Canonic reaction

The flux through the TS is important in reaction dynamics since the reaction rate can be obtained by dividing this flux by the appropriate partition function [35]. Specifically, the classical canonical reaction rate is given by [80]... 

As for the reactions catalyzed by members of this third family of molybdenum enzymes, there are several variations from the principal theme of oxygen atom transfer. Formate dehydrogenase from E. coli catalyzes the oxidation of formate to CO2, a reaction that isotope studies have shown does not pass through a bicarbonate intermediate (Khangulov et al., 1998). Instead, it appears likely that C02is formed by direct hydride transfer from substrate to the molybdenum center. Polysulfide reductase is another molybdenum enzyme that catalyzes a non-canonical reaction the... 

The opposite limit of direct reaction with repulsive energy release also invites interpretation in terms of simple models. The situation has recently been reviewed by Herschbach134 who shows that the appropriate repulsive potential may be determined from photodissociation spectra of the diatomic reactant in the case of the canonical reactions K + CH3I and H + CI2. 

The reaction may be looked for within a class of reactions with a given, chemically relevant property. Such a property may be conservativity or subconservativity (the canonic reaction is never conservative ), reversibility, weak reversibility or acyclicity, small (zero or one) deficiency. When does an inducing reaction exist within a given class to a given differential equation, when is it unique, or if it is not unique then how far is it nonunique ... 

Verify that a polynomial differential equation without negative crosseffect can be induced by a reaction (called canonic reaction) that is constructed in the following way ... 

The canonical reaction type for gas phase dynamics has been the A + BC —> AB + C reaction.20 We have investigated, in collaboration with Casey Hynes, two versions of this reaction in solution, the first in which the interaction between the reagents and the solvent molecules as well as the solvent-solvent... 

The additive nature of stoichiometric equations and heats of reactions allows the tabulation of for a relatively few canonical reactions that... 

It may be iisefiil to mention here one currently widely applied approximation for barrierless reactions, which is now frequently called microcanonical and canonical variational transition state theory (equivalent to the minimum density of states and maximum free energy transition state theory in figure A3,4,7. This type of theory can be understood by considering the partition fiinctions Q r ) as fiinctions of r similar to equation (A3,4.108) but with F (r ) instead of V Obviously 2(r J > Q so that the best possible choice for a... 

Quack M 1984 On the mechanism of reversible unimolecular reactions and the canonical ( high pressure ) limit of the rate coefficient at low pressures Ber. Bunsenges. Phys. Chem. 88 94-100... 

Poliak E 1990 Variational transition state theory for activated rate processes J. Chem. Phys. 93 1116 Poliak E 1991 Variational transition state theory for reactions in condensed phases J. Phys. Chem. 95 533 Frishman A and Poliak E 1992 Canonical variational transition state theory for dissipative systems application to generalized Langevin equations J. Chem. Phys. 96 8877... 

Day P N and Truhlar D G 1991 Benchmark calculations of thermal reaction rates. II. Direct calculation of the flux autocorrelation function for a canonical ensemble J. Chem. Phys. 94 2045-56... 

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. 

Hu X and Hase W L 1989 Properties of canonical variational transition state theory for association reactions without potential energy barriers J. Rhys. Chem. 93 6029-38... 

Several VTST techniques exist. Canonical variational theory (CVT), improved canonical variational theory (ICVT), and microcanonical variational theory (pVT) are the most frequently used. The microcanonical theory tends to be the most accurate, and canonical theory the least accurate. All these techniques tend to lose accuracy at higher temperatures. At higher temperatures, excited states, which are more difficult to compute accurately, play an increasingly important role, as do trajectories far from the transition structure. For very small molecules, errors at room temperature are often less than 10%. At high temperatures, computed reaction rates could be in error by an order of magnitude. 

In valence bond terms the pyrazine ring may be represented as a resonance hybrid of a number of canonical structures (e.g. 1-4), with charge separated structures such as (3) contributing significantly, as evidenced by the polar character of the C=N bond in a number of reactions. The fusion of one or two benzene rings in quinoxaline (5) and phenazine (6) clearly increases the number of resonance structures which are available to these systems. 

Hydroxy-imidazoles, -oxazoles and -thiazoles (484 Z = NR, O, S) can isomerize to 2-azolinones (485a). These compounds all exist predominantly in the azolinone form and show many reactions similar to those of the pyridones. They are mesomeric with zwitterionic and carbonyl canonical forms e.g. 485a 485b Z = NR, O, S). 

The chemical reactions of this compound were recently reconsidered, and both structures 64 and 65 were rejected in favor of the zwit-terion formulation 66, which is supported by the presence of a band at S.lfx (3226 cm ) in the infrared spectrum and is merely an alternative canonical form of 64. On the other hand, the ultraviolet spectrum of 4-hydroxypyrrole-2-carboxylic acid (67) resembles that of its ethyl ether, possibly indicating that the 2-acid exists in the hydroxy form. -... 

A criterion for the position of the extent of the mesomerism of type 9 is given by the bond order of the CO bond, a first approximation to W hich can be obtained from the infrared spectrum (v C=0). Unfortunately, relatively little is known of the infrared spectra of amide anions. How-ever, it can be assumed that the mesomeric relationships in the anions 9 can also be deduced from the infrared spectra of the free amides (4), although, of course, the absolute participation of the canonical forms a and b in structures 4 and 9 is different. If Table I is considered from this point of view, the intimate relationship betw-een the position of the amide band 1 (v C=0) and the orientation (0 or N) of methylation of lactams by diazomethane is unmistakeable. Thus the behavior of a lactam tow ard diazomethane can be deduced from the acidity (velocity of reaction) and the C=0 stretching frequency (orientation of methylation). Three major regions can be differentiated (1) 1620-1680 cm h 0-methylation (2) 1680-1720 cm i, O- and A -methylation, w ith kinetic dependence and (3) 1730-1800 em , A -methylation, The factual material in Table I is... 

The resonance interaction of chlorine with the benzene ring can be represented as shown in 13 or 14, and both of these representations have been used in the literature to save space. However, we shall not use the curved-arrow method of 13 since arrows will be used in this book to express the actual movement of electrons in reactions. We will use representations like 14 or else write out the canonical forms. The convention used in dashed-line formulas like 14 is that bonds that are present in all canonical forms are drawn as solid lines, while bonds that are not present in all forms are drawn as dashed lines. In most resonance, a bonds are not involved, and only the n or unshared electrons are put in, in different ways. This means that if we write one canonical form for a molecule, we can then write the others by merely moving n and unshared electrons. 

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