Stepwise transformations

Nature, however, has performed more than simple stepwise transformations using a combination of enzymes in so-called multienzyme complexes, it performs multistep synthetic processes. A well-known example in this context is the biosynthesis of fatty acids. Thus, Nature can be quoted as the inventor of domino reactions. Usually, as has been described earlier in this book, domino processes are initiated by the application of an organic or inorganic reagent, or by thermal or photochemical treatment. The use of enzymes in a flask for initiating a domino reaction is a rather new development. One of the first examples for this type of reaction dates back to 1981 [3], although it should be noted that in 1976 a bio-triggered domino reaction was observed as an undesired side reaction by serendipity [4]. 

Chisholm and his group recently succeeded in transforming a metal carbonyl into a stable fi4-carbido complex W4( 4-C)(/t-NMe)(0-i-Pr)12 1 The 13C-NMR signal for the (/ 4-C)4 ligand is 366.8 ppm [5] which can be considered as a realistic model of a surface bound carbido species in the sense of the original proposal by Fischer and Tropsch (Fig. 2). Upon addition of hydrogen, surface bound carbide can be stepwise transformed into methane. 

Having established structural and electronic analogies between metal oxides and alkoxides of molybdenum and tungsten, the key remaining feature to be examined is the reactivity patterns of the metal-alkoxides. Metal-metal bonds provide both a source and a returning place for electrons in oxidative-addition and reductive elimination reactions. Stepwise transformations of M-M bond order, from 3 to 4 (37,38), 3 to 2 and 1 (39) have now been documented. The alkoxides M2(0R)6 (MiM) are coordinatively unsaturated, as is evident from their facile reversible reactions with donor ligands, eq. 1, and are readily oxidized in addition reactions of the type shown in equations 2 (39) and 3 (39). 

The last sequence in particular demonstrates the same sort of stepwise transformation observed in the rhenium chemistry described above. 

As described in Section 13.03.1 and CHEC-II(1996) <1996CHEC-II(9)67>, thiepines are thermally unstable through valence isomerization to the corresponding thianorcaradienes, followed by irreversible cheleotropic loss of sulfur. Thiepines, as unstable intermediates, have been postulated in some stepwise transformations. 

Scheme 1.1 Alternative concerted and stepwise transformations of one molecule into another.

Kramer, A., Stigler, R.-D., Knaute, T., Hoffmann, B and Schneider-Mergener, J. (1998) Stepwise transformation of a cholera toxin an a p24 (HIV-1) epitope into D-peptide analogs. Protein Eng. 11, 941-948. 

Figure 5. Stepwise transformation of Cr( j3- 31(5)3 anchored onto silica to form a monolayer (from Ref. 15, FM = full monolayer).

An example of a reaction sequence involving both C—H and (3-C—C activation reactions is the stepwise transformation of a neopentyl into a trimeth-ylenemethyl ligand in (SiP3)Ru complexes [SiP3 = MeSi(CH2PMe2)3] 119... 

In the consideration of chemical transformations, we shall distinguish elementary and combined (stepwise) stoichiometric transformations. The elemen tary chemical transformations are those that run through the formation of only one transition state. The transition state is not thermalized, or at least not thermalized at the reaction coordinate. The stepwise transformations comprise the formation of some intermediate products, which we shall always consider as thermalized. 

Let two stoichiometric stepwise reactions, which involve some combi nation of elementary chemical reactions, be concurrent in the system. Indicate these stepwise reactions by indices 21 and 22. It is evident that for stoichiometric stepwise transformations, the elementary reactions can be omitted in the equation for djS/dt ... 

The latter inequality contradicts the condition of the spontaneous mode of stepwise reaction 22. Therefore, in this case the two stepwise reactions under consideration must be interdependent, or conjugate. The former reaction, which is thermodynamically allowed to be spontaneous, is referred to as conjugating, while the latter reaction is referred to as conju gated to the former one. Chapter 2 will demonstrate that the conjugation occurs only in cases when the stepwise processes encompass elementary stages with common (for the stepwise reactions) intermediates omitted in the equation to describe these stoichiometric stepwise transformations. 

Apparently, thermodynamic rushes for the series of transformations under consideration and, as a result, chemical potentials of the intermediates in their stationary states must decrease progressively while passing from one intermediate to another. When the stepwise transformation may follow sev eral parallel pathways of consecutive elementary transformations, the said relationship between the stationary chemical potentials of the intermediates must be met for each of the possible pathways of the stepwise reaction. 

Hence, the correct thermodynamic criterion of the kinetic irreversibility at any step in the chemical transformation chain is a considerable (against quantity RT) change in the chemical potential of the reaction groups related to this step—that is, A j > RT. Note that the criterion is valid for both elementary and stepwise reaction, although in the latter case, one must consider the affinity for the stepwise transformation A,2 > RT. 

Among the thermodynamic parameters of thermalized reactants, only parameters of external reactants R and P influence the rate vj in this example. The most considerable is the influence of the reactant with the greatest ther modynamic rush—for example, R. This also means that reactant R is the initial reactant in the stepwise transformation (i.e., the reaction goes from R toward P). This statement is illustrated diagrammaticaUy in Figure 1.7. 

