Intermediate linear scheme transformation

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. 

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. 

When the cis/trans stereoselectivity of cyclopropanation with ethyl diazoacetate in the presence of CuCl P(0-z-Pr)3, Rh6(CO)16 or PdCl2 2 PhCN was plotted against that obtained with Rh2(OAc)4, a linear correlation was observed in every case, with slopes of 1.74,1.04 and 0.59, respectively (based on 22 olefins, T = 298 K) S9). These relationships as well as the results of regioselectivity studies carried out with 1,3-dienes point to the similar nature of the intermediates involved in Cu-, Rh-and Pd-catalyzed cyclopropanation. Furthermore, obvious parallels in reactivity in the transformations of Scheme 45 for a variety of catalysts based on Cu, Rh, Fe, Ru, Re and Mo suggest the conclusion that electrophilic metal carbenes are not only involved in cyclopropanation but also in ylide-forming reactions66. ... 

Numerous studies aimed at the understanding of the mechanism of these processes rapidly appeared. In this context, Murai examined the behavior of acyclic linear dienyne systems in order to trap any carbenoid intermediate by a pendant olefin (Scheme 82).302 A remarkable tetracyclic assembly took place and gave the unprecedented tetracyclo[6.4.0.0]-undecane derivatives as single diastereomer, such as 321 in Scheme 82. This transformation proved to be relatively general as shown by the variation of the starting materials. The reaction can be catalyzed by different organometallic complexes of the group 8-10 elements (ruthenium, rhodium, iridium, and platinum). Formally, this reaction involves two cyclopropanations as if both carbon atoms of the alkyne moiety have acted as carbenes, which results in the formation of four carbon-carbon bonds. 

When R2 substituent is flourocontaining alkyl group, the transformation 17 18 becomes hindered and its proceeding requires some special methods. For example, in [48] Biginelli-like cyclocondensations based on three-component treatment of 3-amino-l,2,4-triazole or 5-aminotetrazole with aldehydes and fluorinated 1,3-dicarbonyl compounds were investigated. It was shown that the reaction can directly lead to dihydroazolopyrimidines 20, but in the most cases intermediate tetrahydroderivatives 19 were obtained (Scheme 10). To carry out dehydration reaction, refluxing of tetrahydroderivatives 19 in toluene in the presence of p-TSA with removal of the liberated water by azeotropic distillation was used. The same situation was observed for the linear reaction proceeding via the formation of unsaturated esters 21. 

It is generally agreed that the CL obtained with luminol (124) is based on the series of transformations shown in Scheme 3, where the analyte (oxidant) as such or in combination with a catalyst produces a free radical (125), which in turn captures a superoxide anion to yield an endoperoxide (126), which on elimination of N2 produces an excited intermediate (127), which finally settles down to the 3-aminophthalate ion (128) on emission of a photon. A linear correlation may be established between the intensity of the CL emission and the concentration of the analyte334. 

An indirect method has been used to determine relative rate constants for the excitation step in peroxyoxalate CL from the imidazole (IM-H)-catalyzed reaction of bis(2,4,6-trichlorophenyl) oxalate (TCPO) with hydrogen peroxide in the presence of various ACTs18. In this case, the HEI is formed in slow reaction steps and its interaction with the ACT is not observed kinetically. However, application of the steady-state approximation to the reduced kinetic scheme for this transformation (Scheme 6) leads to a linear relationship of 1/S vs. 1/[ACT] (equation 5) and to the ratio of the chemiluminescence parameters /ic vrAi), which is a direct measure of the rate constant of the excitation step. Therefore, this method allows for the determination of relative rate constants for the excitation step in a complex reaction system, where this step cannot be observed directly by kinetic measurements18. The singlet quantum yield at infinite activator concentrations ( °), where all high-energy intermediates formed interact with the activator, is also obtained from this relationship (equation 5). 

