Chemical reaction description

To realize the import of this approach to chemical reaction descriptions, let us consider the elementary electron transfer process at an adiabatic level ... 

As it has appeared in recent years that many hmdamental aspects of elementary chemical reactions in solution can be understood on the basis of the dependence of reaction rate coefficients on solvent density [2, 3, 4 and 5], increasing attention is paid to reaction kinetics in the gas-to-liquid transition range and supercritical fluids under varying pressure. In this way, the essential differences between the regime of binary collisions in the low-pressure gas phase and tliat of a dense enviromnent with typical many-body interactions become apparent. An extremely useful approach in this respect is the investigation of rate coefficients, reaction yields and concentration-time profiles of some typical model reactions over as wide a pressure range as possible, which pemiits the continuous and well controlled variation of the physical properties of the solvent. Among these the most important are density, polarity and viscosity in a contimiiim description or collision frequency. 

As reactants transfonn to products in a chemical reaction, reactant bonds are broken and refomied for the products. Different theoretical models are used to describe this process ranging from time-dependent classical or quantum dynamics [1,2], in which the motions of individual atoms are propagated, to models based on the postidates of statistical mechanics [3], The validity of the latter models depends on whether statistical mechanical treatments represent the actual nature of the atomic motions during the chemical reaction. Such a statistical mechanical description has been widely used in imimolecular kinetics [4] and appears to be an accurate model for many reactions. It is particularly instructive to discuss statistical models for unimolecular reactions, since the model may be fomuilated at the elementary microcanonical level and then averaged to obtain the canonical model. 

Zhu I, Wdom A and Champion P M 1997 A multidimensional Landau-Zener description of chemical reaction dynamics and vibrational coherence J. Chem. Phys. 107 2859-71... 

CIDNP involves the observation of diamagnetic products fonned from chemical reactions which have radical intemiediates. We first define the geminate radical pair (RP) as the two molecules which are bom in a radical reaction with a well defined phase relation (singlet or triplet) between their spins. Because the spin physics of the radical pair are a fiindamental part of any description of the origins of CIDNP, it is instmctive to begin with a discussion of the radical-pair spin Hamiltonian. The Hamiltonian can be used in conjunction with an appropriate basis set to obtain the energetics and populations of the RP spin states. A suitable Hamiltonian for a radical pair consisting of radicals 1 and 2 is shown in equation (B1.16.1) below [12]. 

The molecular beam and laser teclmiques described in this section, especially in combination with theoretical treatments using accurate PESs and a quantum mechanical description of the collisional event, have revealed considerable detail about the dynamics of chemical reactions. Several aspects of reactive scattering are currently drawing special attention. The measurement of vector correlations, for example as described in section B2.3.3.5. continue to be of particular interest, especially the interplay between the product angular distribution and rotational polarization. 

The concept of macroscopic kinetics avoids the difficulties of microscopic kinetics [46, 47] This method allows a very compact description of different non-thennal plasma chemical reactors working with continuous gas flows or closed reactor systems. The state of the plasma chemical reaction is investigated, not in the active plasma zone, but... 

The description of chemical reactions as trajectories in phase space requires that the concentrations of all chemical species be measured as a function of time, something that is rarely done in reaction kinetics studies. In addition, the underlying set of reaction intennediates is often unknown and the number of these may be very large. Usually, experimental data on the time variation of the concentration of a single chemical species or a small number of species are collected. (Some experiments focus on the simultaneous measurement of the concentrations of many chemical species and correlations in such data can be used to deduce the chemical mechanism [7].)... 

The trajectory description problem of chemical reactions is resolved by using phase-space reconstmction from a single time series [8] this method uses delayed data at times t, t+ip t+X2,.. ., for an -dimensional attractor,... 

In a two-lowest-electronic-state Bom-Huang description for a chemical reaction, the nuclei can move on both of two corresponding PESs during the reaction, due to the electronically non-adiabatic couplings between those states. A reactive scattering formalism for such a reaction involving a triatomic system... 

The Car-Parrinello quantum molecular dynamics technique, introduced by Car and Parrinello in 1985 [1], has been applied to a variety of problems, mainly in physics. The apparent efficiency of the technique, and the fact that it combines a description at the quantum mechanical level with explicit molecular dynamics, suggests that this technique might be ideally suited to study chemical reactions. The bond breaking and formation phenomena characteristic of chemical reactions require a quantum mechanical description, and these phenomena inherently involve molecular dynamics. In 1994 it was shown for the first time that this technique may indeed be applied efficiently to the study of, in that particular application catalytic, chemical reactions [2]. We will discuss the results from this and related studies we have performed. 

Representation of Atmospheric Chemistry Through Chemical Mechanisms. A complete description of atmospheric chemistry within an air quaUty model would require tracking the kinetics of many hundreds of compounds through thousands of chemical reactions. Fortunately, in modeling the dynamics of reactive compounds such as peroxyacetyl nitrate [2278-22-0] (PAN), C2H2NO, O, and NO2, it is not necessary to foUow every compound. Instead, a compact representation of the atmospheric chemistry is used. Chemical mechanisms represent a compromise between an exhaustive description of the chemistry and computational tractabiUty. The level of chemical detail is balanced against computational time, which increases as the number of species and reactions increases. Instead of the hundreds of species present in the atmosphere, chemical mechanisms include on the order of 50 species and 100 reactions. 

