Narrow Results

In this paper, we study the breakdown of normal hyperbolicity and its consequences for reaction dynamics; in particular, the dividing surface, the flux through the dividing surface (DS), and the gap time distribution. Our approach is to study these questions using simple, two degree-of-freedom Hamiltonian models where calculations for the different geometrical and dynamical quantities can be carried out exactly. For our examples, we show that resonances within the normally hyperbolic invariant manifold may, or may not, lead to a "loss of normal hyperbolicity". Moreover, we show that the onset of such resonances results in a change in topology of the dividing surface, but does not affect our ability to define a DS. The flux through the DS varies continuously with energy, even as the energy is varied in such a way that normal hyperbolicity is lost. For our examples, the gap time distributions exhibit singularities at energies corresponding to the existence of homoclinic orbits in the DS, but these singularities are not associated with loss of normal hyperbolicity.

Complementary to existing applications of Lagrangian descriptors as an exploratory method, we use Lagrangian descriptors to find invariant manifolds in a system where some invariant structures have already been identified. In this case, we use the parametrization of a periodic orbit to construct a Lagrangian descriptor that will be locally minimized on its invariant manifolds. The procedure is applicable (but not limited) to systems with highly unstable periodic orbits, such as the isokinetic Chesnavich CH${}_4^{+}$ model subject to a Hamiltonian isokinetic theromostat. Aside from its low computational requirements, the method enables us to study the invariant structures responsible for roaming in the isokinetic Chesnavich CH${}_4^{+}$ model.

We consider here the effect of Fermi resonance on the rate of stochastic transitions over potential barriers. As a typical phenomenon for Fermi resonance we investigate the fading of the energy between the oscillations in different degrees of freedom. Due to this fading phenomenon we see from time to time rather large amplitudes of oscillations along the reaction path which may support transitions over reaction barriers in the underdamped regime. As as an application we study the influence of Fermi resonance on enzyme reactions. In particular we investigate the possible effect of Fermi resonance on the breaking of peptide bonds.

We review in this article a recently proposed energy-global method that is capable of calculating the entire transition amplitude matrix with a single Lanczos propagation. This method requires neither explicit computation nor storage of the eigenfunctions, rendering it extremely memory efficient. Procedures are proposed to handle situations where "spurious" eigenvalues aggregate around true eigenvalues due to round-off errors. This method is amenable to both real-symmetric and complex-symmetric Hamiltonians. Applications to molecular spectra and reactive scattering are presented. Its relationships with other methods are also discussed.

We report a dynamics study of the reaction using an improved double many-body expansion (DMBE II) potential energy surface for the ground triplet state of O₄. Values of the calculated cross section, vibrational and rotational distributions, as well as thermal rate coefficient as a function of temperature are given. While some discrepancy with experiment is found in the rotational distribution of the product O₂ molecules with vibrational quantum number v = 12, the agreement is quite good for the thermal rate coefficient over the whole range of temperatures where theory and experiment overlap. No breakdown of a previously suggested spectator bond mechanism is observed. Reasons to support such an evidence are given from ab initio calculations by looking at the variation of the energy and calculated bond distances as a function of the intrinsic reaction coordinate along the products channel.

A local linear least square (LLLS) method to fit multidimensional potential energy surface for quantum dynamics calculation is presented. The method uses only energy data points within a local area in multidimentional space. The potential is fit using a linear least square method with singular value decomposition. The method is tested in quantum dynamical calculation for three-dimensional H + H₂ reaction. The result indicates that the local linear least square fitting is accurate and computationally efficient.

Since there is no exact solution for problems in physics and chemistry, extrapolation methods may assume a key role in quantitative quantum chemistry. Two topics where it bears considerable impact are addressed, both at the heart of computational quantum chemistry: electronic structure and reaction dynamics. In the first, the problem of extrapolating the energy obtained by solving the electronic Schrödinger equation to the limit of the complete one-electron basis set is addressed. With the uniform-singlet-and-triplet-extrapolation (USTE) scheme at the focal point, the emphasis is on recent updates covering from the energy itself to other molecular properties. The second topic refers to extrapolation of quantum mechanical reactive scattering probabilities from zero total angular momentum to any of the values that it may assume when running quasiclassical trajectories, QCT/QM-$\alpha$J. With the extrapolation guided in both cases by physically motivated asymptotic theories, realism is seeked by avoiding unsecure jumps into the unknown. Although, mostly review oriented, a few issues are addressed for the first time here and there. Prospects for future work conclude the overview.

This chapter focuses on very recent progress in reactive scattering studies using the Crossed Molecular Beam (CMB) technique with mass spectrometric detection, as made possible by the successful implementation in our laboratory of the soft (i.e., low energy) electron-impact ionization method for product detection. Analogously to the approach of soft photoionization by tunable VUV synchrotron radiation, soft electron-impact ionization permits one to reduce or even eliminate the problem of dissociative ionization of reactants, products and residual background gases which may seriously interfere with product detection and which has severely undermined so far the "universality" of the mass spectrometric detection method in CMB experiments. In addition, in contrast to when using photoionization, it also permits one to more readily determine product branching ratios. All this opens up completely new opportunities in reaction dynamics.

To illustrate the capabilities of the new experimental approach based on soft electron-impact ionization, measurements of reactive differential cross-sections for some polyatomic multichannel reactions, which play a fundamental role for our basic understanding of reaction phenomena, are presented and discussed. The examples include reactions of ground state oxygen atom, O(³P), and carbon atom, C(³P), with unsaturated hydrocarbons (acetylene and ethylene), which are of great relevance in combustion and astrophysical chemistry. For these reactions the reactive differential cross-sections have been recently measured for each energetically allowed channel and the branching ratios derived, the results being discussed in the light of theoretical information on the relevant potential energy surfaces.

Another new twist in CMB reactive scattering which has very recently been implemented in our laboratory, will also be briefly discussed in this chapter. It consists in carrying out CMB experiments with a crossing angle of the reactant beams of 135°, rather than the conventional 90°. The new geometrical arrangement is able to provide not only an increased collision energy, but also an increased angular and velocity resolution.

The future prospects opened up by soft electron-impact ionization for product detection in CMB studies of atom/radical reactions with polyatomic molecules/radicals are briefly examined.

The following sections are included:

• Introduction

• Experimental

• Photochemistry
  • Dimethyl Sulfoxide
  • Substituted Ethylenes
    • Acrylonitrile
    • Vinyl Chloride
  • Oxalyl Chloride
  • Propyne and Allene

• Reactive Scattering
  • Crossed-Beam Reaction Dynamics: Cl + Propane
  • CI + n-Pentane

• Conclusion

• Acknowledgments

• References

The main aim of the present study is to evaluate the fusion probabilities and investigate competing quasifission process in the reactions with heavy ions leading to the formation of superheavy composite systems. The mass-energy distributions, as well as capture cross-sections of fission-like fragments for the reactions of ²²Ne, ²⁶Mg, ³⁶S, ⁴⁸Ca, ⁵⁸Fe and ⁶⁴Ni ions with actinides leading to the formation of superheavy compound systems with Z=102-120 at energies near the Coulomb barrier have been measured. The relative contribution of quasifission to the capture cross section becomes dominant for superheavy composite systems. Fusion-fission cross sections were estimated from the analysis of mass and total kinetic energy distributions.