Molecular dynamics unimolecular reaction rate theory

Recent years have also witnessed exciting developments in the active control of unimolecular reactions [30,31]. Reactants can be prepared and their evolution interfered with on very short time scales, and coherent hght sources can be used to imprint information on molecular systems so as to produce more or less of specified products. Because a well-controlled unimolecular reaction is highly nonstatistical and presents an excellent example in which any statistical theory of the reaction dynamics would terribly fail, it is instmctive to comment on how to view the vast control possibihties, on the one hand, and various statistical theories of reaction rate, on the other hand. Note first that a controlled unimolecular reaction, most often subject to one or more external fields and manipulated within a very short time scale, undergoes nonequilibrium processes and is therefore not expected to be describable by any unimolecular reaction rate theory that assumes the existence of an equilibrium distribution of the internal energy of the molecule. Second, strong deviations Ifom statistical behavior in an uncontrolled unimolecular reaction can imply the existence of order in chaos and thus more possibilities for inexpensive active control of product formation. Third, most control scenarios rely on quantum interference effects that are neglected in classical reaction rate theory. Clearly, then, studies of controlled reaction dynamics and studies of statistical reaction rate theory complement each other. 

In ordinary unimolecular reaction rate theory, the usual assumptions of strong collisions and random distribution of the internal energy simply serve to wash out precisely those features of the molecular dynamics that become of primary importance in the cases of photochemical, chemical, and electron impact excitation. Whereas evaluation of all the consequences is incomplete at present, it is already clear that the representation of an excited molecule in terms of the properties of resonant scattering states holds promise for the elucidation of those aspects of the internal dynamics that are important in photochemistry. 

With this brief overview of classical theories of unimolecular reaction rate, one might wonder why classical mechanics is so useful in treating molecular systems that are microscopic, and one might question when a classical statistical theory should be replaced by a corresponding quantum theory. These general questions bring up the important issue of quantum-classical correspondence in general and the field of quantum chaos [27-29] (i.e., the quantum dynamics of classically chaotic systems) in particular. For example, is it possible to translate the above classical concepts (e.g., phase space separatrix, NHIM, reactive islands) into quantum mechanics, and if yes, how What is the consequence of... 

Initiated by the chemical dynamics simulations of Bunker [37,38] for the unimolecular decomposition of model triatomic molecules, computational chemistry has had an enormous impact on the development of unimolecular rate theory. Some of the calculations have been exploratory, in that potential energy functions have been used which do not represent a specific molecule or molecules, but instead describe general properties of a broad class of molecules. Such calculations have provided fundamental information concerning the unimolecular dissociation dynamics of molecules. The goal of other chemical dynamics simulations has been to accurately describe the unimolecular decomposition of specific molecules and make direct comparisons with experiment. The microscopic chemical dynamics obtained from these simulations is the detailed information required to formulate an accurate theory of unimolecular reaction rates. The role of computational chemistry in unimolecular kinetics was aptly described by Bunker [37] when he wrote The usual approach to chemical kinetic theory has been to base one s decisions on the relevance of various features of molecular motion upon the outcome of laboratory experiments. There is, however, no reason (other than the arduous calculations involved) why the bridge between experimental and theoretical reality might not equally well start on the opposite side of the gap. In this paper... results are reported of the simulation of the motion of large numbers of triatomic molecules by... 

The Langmuir-Hinshelwood picture is essentially that of Fig. XVIII-14. If the process is unimolecular, the species meanders around on the surface until it receives the activation energy to go over to product(s), which then desorb. If the process is bimolecular, two species diffuse around until a reactive encounter occurs. The reaction will be diffusion controlled if it occurs on every encounter (see Ref. 211) the theory of surface diffusional encounters has been treated (see Ref. 212) the subject may also be approached by means of Monte Carlo/molecular dynamics techniques [213]. In the case of activated bimolecular reactions, however, there will in general be many encounters before the reactive one, and the rate law for the surface reaction is generally written by analogy to the mass action law for solutions. That is, for a bimolecular process, the rate is taken to be proportional to the product of the two surface concentrations. It is interesting, however, that essentially the same rate law is obtained if the adsorption is strictly localized and species react only if they happen to adsorb on adjacent sites (note Ref. 214). (The apparent rate law, that is, the rate law in terms of gas pressures, depends on the form of the adsorption isotherm, as discussed in the next section.)... 