Descriptions of Physical Objects, Processes, or Abstract Concepts. Eor example, pumps can be described as devices that move fluids. They have input and output ports, need a source of energy, and may have mechanical components such as impellers or pistons. Similarly, the process of flow can be described as a coherent movement of a Hquid, gas, or coUections of soHd particles. Flow is characterized by direction and rate of movement (flow rate). An example of an abstract concept is chemical reaction, which can be described in terms of reactants and conditions. Descriptions such as these can be viewed as stmctured coUections of atomic facts about some common entity. In cases where the descriptions are known to be partial or incomplete, the representation scheme has to be able to express the associated uncertainty. 

Those based on strictly empirical descriptions Mathematical models based on physical and chemical laws (e.g., mass and energy balances, thermodynamics, chemical reaction kinefics) are frequently employed in optimization apphcations. These models are conceptually attractive because a gener model for any system size can be developed before the system is constructed. On the other hand, an empirical model can be devised that simply correlates input-output data without any physiochemical analysis of the process. For... 

General description. Porosity refers to cavities formed within the weld metal during the solidification process. Such cavities may form due to decreased solubility of a gas as the molten weld metal cools or due to gas-producing chemical reactions within the weld metal itself. At times, cavities can form a continuous channel through the weld metal (worm holes, piping), resulting in leaks (Case History 15.3). 

A more general, and for the moment, less detailed description of the progress of chemical reactions, was developed in the transition state theory of kinetics. This approach considers tire reacting molecules at the point of collision to form a complex intermediate molecule before the final products are formed. This molecular species is assumed to be in thermodynamic equilibrium with the reactant species. An equilibrium constant can therefore be described for the activation process, and this, in turn, can be related to a Gibbs energy of activation ... 

Judging from our present knowledge, such a description is far from the whole story. The article of Benderskii and Goldanskii [1992] addressed mostly the vast amount of experimental data accumulated thus far. On the other hand, the major applications of QTST involved gas-phase chemical reactions, where quantum effects were not dominant. All this implies that there is a gap between the possibilities offered by modern quantum theory and the problems of low-temperature chemistry, which apparently are the natural arena for testing this theory. This prompted us to propose a new look at this field, and to consistently describe the theoretical approaches which are adequate even at T = 0. 

Comparison of (1.14), (2.47a) and (2.60a) reveals the universality of the golden rule in the description of both the nonadiabatic and adiabatic chemical reactions. However, the matrix elements entering into the golden-rule formula have quite a different nature. In the case of an adiabatic reaction it comes from tunneling along the reaction coordinate, while for a nonadiabatic... 

The low-temperature chemistry evolved from the macroscopic description of a variety of chemical conversions in the condensed phase to microscopic models, merging with the general trend of present-day rate theory to include quantum effects and to work out a consistent quantal description of chemical reactions. Even though for unbound reactant and product states, i.e., for a gas-phase situation, the use of scattering theory allows one to introduce a formally exact concept of the rate constant as expressed via the flux-flux or related correlation functions, the applicability of this formulation to bound potential energy surfaces still remains an open question. 

Tubular reactors have empty spaces only between the catalyst particles. This eliminates one big disadvantage of CSTRs. On the other hand, the mathematical description and analysis of the data become more complicated. For chemical reaction studies it is still useful to detect major changes or differences in reaction mechanism. 

Even, limited PSAs use and contain much information. This information may come as memos and process reports and flow sheets, equipment layout, system descriptions, toxic inventory, hazardous chemical reactions, test, maintenance and operating descriptions. From this, data and analyses are prepared regarding release quantities, doses, equipment reliability, probability of exposure, and the risk to workers, public, and environment. An executive summary analysis is detailed, and recommendations made for risk reduction. Thus the information will be text, calculations of envelope fracture stresses, temperatures, fire propagation, air dispersion, doses, and failure probabilities - primarily in tabular form. 

In most cases of interest, shock-induced chemical reactions in solids are studied in mixtures of powders of the potential reactants. In the earlier description of conceptual models it was emphasized that the pores provide space in which the potential reactants can be more intimately mixed in order... 

Within this context, the following sections are devoted to the description of the state of the art in the modeling and simulation of surface chemical reactions of simple systems using Monte Carlo techniques. 

Mechanism (Section 4.8) The sequence of steps that describes how a chemical reaction occurs a description of the intermediates and transition states that are involved during the transformation of reactants to products. 

What happens in a chemical reaction during the period between the initial (reactant) state and the final (product) state An answer to this question constitutes a description of the mechanism of the reaction. The study of reaction mechanisms is a major application of chemical kinetics, and most of this book is devoted to this application an introduction is given in Section 1.2. 

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