Calculations catalytic cycle

Scheme 8.12 Calculated catalytic cycle and Gibbs free energies (AG) of 2M3BN isomerization employing Rucaphos 12d as a ligand [38, 44],...

To fully elucidate the mechanism of the reaction a computational study using the M06 functional was undertaken. Most of the overall mechanism, such as the involvement of a P-hydride elimination, a migratory insertion, and some details on the structure of the active catalyst, had been determined experimentally. Therefore, the main challenge to be solved by this computational study was to confirm the mechanistic proposal and clarify the fine details such as the distinction between the two pathways in which either the hydride (pathway a) or the amine (pathway b) are located trans to the alkoxide. The full calculated, catalytic cycle is shown in Scheme 8.12. 

Complex a is readily converted into a Fe-y-H agnostic complex b within an early picosecond timescale and then the 7i-allyl hydride complex c is generated by hydride abstraction. The energy level of the 2-alkene isomer d, which is calculated by DPT experiments, is similar to that of the 1-alkene complex b. In the next step, Fe (CO)3(t -l-alkene)(ri -2-alkene) f, which is generated via intramolecular isomerization of the coordinated 1-alkene to 2-alkene and the coordination of another 1-alkene, is a thermodynamically favored product rather than formation of a Fe(CO)3(ri -l-alkene)2 e. Subsequently, release of the 2-aIkene from f regenerates the active species b to complete the catalytic cycle. 

The next step involves the generation of the new aUcene by P-hydride elimination, throngh an agostic interaction, and evolution to a hydride-paUadium complex. The calculated potential surfaces for the overall insertion-elimination process are quite flat and globally exothermic [11,15], Finally, the reductive elimination of the hydride-Pd(ll) complex, which is favoured by steric factors related to the buUdness of the iV-substituents on the carbene [13], provides the active species that can enter into a new catalytic cycle. 

Figure 2-9. Reaction scheme for the complete catalytic cycle in glutathione peroxidase (left). Numbers represent calculated reaction barriers using the active-site model. The detailed potential energy diagram for the first elementary reaction, (E-SeH) + H2O2 - (E-SeOH) + H2O, calculated using both the active-site (dashed line) and ONIOM model (grey line) is shown to the right (Adapted from Prabhakar et al. [28, 65], Reprinted with permission. Copyright 2005, 2006 American Chemical Society.)...

Fig. 5. Energy profile (AG/kcal mol-1) of a catalytic cycle of N2 in a Mo-pentaphosphine complex with reduction by decamethylchromocene and protonation by HLut+ obtained by DFT calculations (31).

An informative set of calculations was carried out by Brandt et al, coupled to experimental studies that demonstrated first-order dependence of the turnover rate on both catalyst and H2, and zero-order dependence on alkene (a-methyl-(E)-stilbene) concentration [71]. The incentive for this investigation was the absence of any characterized advanced intermediates on the catalytic pathway. As a result of the computation, a catalytic cycle (for ethene) was proposed in which H2 addition to iridium was followed by alkene coordination and migratory insertion. The critical difference in this study was the proposal that a second molecule of H2 is involved that facilitates formation of the Ir alkylhydride intermediate. In addition, the reductive elimination of R-H and re-addition of H2 are concerted. This postulate was subsequently challenged. For hydrogenation of styrene by the standard Pfaltz catalyst, ES-MS analysis of the intermediates formed at different stages in the catalytic cycle revealed only Ir(I) and Ir(III) species, supporting a cycle (at least under low-pressure conditions in the gas... 

The Hartree-Fock method was in any case the method of choice for the first quantitative calculations related to homogeneous catalysis. It was the method, for instance, on a study of the bonding between manganese and hydride in Mn-H, published in 1973 [28]. The first studies on single steps of catalytic cycles in the early 1980 s used the HF method [29]. And it was also the method applied in the first calculation of a full catalytic cycle, which was the hydrogenation of olefins with the Wilkinson catalyst in 1987 [30]. The limitations of the method were nevertheless soon noticed, and already in the late 1980 s, the importance of electron correlation was being recognized [31]. These approaches will be discussed in detail in the next section. 

The previous section has described how one can compute accurately a system of about 30 atoms including one transition metal. The problem is, as mentioned above, that these are usually not the real catalysts, but model systems where the bulky substituents have been replaced by hydrogen atoms. Calculations on model systems are usually at least indicative of the nature and the energy barriers of the steps involved in a catalytic cycle, but they are often unable to provide information on some of the most interesting features, namely enantioselectivity and regioselectivity. The reason for this failure is simply that selectivity is often associated to the presence of the bulky substituents which are deleted when defining the model system. 

For an ea HRh(CO)(alkene)(diphosphine), in which the hydride is assumed, as in Figure 3, to be in axial position, alkene have two coordination sites available, four conformations for each site, two rotation sides, N ligand conformations, and therefore 16xN TS s. Computation of the full catalytic cycle, all intermediates and TS s, from the entry of the substrate to the departure and regeneration of the catalyst, complemented with IRC calculations to confirm the connection between TS s and intermediates is out of reach for current computational resources. However, suitable modeling strategies can reduce of the problem, and still provide useful insight. 

Figure 12. Calculated reaction profile with QM/MM model B of the catalytic cycle for the most favoured pathway.

Figure 12 shows the reaction profile for the hydrosilylation process involving the most stable fi3-sily 1-ally 1 complex, 10a-anti, calculated with model B. Examination of the reaction profile suggests that the rate determining step of the catalytic cycle is the reductive elimination. More specifically, the transfer of the silyl moiety to the (J-carbon of the styrene. Since recoordination of the pyrazole ligand occurs in this step, it is possible that enhancement of this ligands ability to recombined with the Pd center may lead to improved activities. 

In order to rationalize the factors determining the enantioselectivity of the hydrosilylation of the para-substituted styrenes, we have calculated the relative thermodynamic stabilities of all the intermediates of the catalytic cycle that are precursors of the two enantiomeric products as a function of the para-substituted substrates. Since, the 5 configuration product was formed in 64% ee from styrene, whereas 4-(dimethylamino)styrene afforded the R product with 64% ee [6], we have performed all calculations with these two different substrates. We shall demonstrate, in fact, that the relative thermodynamic stabilities of the fi3-allylic complexes are decisive for both the regio and the stereoselectivity. 

In the calculations performed with model B the to-7i-complex is destabilized by 1.6 kcal/mol with respect to the corresponding endo isomer. If we were to follow the more stable endo rc-complex isomer through the Chalk-Harrod mechanism, this would lead to the R form of the product as shown on the left-hand-side of Figure 15. Since it is actually the S form of the product that dominates when styrene is the substrate, the formation of the tt-complex cannot be the stereodetermining step of the catalytic cycle. 

As an inversion of enantioselectivity was observed experimentally for 4-(dimethylamino)styrene, (64% R ee) as compared to styrene (64% S ee), we have recalculated the relative thermodynamic stabilities of endo and exo isomers for each step of the catalytic cycle using this second substrate. These calculations allow us to verify the quality of our findings by checking if an inversion in the relative stabilities of the endo and the exo-ri3-silyl-allyl intermediates (with the endo being more stable than the exo) is observed with 4-(dimethylamino)styrene. Using 4-(dimethylamino)styrene as the substrate, the calculated relative stabilities of the intermediates in the Chalk-Harrod mechanism are shown as parenthetic values in Figure 15. 

---