Models for solution reaction dynamics

This series of papers " " has presented a detailed picture of how the model Cl + CI2 reaction in rare gas solvent occurs. Such detail can more easily be observed and understood because of the relative simplicity of the solvent-reactant and intrasolvent forces. As we shall discuss later in this section, such a level of detail makes possible a comparison with numerous simple models for solution reaction dynamics. As we shall see presently, this simplicity does not always exist, and the extension of these simple models to more complex chemical reactions in more complex solvents is still to be developed. 

THE INTERACTION BETWEEN SIMULATION AND MODELS FOR SOLUTION REACTION DYNAMICS... 

Another use for standard models is as a target. It is important to determine at what point the model breaks down and whether that point is significant in realistic chemical dynamics. Some of the more important developments in the tests of Grote-Hynes theory have been in the application of variational transition state theory (VTST) to models of solution reaction dynamics. The origin of the use of VTST in solution dynamics is in the observation that the GLE can be equivalently formulated in Hamiltonian terms by a reaction coordinate coupled to a bath of harmonic oscillators. It has been shown by van der... 

In the next section a brief layout of simulation methods will be given. Then, some basic properties of the models used in computer simulations of electrochemical interfaces on the molecular level will be discussed. In the following three large sections, the vast body of simulation results will be reviewed structure and dynamics of the water/metal interface, structure and dynamics of the electrolyte solution/metal interface, and microscopic models for electrode reactions will be analyzed on the basis of examples taken mostly from my own work. A brief account of work on the adsorption of organic molecules at interfaces and of liquid/liquid interfaces complements the material. In the final section, a brief summary together with perspectives on future work will be given. 

Chapter 3 by Robert M. Whitnell and Kent R. Wilson extends some of the concepts delineated in Chapter 2. The chapter on computational molecular dynamics of chemical reactions in solution is a definitive, long-awaited bridge between the organic and chemical physics communities. Techniques for simulating reaction dynamics are covered in nonmathematical language. Work on thermally activated reactions, such as isomerization, atom exchange, 5 2, and S l reactions, as well as ion-pair association, and proton transfers, are reviewed. For nonthermally activated reactions, a variety of photodissociations and isomerizations are discussed. The interplay of computer simulations of solution reaction dynamics and models of the reactions is explained. 

In addition to analytical models, we would like simple pictures for solution reactions. If we are to calibrate our intuition, we need to develop appropriate dynamical images, internal movies to understand how solution reactions actually take place. Many of the important questions of physical organic chemistry can now in principle be answered by molecular dynamics simulations. Some of the pictures we would like to develop include i) How does the nature of the solvent determine the branching ratio among different thermodynamically allowed products ii) How is stereochemistry determined in solution ... 

A numerical tool, sensitivity analysis, which can be used to study the effects of parameter perturbations on systems of dynamical equations is briefly described. A straightforward application of the methods of sensitivity analysis to ordinary differential equation models for oscillating reactions is found to yield results which are difficult to physically interpret. In this work it is shown that the standard sensitivity analysis of equations with periodic solutions yields an expansion that contains secular terms. A Lindstedt-Poincare approach is taken instead, and it is found that physically meaningful sensitivity information can be extracted from the straightforward sensitivity analysis results, in some cases. In the other cases, it is found that structural stability/instability can be assessed with this modification of sensitivity analysis. Illustration is given for the Lotka-Volterra oscillator. 

Many additional refinements have been made, primarily to take into account more aspects of the microscopic solvent structure, within the framework of diffiision models of bimolecular chemical reactions that encompass also many-body and dynamic effects, such as, for example, treatments based on kinetic theory [35]. One should keep in mind, however, that in many cases die practical value of these advanced theoretical models for a quantitative analysis or prediction of reaction rate data in solution may be limited. 

The stress depends on the extent of reaction, p(tf), which progresses with time. However, it is not enough to enter the instantaneous value of p(t ). Needed is some integral over the crosslinking history. The solution of the mutation problem would require a constitutive model for the fading memory functional Gf Zflt, t p(t") which is not yet available. This restricts the applicability of dynamic mechanical experiments to slowly crosslinking systems. 

A. Warshel, J. Bentzien, Energetics and Dynamics of Transition States of Reactions in Enzymes and Solutions, in Transition State Modeling for Catalysis, D.G. Truhlar, K. Morokuma (eds), American Chemical Society, Washington, DC, 1999,489-499. 

We have reviewed above the GH approach to reaction rate constants in solution, together with simple models that give a deeper perspective on the reaction dynamics and various aspects of the generalized frictional influence on the rates. The fact that the theory has always been found to agree with Molecular Dynamics computer simulation results for realistic models of many and varied reaction types gives confidence that it may be used to analyze real experimental results. 

