Intermediate linear scheme

With due regards of the properties of expression (3.6), one can find the Lyapunov functionals for various types of kinetic schemes. This can be done, for example, by consecutive integrating kinetic equations of type (3.10) over rushes of each of the intermediates and combining the results into one expression. Such a procedure is always available for the intermediate linear schemes of the transformations. 

The expressions of the derived type (4.10) are valid for the intermediate linear schemes of catalytic stepwise reactions over a wide range of condi tions. Therefore, the stationary rate vj of the overall stepwise process can be treated here as proportional to the difference of thermodynamic rushes of the initial reactants and final products of the catalytic reaction. This is in line with the Horiuti Boreskov relation (1.36) (see Section 1.3.2) that describes the dependence of the stationary rates of many catalytic processes on the degree of their thermodynamic nonequilibricity. 

Thermolysis of 3-(ort o-anisoyl)-l-(l-piperidinyl)-3-cyclobutenes 807 in the presence of mesitylene affords angular-fused xanthones 809 via formation and ring closure of the intermediate 808 (Scheme 226) <1997TL3663>. Linear-fused xanthones 810 are prepared by nucleophilic addition of aryl and heteroaryl lithiates to dithiane protected benzopyrone-fused cyclobutenediones 811 followed by hydroysis of the dithiane protecting group (Scheme 227) <1996JA12473>. 

In the case of Brpnsted acidity, two reaction mechanisms have been suggested the formation of carbenium ion intermediate species (Scheme 6.2), which lead to the formation of branched oligomers[20] and the formation of a surface alkoxy structure intermediate, which leads to the formation of linear oligomers1191 (Scheme 6.3). In this case, the formation of alkoxy species has been recently... 

It is easy to demonstrate that the condition q < 0 is always met for the kinetic schemes that are linear with respect to the sole intermediate. The case of q > 0 is only possible in the intermediate nonlinear schemes, but the nonlinearity is an insufficient condition. We shall demonstrate this by analyzing simple nonlinear schemes. 

It is always much more difficult to analyze the intermediate nonlinear schemes than to analyze the linear schemes. Usually, there is no general analytic solution here, and only a narrow range of conditions can be con sidered via analyzing simple mathematical expressions without the help of computers. In some cases, one can use the mathematical solutions obtained for similar noncatalytic stepwise transformations, but these solutions must stiU be corrected via the balance for aU possible forms of active centers that should be then taken into account. 

The Lyapunov function O in the form of type (4.71) definite quadratic expression can be constructed for many other simple schemes of catalytic transformations, too, to allow the conclusion about stability of the catalyst in these systems. In particular, this conclusion is true in the case of any intermediate linear transformations—that is, one free of interactions between active centers of the catalyst. The conclusion also is vahd for the cases of more complex schemes that imply possibilities of the forma tion and coexistence of intermediates of the stepwise transformations, which escape the catalyst surface for the gas (liquid) phase provided that the intermediate catalytic complexes do not interact with one another. 

It is controversial whether DNJ 9 can be regarded as a true transition-state analog. Although protonated DNJ does mimic the charge development of the oxocarbenium intermediate 6 (Scheme 16.1), it adopts a chair conformation instead of the expected halfchair conformation of 6. A linear free-energy relationship analysis vs. which tested... 

ChemBase includes a relatively efficient and easy-to-use interface for creating short, linear schemes containing several intermediates. ChemBase does not allow the user to assign atom-atom mappings, and its earlier releases did not allow the assignment of reaction centres. Reaction searches in ChemBase can also retrieve false hits where the direction of the arrow is reversed, relative to the search query, since its internal data structure does not differentiate the sequential roles of intermediates. 

One typical example of the occurrence of halogen braiding in a transient species is the bromination of alkenes its textbook description involves a non-covalent precursor complex 10, in which the Br-Br - alkene angle is linear (Scheme 4). Subsequently, the Br-Br bond is broken, and a bromonium intermediate 11 is created. The latter process could also be described as a debromination of the strong halogen-bond donor dibromine by the alkene, or as an X-philic [69] SN2-type reaction at bromine. 

