Substrate-catalyst complex

Reinhoudt at al. have recently reported [48] the preparation of a calix[4]arene functionalized with two Zn(II) centers 25, which is highly efficient on transesterification of HPNP. The dimer complex is reported to be 50 times more active (in 50 (v/v)% acetonitrile-water at pH = 7.4 and I = 298 K) than the corresponding monomer (26) which is itself 6 times more active than 27, implying the contribution of the calix[4]arene moiety in the mechanism. The saturation kinetic experiments showed high association constant for the catalyst-substrate complex (K -... 

The results were interpreted in terms of the model proposed by Balia and co-workers (36). It is reasonable to assume that the micelle formation produces a somewhat organized pattern of the metal centers and, due to the shortened distance between the copper(II) containing head groups, the coordination of catechol to two metal centers may increase the stability of the catalyst substrate complex. Perhaps, the same principles... 

The catalyst-substrate complexes deserve some additional comments. The two possible diastereomers for C2-symmetrical diphosphines interconvert inter- and intramolecularly, the latter being the dominant mechanism [76] (Scheme 1.22). A second property - at least of some catalyst-substrate complexes - is that the reactivity of the minor diastereomer toward H2 is notably higher than that of the major diastereomer. 

Extensive computational calculations have been performed by using molecular mechanics (MM) [79], quantum mechanics (QM) [80], or combined MM/QM methods [81]. As major contributions, these theoretical studies predict the greater stability of the major isomer, explain the higher reactivity of the minor diastereomer, introduce the formation of a dihydrogen adduct as intermediate in the oxidative addition of H2 to the catalyst-substrate complexes, and propose the migratory insertion, instead of the oxidative addition, as a turnover-limiting step. 

Most catalytic cycles are characterized by the fact that, prior to the rate-determining step [18], intermediates are coupled by equilibria in the catalytic cycle. For that reason Michaelis-Menten kinetics, which originally were published in the field of enzyme catalysis at the start of the last century, are of fundamental importance for homogeneous catalysis. As shown in the reaction sequence of Scheme 10.1, the active catalyst first reacts with the substrate in a pre-equilibrium to give the catalyst-substrate complex [20]. In the rate-determining step, this complex finally reacts to form the product, releasing the catalyst... 

A more detailed examination shows that, in case of equilibrium approximation, the value of fCM corresponds to the inverse stability constant of the catalyst-substrate complex, whereas in the case of the steady-state approach the rate constant of the (irreversible) product formation is additionally included. As one cannot at first decide whether or not the equilibrium approximation is reasonable for a concrete system, care should be taken in interpreting KM-values as inverse stability constants. At best, the reciprocal of KM represents a lower limit of a stability constant In other words, the stability constant quantifying the preequilibrium can never be smaller than the reciprocal of the Michaelis constant, but can well be significantly higher. 

The Michaelis constant has the dimension of a concentration and characterizes - independently of the method of approximation - the substrate concentration at which the ratio of free catalyst to catalyst-substrate complex equals unity. At this point, exactly one-half of the catalyst is complexed by the substrate. Likewise, one finds that at a value of [S = 10 Kki, the ratio of [E]/[ES]... 

Derivation of Michaelis-Menten Kinetics with Various Catalyst-Substrate Complexes... 

The rate law for two diastereomeric catalyst-substrate complexes -symmetric ligands) resulting from Michaelis-Menten kinetics (Eq. (11)) has already been utilized by Halpern et al. for the kinetic analysis of hydrogenations according to Scheme 10.2, and corresponds to Eq. (3) of this study. 

The value l/KM corresponds to the ratio of concentrations of the sum of all catalyst-substrate complexes to the product [solvent complex]-[substrate], and thus is a measure of how much catalyst-substrate complex is present [60]. 

The k0bs-values are all to be interpreted as the sum of all rate constants for the oxidative addition of hydrogen, each multiplied by the mole fraction of the corresponding catalyst-substrate complex. Hence this gross-rate constant is dependent only on the ratio of intermediates, and not on their absolute concentrations. 

NMR-analyses suggest that the hydrogenation runs corresponding to Scheme 10.3. Three of the four possible catalyst-substrate complexes are detectable in the 31P-NMR-spectrum [57 f]. 

Interpretation of the reciprocals of the Michaelis constants allows the following conclusions to be made regarding hydrogenations under specified experimental conditions. In the case of the methyl and cyclohexyl ligand, the prevailing form of the catalyst in solution is the catalyst-substrate complex. However, for the other examples of first-order reactions, large Michaelis constants (or very... 

In addition to comparisons of activity of various catalysts, the choice of an appropriate solvent represents yet another problem in catalysis. The choice is usually made by direct comparison of the activity of a catalyst in various solvents. Nonetheless, analogous problems as mentioned above must be considered. Variable substrate concentrations can lead to seemingly different orders in the activity of solvents. The reason for this is based on the fact that macroscopic activity is caused by different amounts of catalyst-substrate complex. 

