Abstract:The energetic span model allows the estimation of the turnover frequency (TOF) of a catalytic reaction from its calculated energy profile. Furthermore, by identifying the TOF determining intermediate and the TOF determining transition state, the model shows that the concept of ''determining states'' is more useful and correct than the concept of ''determining steps.'' This article illustrates the application of the model and provides an introduction to its concepts using instructive examples. The first part explains the model in its current state of development, whereas in the second part the degree of TOF control of the reactant and product concentrations is introduced. With this information, it is possible to give explicit recommendations regarding the conditions to be applied in the experiment, e.g., which reactant promotes the reaction or if a product kinetically inhibits it. At the end, we present the AUTOF program that allows the user to apply the complete model in a black box fashion.

A prototypical catalytic cycle for the direct carboxylation of unactivated arene C-H bonds with CO(2) based on ruthenium(II) pincer complexes as catalysts is proposed and investigated by density functional theory (DFT) methods. The energetic span model is used to predict the turnover frequency (TOF) of various potential catalysts, evaluating their efficiency for this reaction. In addition to modifications of the catalyst structure, we also investigated the effect of the substrate, the solvent, and the influence of a base on the thermodynamics and kinetics of the reaction. Turnover frequencies in the range of 10(5)-10(7) h(-1) are predicted for the best systems. Alternative reaction pathways that might prevent the reaction are also investigated. In all cases, either the respective intermediates are found to be unstable or activation barriers are found to be very high, thereby indicating that these alternative pathways will not interfere with the proposed catalytic cycle. As a result, several ruthenium pincer complexes are suggested as very promising candidates for experimental investigation as catalysts for the carboxylation of arene C-H bonds with CO(2).

The new approach for palladium-catalyzed cross-coupling of two non-activated aromatic compounds (D. R. Stuart, K. Fagnou, Science 2007, 316, 1172) was studied theoretically. The energetic span model (S. Kozuch, S. Shaik, Acc. Chem. Res. 2011, 44, 101, and references therein) was employed to analyze the kinetic behavior of the catalytic cycle. The computed energy profile, combined with the energetic span model, accounts for the experimental selectivity, which favors the hetero-coupling of benzene with indole. This selectivity is driven by a fine balance of the entropic contributions and the high ratio of concentrations used for benzene over indole. This analysis may allow future theoretical predictions of how different aromatic compounds can be effectively coupled.

The catalytic hydroamination of ethylene with ammonia was investigated by means of density functional theory (DFT) calculations. An initial computational screening of key reaction steps (C-N bond formation, N-H bond cleavage), which are assumed to be part of a catalytic cycle, was carried out for complexes with the [M(L)]-complex fragment (M=Rh, Ir; L=NCN, PCP; NCN=2,5-bis(dimethylaminomethyl)benzene, PCP=2,5-bis- (dimethylphosphanylmethyl)benzene). Based on the evaluation of activation barriers, this screening showed the rhodium compound with the NCN ligand to be the most promising catalyst system. A detailed investigation was carried out starting with the hypothetical catalyst precursor [Rh(NCN)(H)(2)(H(2))] (1). A variety of activation pathways to yield the catalytically active species [Rh(NCN)(H)(NH(2))] (5), as well as [Rh(NCN)(C(2)H(5))(NH(2))] (17), were identified. With 5 and 17 several closed catalytic cycles could be calculated. One of the calculated cycles is favoured kinetically and bond-forming events have activation barriers low enough to be put into practice. The calculations also show that for experimental realisation the synthesis of 1 is not necessary, as the synthesis of 17 would establish an active catalyst directly without the need for activation. Oligomerisation of ethylene would be possible in principle and would be expected as a competitive side reaction. Accordingly not only ethylamine would be observed in an experimental system, as amines with longer carbon chains also can be formed.

Very few cases of oxidative addition of NH(3) to transition-metal complexes forming terminal amide hydrides have been experimentally observed. Here, two examples with the iridium pincer complexes [Ir(PCP)(NH(3))] A1 with PCP = [κ(3)-(tBu(2)P-C(2)H(4))(2)CH](-) and [Ir(PSiP)(NH(3))] B1 with PSiP = [κ(3)-(2-Cy(2)P-C(6)H(4))(2)SiMe](-) were investigated by DFT calculations applying the M06L density functional to successfully reproduce the trend of the experimentally observed thermochemical stabilities. According to the calculations, the corresponding hydrido-amido complexes A2 and B2 are more stable than the corresponding ammine complexes by ΔG = -2.8 and -2.6 kcal  mol(-1), respectively. Complexes such as A2 and B2 are ideally suited entry points to catalytic cycles for the hydroamination of ethylene with ammonia. Therefore, the relevant stationary points of the potentially available cycles were studied computationally to verify if these complexes can catalyze the hydroamination. As a result, complex A2 will clearly not catalyze the hydroamination as all energy spans calculated range close to 40 kcal  mol(-1) or higher. The energy spans obtained with B2 are significantly lower in some cases and range around 35 kcal  mol(-1), further indicating that no turnover can be expected. By systematically varying the structure of B2, the energy span could be reduced to 28.8 kcal  mol(-1) corresponding to a TOF of 17 h(-1) at a reaction temperature of 140 °C. A reoptimization of relevant structures under the inclusion of cyclohexane as a typical solvent reduces the calculated TOF to 6.0 h(-1).