Reaction dynamics quantum scattering theories

Since chemical dynamics is dictated by quantum mechanics, one begins with quantum scattering theories of reaction dynamics or molecular energy flow. 

Miller W H 1994 S-matrix version of the Kohn variational principle for quantum scattering theory of chemical reactions Adv. Mol. Vibrations and Collision Dynamics vol 2A, ed J M Bowman (Greenwich, CT JAI Press) pp 1-32... 

A quite different approach to using gas phase dynamics in solution reactions is due to Charutz and Levine. They recast the classical Hamiltonian into an interaction picture that has been used, for example, in the propagation of quantum wavepackets. The picture that Charutz and Levine develop is that just as there are constants of the motion in quantum scattering theory that characterize the reactant and product states, similar constants can be calculated for the classical mechanics of reaction dynamics in solution. While the theoretical treatment is too complicated to present fully here, Charutz and Levine applied this picture to the model Cl -I- CI2 reaction in rare gas solution. They show that momentum of the atom—diatom relative motion is one of the con-... 

The foundations of the modem tireory of elementary gas-phase reactions lie in the time-dependent molecular quantum dynamics and molecular scattering theory, which provides the link between time-dependent quantum dynamics and chemical kinetics (see also chapter A3.11). A brief outline of the steps hr the development is as follows [27],... 

Experiments have also played a critical role in the development of potential energy surfaces and reaction dynamics. In the earliest days of quantum chemistry, experimentally determined thermal rate constants were available to test and improve dynamical theories. Much more detailed information can now be obtained by experimental measurement. Today experimentalists routinely use molecular beam and laser techniques to examine how reaction cross-sections depend upon collision energies, the states of the reactants and products, and scattering angles. 

Mark Thachuk joined the UBC Department of Chemistry in 1996. His research program focuses on the study of the dynamics and rates of chemical reactions and processes by mathematical and computational techniques. Typically, such investigations utilize classical, semiclassical, or quantum mechanics, and combine scattering theory with reaction rate and kinetic theories. 

In the volumes to come, special attention will be devoted to the following subjects the quantum theory of closed states, particularly the electronic structure of atoms, molecules, and crystals the quantum theory of scattering states, dealing also with the theory of chemical reactions the quantum theory of time-dependent phenomena, including the problem of electron transfer and radiation theory molecular dynamics statistical mechanics and general quantum statistics condensed matter theory in general quantum biochemistry and quantum pharmacology the theory of numerical analysis and computational techniques. 

Clary, D.C. (1994) Four-atom reaction dynamics, J. Phys. Chem. 98, 10678-10688. Pack, R.T. and Parker, G.A. (1987) Quantum reactive scattering in three dimensions using hyperspherical (APH) coordinates. Theory, J. Chem. Phys. 87, 3888-3921. Truhlar, D.G., Mead, C.A. and Brandt, 5I.A. (1975) Time-Reversal Invariance, Representations for Scattering Wavcfunctions, Symmetry of the Scattering Matrix, and Differential Cross-Sections, Adv. Chem. Phys. 33, 295-344. 

The quantum theory of reactive scattering and the calculation of potential energy surfaces are reviewed elsewhere in this volume. Here attention will be confined to two recent theoretical models which are both simple and should be widely applicable. Thus, they are appropriate to the analysis of experimental data at an early stage, in order to help discern the nature of the reaction dynamics. 

Scattering theory has been a subject of interest from the beginning of quantum theory as a way to probe interactions between atoms and molecules. The many-body character of the interaction has proven a very difficult problem to deal with. For a proper description of the interaction, any model should incorporate dynamical effects such as electron transfer, rotations and vibrations, nuclear displacement, bond breaking and bond making (chemical reactions), photon emission and absorption, and ionization. 

This book describes the proceedings of a NATO Advanced Research Workshop held at CECAM, Orsay, France in June, 1983. The Workshop concentrated on a critical examination and discussion of the recent developments in the theory of chemical reaction dynamics, with particular emphasis on quantum theories. Several papers focus on exact theories for reactions. Exact calculations on three-dimensional reactions are very hard to perform, but the results are valuable in testing the accuracy of approximate theories which can be applied, with less expense, to a wider variety of reactions. Indeed, critical discussions of the merits and defects of approximate theories, such as sudden, distorted-wave, reduced dimensionality and transition-state methods, form a major part of the book. The theories developed for chemical reactions have found useful extensions into other areas of chemistry and physics. This is illustrated by papers describing topics such as photodissociation, electron-scattering, molecular vibrations and collision-induced dissociation. Furthermore, the important topic of how to treat potential energy surfaces in reaction dynamics calculations is also discussed. 

This paper also provided much of the early stimulus for developing semiclassical and quantum mechanical theories of chemical reaction dynamics, which is a research field that continues to be active. In addition, this paper provided the foundation for molecular dynamics studies of chemical reactions in condensed phases, including applications to gas-surface scattering and bio-molecular simulation. 

There are two classes in applications of quantum nuclear dynamics one is the stationary-state scattering theory to treat reactive scattering (chemical reactions), and the other is time-dependent wavepacket method. Here... 

This reaction has been the focus of much experimental and theoretical effort. For example, some theoretical techniques with which the dynamics have been investigated include quasiclassical trajectories[36], variational transition state theory[37], collinear 1-D quantum scattering[38], and an approximate 3-D quantum treatment[39-40]. Recently, Zhang and Miller[41] reported the first accurate 3-D quantum reaction probabilities for this system... 

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