Equilibrium scheme

Compounds of this type possess a definite Aj-selenazoline structure, while homologous compounds with at least one labile hydrogen on the 2-amino group can exist as a tautomeric equilibrium (Scheme 64). 

For 2-hydroxybenzimidazole, the oxo tautomer 116b is considered as a dominant form in equilibrium (Scheme 46) [76AHC(S1), p. 361],... 

However, for derivatives of 2,4-diaminothiazole 214 evidence exists for the amino-imino tautomeric equilibrium (Scheme 71) [76AHC(S1), p. 460]. 

There is no doubt that the carbinol equilibrium (Scheme 3-15) is comparable to the nitrous acid protonation-dehydration equilibrium (Scheme 3-8) if one disregards the nitrosoacidium ion intermediate. 

In polar solvents the equilibrium (Scheme 6-43) is almost completely on the side of the open structure 6.63 a <- 6.63 b. Irradiation at A > 350 nm results in selective quantitative cleavage of the diazocyclohexadienone with loss of N2 and a ring-contraction to give a five-membered ring of the carbene intermediate, 6-fulvenone (6.65). 

The first step was found to be a fast pre-equilibrium (Scheme 12-8). The dependence of the measured azo coupling rate constants on the acidity function and the effect of electron-withdrawing substituents in the benzenediazo methyl ether resulting in reduced rate constants are consistent with a mechanism in which the slow step is a first-order dissociation of the protonated diazo ether to give the diazonium ion (Scheme 12-9). The azo coupling proper (Scheme 12-10) is faster than the dissociation, since the overall rate constant is found to be independent of the naphthol con-... 

The classic example of this group is l-phenyl-3-methyl-5-pyrazolone (12.60), which was mentioned previously. The question of whether this compound and its derivatives react as enols or ketones, which was fervently discussed in former years, is now irrelevant, since it is known that normally only the mutual conjugate base of enol and ketone in the equilibrium (Scheme 12-33) participates in the actual substitution step. 

Figure 3.1 Equilibrium scheme for enzyme turnover in the presence and absence of reversible inhibitors...

An ecosystem can be thought of as a representative segment or model of the environment in which one is interested. Three such model ecosystems will be discussed (Figures 1 and 2). A terrestrial model, a model pond, and a model ecosystem, which combines the first two models, are described in terms of equilibrium schemes and compartmental parameters. The selection of a particular model will depend on the questions asked regarding the chemical. For example, if one is interested in the partitioning behavior of a soil-applied pesticide the terrestrial model would be employed. The model pond would be selected for aquatic partitioning questions and the model ecosystem would be employed if overall environmental distribution is considered. 

Reactions of Halogenation and Nitrosation Nitrones with protons in the a-alkyl group can occur in tautomeric nitrone-hydroxylamine equilibrium (Scheme 2.117) similar to keto-enol and imine-enamine tautomerisms. 

Novel calculations on the tetrazolo[l,5-tf]pyridine-2-azidopyridine equilibrium (Scheme 2, 1-7) in the case of 5-substituted derivatives using ab initio (6-31G /MP2) methods appeared recently <2000T8775>. It has been shown that these substituents sensitively influence the equilibrium as revealed by the calculated energies shown in Table 1. 

In contrast with the oxocarboxylic acids, which readily participate in tautomeric equilibria in solution, their open-chain and cyclic N-unsubsti-tuted and A-monosubstituted amide isomers are more stable. In most cases, the tautomeric equilibrium (Scheme 3) is not observed in neutral aprotic solvents at ambient temperature. In protic solvents, e.g., CD3OD, intercon-... 

A two-substrate, two-product enzyme-catalyzed reaction scheme in which both the substrates (A and B) and the products (P and Q) bind and are released in any order. Note that this definition does not imply that there is an equal preference for each order (that is, it is not a requirement that the flux of the reaction sequence in which A binds first has to equal the flux of the reaction sequence in which B binds first). In fact, except for rapid equilibrium schemes, this is rarely true. There usually is a distinct preference for a particular pathway in a random mechanism. A number of kinetic tools and protocols... 