Then we decided to compare two approaches to the synthesis of cyclic dimers 41 which were described above. The first, via intermediate N,N -bis(bromobiphenyl) substituted polyamines 42 and 44, was complicated by the formation of linear oligomers 43 and 45 (Scheme 19). In the case of 3,3 -dibromobiphenyl 39 Xanthphos proved to be more efficient than BINAP due to its ability to suppress iV,iV-diaiylation of primary amines. The yields of target ( clodimers 38 and 41 were shown to be strongly dependent on the nature of polyamines, and the reactions also gave rise to by-products like cyclotetramers, cyclohexamers and linear oligomers. The attempts to use intermediate linear derivatives 42 and 44 in situ were unsuccessful. 

According to the linear scheme (Fig. 2a), a substance undergoes reaction which possesses a basic structure approximating more and more to the end product during the synthetic process. This method of synthesis, as an example of which may be taken the production of estrone by Anner and Miescher (Schemes 8 and 12), presents the maximum difficulties, since there is a progressive decrease in the yields of the key intermediates of the synthesis. Consequently, the production in high yield of optically active steroids in particular, by total synthesis, requires the earliest possible resolution of racemates. ... 

The action of ammonia on N-(5-aryl-l,3-oxathioI-2-ylidene) tertiary iminium salts (7) affords linear intermediates that cyclize to 2-amino-4-phenylthiazoles (Scheme 7) (45). 

The action of ammonia on N-(aryl-i,3-oxathiol-2-ylidine) tertiary im-inium salts (254) yields linear intermediates (255) that cyclize to 2-amino-4-phenyl thiazoles (256) on crystallization from acetic acid (Scheme 129) (730). 

Thiirane 1,1-dioxides extrude sulfur dioxide readily (70S393) at temperatures usually in the range 50-100 °C, although some, such as c/s-2,3-diphenylthiirane 1,1-dioxide or 2-p-nitrophenylthiirane 1,1-dioxide, lose sulfur dioxide at room temperature. The extrusion is usually stereospeciflc (Scheme 10) and a concerted, non-linear chelotropic expulsion of sulfur dioxide or a singlet diradical mechanism in which loss of sulfur dioxide occurs faster than bond rotation may be involved. The latter mechanism is likely for episulfones with substituents which can stabilize the intermediate diradical. The Ramberg-Backlund reaction (B-77MI50600) in which a-halosulfones are converted to alkenes in the presence of base, involves formation of an episulfone from which sulfur dioxide is removed either thermally or by base (Scheme 11). A similar conversion of a,a -dihalosulfones to alkenes is effected by triphenylphosphine. Thermolysis of a-thiolactone (5) results in loss of carbon monoxide rather than sulfur (Scheme 12). 

Equation (3-178) suggests that a plot of A obs/[ROH] vs. [N] will be linear. Because the conversion to the intermediate is quantitative, [N] = [N]o — [AXJq. Plots according to Eq. (3-178) were linear, permitting ky and A in to be estimated. Turning to the acetic anhydride—alcohol system, it is inferred that (in the absence of water) itj/lLi is close to zero (Scheme XXIV). Although the intermediate could not be detected spectrally, its possible presence is admitted in the rate equation for the loss of anhydride ... 

The hydrolysis proceeds via a diazafulvene intermediate, which in these systems can be formed without a total loss of aromatic character of the tricycle. It is tempting to suggest that, using this reasoning, linearly annelated 2-trifluoromethyl-imidazo[4,5-g]quinoline should be inert toward alkaline hydrolysis, as formation of the diazafulvene intermediate will again involve total dearomatization of the heterocyclic system (Scheme 36). 

Bradshaw et al. 67) were the first to propose a reaction pathway that is compatible with a transalkylidenation scheme. They suggested that the reaction proceeds via a quasi-cyclobutane intermediate. Applied to linear alkenes, this is pictured as follows ... 

Based on the assumption that this reaction goes through Jt-allyl Mo intermediates (A and B), the result from either linear carbonate (L-C) or branched carbonate (B-C) should give exactly the same result if the equilibrium between A and B is much faster than nucleophilic addition of sodium dimethyl malonate to A or B (Curtain-Hammett) as shown in Scheme 2.17. 

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