Bimolecular scattering

Optimized Bimolecular Scattering Total Suppression of ReadthA Event In Section 7.3.1 we considered optimizing reactive scattering by varyj the coefficients a,- of a superposition of states. In this section we show that whefi j number of initial open states in the reactant space exceeds the number of open st8jj ... 

Coherent control of bimolecular scattering. Adv. Chem. Phys. 101, 295. 

For themial unimolecular reactions with bimolecular collisional activation steps and for bimolecular reactions, more specifically one takes the limit of tire time evolution operator for - co and t —> + co to describe isolated binary collision events. The corresponding matrix representation of f)is called the scattering matrix or S-matrix with matrix elements... 

Flowever, in order to deliver on its promise and maximize its impact on the broader field of chemistry, the methodology of reaction dynamics must be extended toward more complex reactions involving polyatomic molecules and radicals for which even the primary products may not be known. There certainly have been examples of this notably the crossed molecular beams work by Lee [59] on the reactions of O atoms with a series of hydrocarbons. In such cases the spectroscopy of the products is often too complicated to investigate using laser-based techniques, but the recent marriage of intense syncluotron radiation light sources with state-of-the-art scattering instruments holds considerable promise for the elucidation of the bimolecular and photodissociation dynamics of these more complex species. 

Manolopoulos D E, Dmello M and Wyatt R E 1989 Quantum reactive scattering via the log derivative version of the Kohn variational principle—general theory for bimolecular chemical reactions J. Chem. Phys. 91 6096... 

This chapter has provided a brief overview of the application of optimal control theory to the control of molecular processes. It has addressed only the theoretical aspects and approaches to the topic and has not covered the many successful experimental applications [33, 37, 164-183], arising especially from the closed-loop approach of Rabitz [32]. The basic formulae have been presented and carefully derived in Section II and Appendix A, respectively. The theory required for application to photodissociation and unimolecular dissociation processes is also discussed in Section II, while the new equations needed in this connection are derived in Appendix B. An exciting related area of coherent control which has not been treated in this review is that of the control of bimolecular chemical reactions, in which both initial and final states are continuum scattering states [7, 14, 27-29, 184-188]. 

Undoubtedly, the technique most suited to tackle polyatomic multichannel reactions is the crossed molecular beam (CMB) scattering technique with mass spectrometric detection and time-of-flight (TOF) analysis. This technique, based on universal electron-impact (El) ionization coupled with a quadrupole mass filter for mass selection, has been central in the investigation of the dynamics of bimolecular reactions during the past 35 years.1,9-11 El ionization affords, in principle, a universal detection method for all possible reaction products of even a complex reaction exhibiting multiple reaction pathways. Although the technique is not usually able to provide state-resolved information, especially on a polyatomic... 

Various methods are proposed (5, a—g), (6). Among these, the methods in which monomolecular recombination or bimolecular recombination of the carriers are assumed could not be used in our case, because the carrier transport in poly-N-vinylcarbazole is known to be the multi-trapping process of the hole carrier. The values of the trap depthaE of 5°C peak by these several methods are summarized in Tab. 1. Values are widely scattered and it seemed that this is due to the approximations involved in the method of analysis. Our value is calculated by the... 

The considerable progress made in the studies of simple bimolecular reactions (which has led to such fundamental conclusions) was achieved by a more rigorous mathematical treatment of the problem, avoiding the use of the simplest approximations which linearize the kinetic equations. We focus main attention on the many-point density formalism developed in [26, 28, 49] since in our opinion it seems at present to be the only general approach permitting treatment of all the above-mentioned problems, whereas other theoretical methods so far developed, e.g., those of secondary quantization [19, 29-32], and of multiple scattering [72, 73], as well based on... 

Distribution of molecular weights in these homogeneous systems has been uncertain. A recent discussion and review of this topic is that of Bamford, Jenkins, Johnston, and White (10). They assume a simple exponential distribution and consider both transfer and bimolecular termination. Peebles (112) observed conventional polymerization kinetics but he concluded from light scattering results that there are deviations from normal behavior in the higher molecular weight fractions. He associated these with the same mechanism that causes microgel. 

Thus, firstly, the choice of the pure solvent as the reference state for the definition of activities of solutes in fact impairs a fair comparison of the activity of dilute solutes such as general adds to the activity of the solvent itself. Secondly, the observed first-order rate constants k or k0 for the reaction of a solute with the solvent water are usually converted to second-order rate constants by division through the concentration of water, h2o = oA iho, for a comparison with the second-order rate coefficients HA. Again, it is questionable whether the formal h2o coefficients so calculated may be compared with truly bimolecular rate constants kUA for the reactions with dilute general acids HA. It is then no surprise that the values for the rate coefficients determined for the catalytic activity of solvent-derived acids scatter rather widely, often by one or two orders of magnitude, from the regression lines of general adds.74... 

Crossed molecular beams have been used to study nearly as wide a range of alkali metal atom reactions as has been examined by diffusion flames. An excellent review has been provided by Herschbach2. The multi-step mechanism displayed for chemiluminescence studies does not apply to the scattering experiments. Only the initial bimolecular reaction is important at the low pressures used. 

A full six-dimensional PES for the HOCO system has been developed by Schatz and coworkers, particularly L. B. Harding (Kudla et al. 1992 Schatz et al. 1987). This proved to be challenging because of numerous local minima and transition states, and consequently the development of the PES has taken several years. Many points were calculated by using large scale ab initio techniques and the surface was adjusted to reconcile a broad array of experimental data such as nascent product excitations, HOCO decomposition rates, overall bimolecular reaction rates, barrier heights, enthalpy changes, HOCO structural properties, and inelastic scattering data. This PES has been used in several computational studies of the reaction dynamics that employ classical (Kudla and Schatz 1991 Kudla... 

As will be shown throughout this book, quantum control of molecular dynamics has been applied to a wide variety of processes. Within the framework of chemical applications, control over reactive scattering has dominated. In particular, the two primary chemical processes focused upon are photodissociation, in which a molecule is irradiated and dissociates into various products, and bimolecular reactions, in which two molecules collide to produce new products. In this chapter we formulate fie quantum theory of photodissociation, that is, the light-induced breaking of a chemical bond. In doing so we provide an introduction to concepts essential for the 1 remainder of this book. The quantum theory of bimolecular collisions is also briefly ydiscussed. 

This scenario opens up a wide range of possible experimental studies of control bimolecular collisions. Specifically, we need only prepare A and A in a control superposition of two states [e.g., by resonant laser excitation of A(1))] to produf superposition with r/>A(2)), direct them antiparallel in the laboratory, and vary t coefficients in the superposition to affect the reaction probabilities. Control -originates in quantum interference between two degenerate states associated wiili, r the contributions of 0A(1)) A<(2)> and I[Pg.154]

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