: application to the angular scattering of the H + D2(v(i) = 0, j(i) = 0) --> HD(v(f) = 3, j(f) = 0) + D reaction in the energy and time domains.

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).

Nearside-farside and local angular momentum analyses of time-independent scattering amplitudes for the H + D2 (vi = 0, ji = 0) --> HD (vf = 3, jf = 0) + D reaction.

The scattering dynamics of the state-to-state reaction H + D2 (v(i) = 0, j(i) = 0, m(i) = 0) --> HD (v(f) = 3, j(f) = 0, m(f) = 0) + D is investigated, where vi, ji, mi and vf, jf, mf are initial and final vibrational, rotational, and helicity quantum numbers, respectively. We use accurate quantum scattering matrix elements for total energies in the range 1.52-2.50 eV (calculated stepwise in 0.01 eV increments). The theoretical tools used are a nearside-farside (NF) analysis of the partial wave series (PWS) for the scattering amplitude, together with NF local angular momentum (LAM) theory. We find that the backward scattering, which is the energy-domain analog of the time-direct reaction mechanism, is N dominated, whereas the forward scattering (time-delayed analog) is a result of NF interference between the more slowly varying N and F subamplitudes. The LAM analysis reveals the existence of a "trench-ridge" structure. We also resum the PWS up to three times prior to making the NF decomposition. We show that such resummations usually provide an improved physical interpretation of the NF differential cross sections (DCSs) and NF LAMs. We analyze two resummed scattering amplitudes in more detail, where particular values of the resummation parameters give rise to unexpected unphysical behavior in the N and F DCSs over a small angular range. We analyze the cause of this unphysical behavior and describe viable workarounds to the problem. The energy-domain calculations in this paper complement the time-domain results reported earlier by Monks, P. D. D.; Connor, J. N. L.; Althorpe, S. C. J. Phys. Chem. A 2006, 110, 741.

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.