As explained earlier, the pre-equilibria are characterized by the limiting values of Michaelis-Menten kinetics. In the case of first-order reactions with respect to the substrate, we have Kfvl [S]0. Since the pre-equilibria are shifted to the side of educts during hydrogenation, only the solvent complex is detectable. In contrast, in the case of zero-order reactions only catalyst-substrate complexes are expected under stationary hydrogenation conditions in solution. These consequences resulting from Michaelis-Menten kinetics can easily be proven by var-... 

Nonetheless, if zero-order reactions are analyzed in terms of the validity of Mi-chaelis-Menten kinetics, all of the catalyst is present in solution as catalyst-substrate complex up to high conversions. The hydrogenation rate is independent of the substrate concentration two such examples are provided in Figure 10.21. 

Thus, if information is being sought about intermediates for this type of catalysis, it does not make sense to analyze systems that lead to first-order reactions Rather, systems in which the hydrogenation rate is independent of the substrate concentration would be more appropriate. Indeed, for both catalytic systems shown in Figure 10.21, in each case one of the catalyst-substrate complexes could be isolated and characterized by crystal structure analysis (Fig. 10.23). 

Due to re- and si-coordination of prochir-al substrates at a catalyst with C2-sym-metric chiral ligands two diastereomeric catalyst-substrate complexes emerge. In the case of C,-symmetric ligands already four stereoisomer intermediates result. 

An irreversible formation of the catalyst-substrate complex is described in D. D. 

The studies of Thomas and Raja [28] showed a remarkable effect of pore size on enantioselectivity (Table 42.3). The immobilized catalysts were more active than the homogeneous ones, but their enantioselectivity increased dramatically on supports which had smaller-diameter pores. This effect was ascribed to more steric confinement of the catalyst-substrate complex in the narrower pores. This confinement will lead to a larger influence of the chiral directing group on the orientation of the substrate. Although pore diffusion limitation can lead to lower hydrogen concentrations in narrow pores with a possible effect on enantioselectivity (see Section 42.2), this seems not to be the case here, because the immobilized catalyst with the smallest pores is the most active one. 

Catalyst-Substrate Complexes 277 Data from Gross Kinetic Measurements 280 Abbreviations 288 References 288... 

The high levels of enantioselectivity obtained in the asymmetric catalytic carbomagnesa-tion reactions (Tables 6.1 and 6.2) imply an organized (ebthi)Zr—alkene complex interaction with the heterocyclic alkene substrates. When chiral unsaturated pyrans or furans are employed, the resident center of asymmetry may induce differential rates of reaction, such that after -50 % conversion one enantiomer of the chiral alkene can be recovered in high enantiomeric purity. As an example, molecular models indicate that with a 2-substituted pyran, as shown in Fig. 6.2, the mode of addition labeled as I should be significantly favored over II or III, where unfavorable steric interactions between the (ebthi)Zr complex and the olefmic substrate would lead to significant catalyst—substrate complex destabilization. 

The proper treatment of the electronic subtleties at the metal center is not the only challenge for computational modeling of homogeneous catalysis. So far in this chapter we have focused exclusively in the energy variation of the catalyst/substrate complex throughout the catalytic cycle. This would be an exact model of reality if reactions were carried out in gas phase and at 0 K. Since this is conspicously not the common case, there is a whole area of improvement consisting in introducing environment and temperature effects. 

For a possible quantitative description of typical polymer effects we made the assumption that the values of AH and AS found for the low molecular weight catalysts stand for the activation process of the naked catalyst-substrate complex and are independent of cx. So, after subtracting these values the separate polymer effects are found. Then we have to explain why more entropy is gained and more enthalpy is needed for adaptation of the intermediate chains to... 

Figure 10. Schematic of the proposed catalyst-substrate complex, before and in the activated state. The increase of the chain end-to-end distance possibilities is represented by the bases of the cones.

Figure 11. Illustration of Equation 1 for the calculation of the increase in number of intermediate chain conformations accompanying deformation and activation of the polymeric catalyst-substrate complexes...

Anyhow, our study has demonstrated the benefit of "strained" polymeric catalyst-substrate complexes, a phenomenon well-known in enzymology (26) and once indicated by the term "entatic state" (16). 

In cases where hydrogen bond donor/acceptor functions are attached to a (chiral) scaffold, they can steer the assembly of a well defined catalyst-substrate complex. The positions of hydrogen bond donors and acceptors determine the stereoselectivity of the reaction. 

This reaction encompasses a number of interesting features (general Brpnsted acid/ Brpnsted base catalysis, bifunctional catalysis, enantioselective organocatalysis, very short hydrogen bonds, similarity to serine protease mechanism, oxyanion hole), and we were able to obtain a complete set of DFT based data for the entire reaction path, from the starting catalyst-substrate complex to the product complex. 

---