The similar features of stationary processes are characteristic of some step wise reactions with nonmonomolecular transformations of the intermediate as well. For example, the stationary rate of a stepwise process is proportional to the difference of thermodynamic mshes of the initial and final reaction groups for any schemes of stepwise processes with the transformations linear to the intermediates. However, the value of 2 may depend in such cases not only on y but also on thermodynamic mshes of some initial or final reactants. 

Let us look at an example of a simple scheme of transformations that are linear with respect to their intermediates. First, we will consider a stoi chiometric stepwise process ... 

In a similar way, substituting the series of certain transformations at their stationary modes by effective transformations will allow the exact expressions of the reciprocity coefficients Ay to be found for even very complex schemes of cocurrent stepwise transformations, provided that these are linear with respect to the intermediates. Unfortunately, for an arbitrary case of cocurrent stepwise transformations that are nonlinear in respect to their intermediates and proceed far from equilibrium, it is not possible to write general equations that are analogous to the modified Onsager relations. 

Hence, at low coverage of the active centers by the intermediate, the stationary rate, v, of the catalytic reaction under consideration, like that of noncatalytic transformations, is independent of the standard thermodynamic parameters of the thermalized intermediate. In addition to the linear dependence of the stationary rate on the difference between thermodynamic rushes of the initial reactant and the final product, there is also proportionality of the rate on the thermodynamic rush of the free form of the active center and the dependence on the standard thermodynamic parameters of transition states of the elementary reactions in scheme (4.4). 

Using Ugi-4CR as prototypical reaction, a possible reaction leading to twofold and fourfold cyclic adduct is shown in Scheme 17. The first Ugi adduct 58 could react further with FGi and FG2 to afford the cyclic product 59 ((1), Scheme 17). Alternatively, the adduct 58 can react with a second equivalent of a bifunctional substrate 56, FGj and FG2 to provide twofold linear Ugi adduct 60, which could be further transformed to fourfold Ugi cyclic adduct 62 via intermediate 61. The formation of higher-order ohgomers/cyclic oligomers could be competitive making this reaction quite difficult to control. However, it is expected that the overall reaction outcome could in principle be governed by the three-dimensional structure of the bifunctional inputs 56 and 57. 

The formation of the transient thioformyl thioketene 159 and thiacyl thioketene 160 has also been confirmed in flash vacuum pyrolysis (FVP) of l,2-dithiole-3-thiones lb and 158, in the temperature range 800-1000°C, respectively (Scheme 19) <1996TL4805>. A hitherto-unknown transformation of the intermediates 159 and 160, as the most carbon rich carbon sulfides, into linearly shaped carbon subsulfide C3S2 (l,2-propadiene-l,3-dithione) was obtained and identified in an argon matrix at 10 K. 

Fig. 4 shows the dependence of the different hydrocarbons yield on contact time for two catalysts at 673 K. C3-C4 paraffins yield increased linearly with contact time and aromatics content rose also gradually. C3-C4 olefins yield rapidly reached steady values with Ga-silicate while a distinct maximum in their concentration was observed with the Pt/Ga-silicate. The analysis of these trends confirmed suggestions made in the literature [lO] that aromatization process involves several parallel and consecutive stages of both initial paraffin and Intermediates transformations, which can depicted as the following scheme ... 

The added acid most likely plays several roles. First, the acid is necessary for the redox transformation of Pd(0)-BQ to Pd(ll) + HQ in the catalytic cycle [65]. Second, the acid will lead to the formation of a cationic 7t-allylpalladium intermediate which will facilitate coordination of BQ. Third, the acid will protonate the oxygen of the coordinated BQ, and in this way the quinone becomes more electron-withdrawing. It was found that the rate of the reaction increased with the amount of acid, and that there was a linear increase in the range of 0-30 mol% of acid however, adding too much acid catalyzed the destruction of BQ. The stereochemistry of the dialkoxylation is consistent with a trans alkoxypalladation [118] of the diene to give 7t-allyl intermediate 91, followed by external trans attack of alcohol to give the cis-dialkoxy compound 92 (Scheme 11.32). 

---