In many instances, the formation of inactive dimers from active, monomeric catalytic species is observed during catalysis. When weak or unstable ligands are used, even larger rhodium carbonyl clusters like Rh4(CO)i2 and Rh5(CO)i5 can be observed [42-44]. The formation of dimers is often a reversible equilibrium (Scheme 6.2). This only leads to a reduction in the amount of catalyst available and does not kill the catalyst. One of the first examples was the formation of the so-called orange dimer from HRh(PPh3)3CO, already reported by Wilkinson [45]... 

In contrast, at [H+] > 0.1 M, the same reaction results in two or three new EPR signals (glso 1.974, 1.971, and 1.966) in addition to the one already mentioned feso= 1.979).68,75 These EPR signals turn out to be consistent with six-coordinated oxo-Cr(V) species. In this situation, the relative intensity of the EPR signal is pH dependent but is independent of the aldohexose/Cr(VI) ratio. In fact, six-coordinated species are dominant at [H+] > 0.75 M. In addition, both species [six- and five-coordinated oxo-Cr(V) complexes] decay at the same rate, meaning that they are in a rapid equilibrium. Scheme 5 shows the complexation chemistry and the observed Cr(V)-sugar redox processes. 

Of note, the dithiol/disulfide equilibrium (Scheme 6) has been successfully employed as a luminescent molecular switch <2006CEJ689>. 

Using both semi-empirical and ab initio calculations the study of oxepin (6), benzene oxide (7), and their equilibrium (Scheme 2) has been conducted. The fully optimized geometry (90MI902-01) agrees with that experimentally found for several substituted oxepines. The carbon skeleton of benzene oxide is practically planar while the angle between the epoxide ring and the adjacent plane is ca. 106°. The oxepin molecule is boat-shaped with a fold angles between C2—C7 and C3—C6 of ca. 137 and 159°, respectively. 

NMR studies have been mainly applied to elucidating the structural features of Schilf bases in solution. These studies are mainly concerned with SchiiT bases derived from benzaldehyde and its substituents, / -diketones, o-hydroxyacetophenones and o-hydroxyacetonaphthones. They were devoted to obtaining an insight into the keto-enol equilibrium (Scheme 1), syn and anti isomerism and steric distortions in different kinds of solvents. Relevant data and results are described in the following sections. 

The thermal equilibrium (Scheme 3) between the open and closed forms of a spiropyran is the basis of a thermographic system by NCR Corp.232 The spiropyran (109) is coated with a metal salt of a fatty add and a binder. On heating, the spiropyran is converted into the open merocyanine form, while the melting of the salt allows formation of a complex (110), preventing return to the spiro form. 

The 2-(alken-l-yl)cyclopropanecarbaldehyde-l,4-dihydrooxepine equilibrium (Scheme 28) was found to be shifted to the right when alken-l-yl is not vinyl, and this fact was used for the preparation of oxepines from properly substituted cyclopropanes under Dess-Martin oxidation conditions <1993JOC1295>. 

The most investigated type of tautomerism of dihydropyrimidines is the amidine equilibrium (Scheme 3.137). The energies of substituted dihydropyrimidines with these structures are usually similar and the existence of mixtures of tautomeric forms is typical [248]. 

A ligand and receptor exist in an equilibrium (Scheme 5.1) that can be quantified through... 

While occupancy theory is far and away the most widely used model for describing dose-response curves, other theories do exist. One example is allosteric theory. At the center of allosteric theory, sometimes called the two-state model, is the idea that a receptor can exist in conformations that either cause a response (relaxed state) or do not cause a response (tensed state).29 These conformations, represented by T and R, are in equilibrium (Scheme 5.7). 

Also, because such derivatives are to be evaluated at the equilibrium geometry, a key point is the determination of that geometry on the solvated PES, which leads to the so-called indirect solvent effects , which still requires a viable method to calculate free energy gradients (and possibly hessians). The problem of the formulation of free energy derivatives within continuum solvation models is treated elsewhere in this book and for this reason it will not considered here. Instead, it is worth remarking in this context another implication of such a formulation, i.e. that a choice between a complete equilibrium scheme or the account for vibrational and/or electronic nonequilibrium solvent effects [42, 43] should be done (see below). 

The geometrical derivatives of the PCM-TDDFT excitation energy of a given excited state can be used to obtain the equilibrium geometry of that state. From this equilibrium geometry the excited state can reach the ground state by a vertical emission process whose emission energy can be determined by a proper application of the non-equilibrium scheme presented in the previous section. 

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