The same conclusion can be made with the help of classical kinetics Since all of the steps that precede the rate limiting step can be considered as being in equihbrium (see Section 1.4.4), the apparent classical rate con stant for the stepwise transformation is expressed as... 

This specific feature of equations (2.16) is very important. It allows the Onsager equations to be expanded to the systems that are arbitrarily far from the thermodynamic equilibrium. In the case of an arbitrary number of cocurrent stoichiometric stepwise reactions (i = 1,. .., m) that have common intermediates of the transformations, the rates of these stepwise reactions are interdependent. (Here, and are the initial and final reaction groups, respectively, of the stepwise transformations by the channel Si.)... 

Dynamic driving forces = Rjy P j are prescribed by external (in respect to the processes of the intermediate transformations inside the system in its stationary state) parameters, such as the difference between thermody namic rushes of the initial and final reaction groups in corresponding channels of the resulting stepwise transformations. The vahdity of equation (2.17) is easy to check by considering specific pathways of conjugate transformations in a variety of examples presented in Section 2.3.5. 

In fact, the real driving forces of the stepwise processes under consideration here are affinities of the respective stepwise transformations ... 

We must emphasize that in this example, again, Ai2 / A21. However, it is also easy to demonstrate that Li2 = L2i on approaching the equilibrium of the stepwise transformations when the true Onsager coefficients Ly relate to true thermodynamic forces (the affinities of the stepwise processes). 

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. 

Let us prove the GlansdorGPrigogine theorem with an example of an arbitrary spatially homogeneous chemical reactive system. The internal parameters for such a system are the concentrations of intermediates of the stepwise chemical transformations. Any spontaneous changes of the system (and, as a result, changes in internal driving forces) relate namely to changes in the intermediate concentrations. Therefore, the partial force differential dxP may be substituted for by its full analogue related thermodynamic rushes (concentrations) of intermediates (a 1,. .., k) of the stepwise transformations ... 

Here, Ej is the effective value of the truncated rate constant of the stepwise transformation (1.34), while Rs is the total effective electric resistance of the electric circuit that is its analogue. 

As earlier, R and P are the starting reactant and final product, respectively, of the stepwise transformation (see also Section 3.4.1). External parameter R can be taken here as the controlling parameter. The kinetic irreversibility of the second step means that this step is a priori far from thermodynamic equilibrium. This is the necessary condition of the instability of stationary states. Let us check this. 

Example 10 Multiplicity of stable stationary states at the S shaped kinetic characteristics of stepwise transformations... 

When the stationary rate of stepwise transformations is described by an S-shaped dependence, the affinity A,2 of the stepwise reaction (Figure 3.3) the properties of the reactive system can be inspected in the similar way. Like Example 9, in the system there may exist two stable stationary states at certain values of the affinity A,2 and the... 

With the balance for the number of available forms of active centers of a catalyst, the concentrations and, correspondingly, the thermodynamic mshes of the reaction complexes catalytic intermediates)—that is, the thermalized intermediate compounds of the reactant molecule (or molecular fragment) with the active center—appear interrelated through these balance relations in respect of each type of active center. The balance is of primary importance to the kinetics of the stepwise transformations and causes a number ofpecuHarities of the stationary kinetics of the stepwise processes. This makes the kinetic description of the catalytic transformations differ considerably from the descrip tion of the preceding schemes of noncatalytic reactions. For example, in the simplest catalytic stepwise transformation of substance R to substance P,... 

The current or stationary values of chemical potentials of catalytic inter mediates are of principal importance for analyzing the role of the inter mediates in catalytic processes. For example, in the stationary mode of catalytic reactions, the relevant chemical transformations, the reactant-active center complexes—should be described as transitions between the stationary chemical potentials rather than the traditionally considered minimums of potential energy that relate to the standard state of the parti cipants of the stepwise transformation (see, for example, Figure 4.1). 

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. 

In general cases of several concurrent channels of catalytic stepwise transformations... 

Equations like (4.97) and (4.98) may be extremely useful, at least in the preliminary microkinetic analysis of the behavior of complex catalytic transformations with unknown elementary mechanisms The kinetic scheme of the stationary stepwise transformation in such a system is only determined using empirical coefficients Ay, while the sign or the absence of any thermodynamic forces Xj governs the system evolution along a given trajectory. 

Conclusion 2 In some cases the selectivity of conjugate catalytic stepwise transformations can be controlled by varying chemical potentials of not only initial reactants but also of the transformation products. Moreover, stepwise side reactions may be sometimes reversed, while the side products can be even utilized to form the target products. 

The coke deposition on a catalyst under operation of the latter Is a typical reason for the catalyst deactivation. This process also can be considered as a manifestation of nonselectivity in the conversion of various organic compounds. Hence, the practically important problem is to find the conditions of the coking prevention. As an example, let us identify the conditions of no coke deposition on catalysts during the "dry" methane reforming described by a stepwise transformation as follows ... 

One can see that the derived condition of no coke formation during the main stepwise transformation (4.99) differs considerably from the necessary simultaneous satisfaction of a more rigid system of two inequalities (4.101). 

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