For a more detailed analysis of measured transport restrictions and reaction kinetics, a more complex reactor simulation tool developed at Haldor Topsoe was used. The model used for sulphuric acid catalyst assumes plug flow and integrates differential mass and heat balances through the reactor length [16], The bulk effectiveness factor for the catalyst pellets is determined by solution of differential equations for catalytic reaction coupled with mass and heat transport through the porous catalyst pellet and with a film model for external transport restrictions. The model was used both for optimization of particle size and development of intrinsic rate expressions. Even more complex models including radial profiles or dynamic terms may also be used when appropriate. 

Most of the work published to date on molecular dynamic studies of interfacial electron transfer involves the simplified assumption of a two-state model for the electronic degrees of freedom. Consider an ion of charge qj near a solution/metal interface. As a result of electron transfer between the ion and the metal surface, the charge of the ion changes to qj. We will consider both forward and backward electron transfer and assume that = <7 - = -1, so that the forward reaction corresponds to a single electron transfer from the metal to the ion, for example + e ... 

At high pressures, a non-covalent ionic complex can be regarded as a microsolvated ion. It represents the simplest model for ions generated in a dynamic environment, such as in a solvent cage in solution. The main difference is that the behavior of a microsolvated ion is not perturbed by those environmental factors (solvation, ion pairing, etc.) which normally affect the fate of intimate ion-dipole pairs in solution. Hence, a detailed study of the dynamics and the reactivity of microsolvated ions may provide valuable information on the intrinsic factors governing the reaction and how these factors may be influenced by the solvent cage in solution.4 493... 

Even for purely adiabatic reactions, the inadequacies of classical MD simulations are well known. The inability to keep zero-point energy in all of the oscillators of a molecule leads to unphysical behavior of classical trajectories after more than about a picosecond of their time evolution." It also means that some important physical organic phenomena, such as isotope effects, which are easily explained in a TST model, cannot be reproduced with classical molecular dynamics. So it is clear that there is much room for improvement of both the computational and experimental methods currently employed by those of us interested in reaction dynamics of organic molecules. Perhaps some of the readers of this book will be provide some of the solutions to these problems. 

When structural and dynamical information about the solvent molecules themselves is not of primary interest, the solute-solvent system may be made simpler by modeling the secondary subsystem as an infinite (usually isotropic) medium characterized by the same dielecttic constant as the bulk solvent, that is, a dielectric continuum. Theoretical interpretation of chemical reaction rates has a long history already. Until recently, however, only the chemical reactions of systems containing a few atoms in the gas phase could be studied using molecular quantum mechanics due to computational expense. Fortunately, very important advances have been made in the power of computer-simulation techniques for chemical reactions in the condensed phase, accompanied by an impressive progress in computer speed (Gonzalez-Lafont et al., 1996). 

The need to reliably describe liquid systems for practical purposes as condensed matter with high mobility at a given finite temperature initiated attempts, therefore, to make use of statistical mechanical procedures in combination with molecular models taking into account structure and reactivity of all species present in a liquid and a solution, respectively. The two approaches to such a description, namely Monte Carlo (MC) simulations and molecular dynamics (MD), are still the basis for all common theoretical methods to deal with liquid systems. While MC simulations can provide mainly structural and thermodynamical data, MD simulations give also access to time-dependent processes, such as reaction dynamics and vibrational spectra, thus supplying — connected with a higher computational effort — much more insight into the properties of liquids and solutions. 

Han P, Bartels DM (1994) Encounters of H and D atoms with 02 in water relative diffusion and reaction rates. In Gauduel Y, Rossky P (eds) AIP conference proceedings 298. "Ultrafast reaction dynamics and solvent effects." AIP Press, New York, 72 pp Hasegawa K, Patterson LK (1978) Pulse radiolysis studies in model lipid systems formation and behavior of peroxy radicals in fatty acids. Photochem Photobiol 28 817-823 Herdener M, Heigold S, Saran M, Bauer G (2000) Target cell-derived superoxide anions cause efficiency and selectivity of intercellular induction of apoptosis. Free Rad Biol Med 29 1260-1271 Hildenbrand K, Schulte-Frohlinde D (1997) Time-resolved EPR studies on the reaction rates of peroxyl radicals of polyfacrylic acid) and of calf thymus DNA with glutathione. Re-examination of a rate constant for DNA. Int J Radiat Biol 71 377-385 Howard JA (1978) Self-reactions of alkylperoxy radicals in solution (1). In Pryor WA(ed) Organic free radicals. ACS Symp Ser 69 413-432... 

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