A number of MD studies on various unimolecular reactions over the years have shown that there can sometimes be large discrepancies (an order of magnitude or more) between reaction rates obtained from molecular dynamics simulations and those predicted by classical RRKM theory. RRKM theory contains certain assumptions about the nature of prereactive and postreactive molecular dynamics it assumes that all prereactive motion is statistical, that all trajectories will eventually react, and that no trajectory will ever recross the transition state to reform reactants. These assumptions are apparently not always valid otherwise, why would there be discrepancies between trajectory studies and RRKM theory Understanding the reasons for the discrepancies may therefore help us learn something new and interesting about reaction dynamics. 

Detailed Cross-sections and Rates.—The RRKM version of transition-state theory for unimolecular reactions, as developed 25 years ago and sununarized in its useful practical form in recent books, has continued to find wide applications in unimolecular rate theory. As has been pointed out by Marcus in the 1973 Faraday Discussion on molecular beams, it is both a weakness and a strength of transition-state theory that it does not make very detailed statements on specific cross-sections and rates. With such information becoming accessible experimentally, more detailed statistical dynamical theories were to come. We have now four such detailed statistical approaches ... 

Information of a different sort is obtained in a molecular beam experiment, although the means for producing the species undergoing unimolecular decomposition is also chemical activation. Whereas the conventional kinetic studies yield reaction rates for direct comparison with RRKM lifetimes, the beam technique yields product recoil energy distribution which, in principle, contain information regarding exit channel dynamics specifically ignored in RRKM. Comparison of experimental results with RRKM theory is indirect, requiring additional assumptions whose validity must be determined. Fortunately, however, statistical theories of a different sort exist which base their predictions on asymptotic (and therefore measureable) properties of the... 

Classical Dynamics of Nonequilibrium Processes in Fluids Integrating the Classical Equations of Motion Control of Microworld Chemical and Physical Processes Mixed Quantum-Classical Methods Multiphoton Excitation Non-adiabatic Derivative Couplings Photochemistry Rates of Chemical Reactions Reactive Scattering of Polyatomic Molecules Spectroscopy Computational Methods State to State Reactive Scattering Statistical Adiabatic Channel Models Time-dependent Multiconfigurational Hartree Method Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Valence Bond Curve Crossing Models Vibrational Energy Level Calculations Vibronic Dynamics in Polyatomic Molecules Wave Packets. 

Classical Trajectory Simulations Final Conditions Mixed Quantum-Classical Methods Rates of Chemical Reactions State to State Reactive Scattering Trajectory Simulations of Molecular Collisions Classical Treatment Transition State Theory Unimolecular Reaction Dynamics Wave Packets. 

A situation that arises from the intramolecular dynamics of A and completely distinct from apparent non-RRKM behaviour is intrinsic non-RRKM behaviour [9], By this, it is meant that A has a non-random P(t) even if the internal vibrational states of A are prepared randomly. This situation arises when transitions between individual molecular vibrational/rotational states are slower than transitions leading to products. As a result, the vibrational states do not have equal dissociation probabilities. In tenns of classical phase space dynamics, slow transitions between the states occur when the reactant phase space is metrically decomposable [13,14] on the timescale of the imimolecular reaction and there is at least one bottleneck [9] in the molecular phase space other than the one defining the transition state. An intrinsic non-RRKM molecule decays non-exponentially with a time-dependent unimolecular rate constant or exponentially with a rate constant different from that of RRKM theory. 

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