Sebastian Kozuch

How to Conceptualize Catalytic Cycles? The Energetic Span Model

A computational study of a catalytic cycle generates state energies (the E-representation), whereas experiments lead to rate constants (the k-representation). Based on transition state theory (TST), these are equivalent representations. Nevertheless, until recently, there has been no simple way to calculate the efficiency of a catalytic cycle, that is, its turnover frequency (TOF), from a theoretically obtained energy profile. In this Account, we introduce the energetic span model that enables one to evaluate TOFs in a straightforward manner and in affinity with the Curtin-Hammett principle. As shown herein, the model implies a change in our kinetic concepts. Analogous to Ohms law, the catalytic chemical current (the TOF) can be defined by a chemical potential (independent of the mechanism) divided by a chemical resistance (dependent on the mechanism and the nature of the catalyst). This formulation is based on Eyrings TST and corresponds to a steady-state regime. In many catalytic cycles, only one transition state and one intermediate determine the TOF. We call them the TOF-determining transition state (TDTS) and the TOF-determining intermediate (TDI). These key states can be located, from among the many states available to a catalytic cycle, by assessing the degree of TOF control (X(TOF)); this last term resembles the structure-reactivity coefficient in classical physical organic chemistry. The TDTS-TDI energy difference and the reaction driving force define the energetic span (δE) of the cycle. Whenever the TDTS appears after the TDI, δE is the energy difference between these two states; when the opposite is true, we must also add the driving force to this difference. Having δE, the TOF is expressed simply in the Arrhenius-Eyring fashion, wherein δE serves as the apparent activation energy of the cycle. An important lesson from this model is that neither one transition state nor one reaction step possess all the kinetic information that determines the efficiency of a catalyst. Additionally, the TDI and TDTS are not necessarily the highest and lowest states, nor do they have to be adjoined as a single step. As such, we can conclude that a change in the conceptualization of catalytic cycles is in order: in catalysis, there are no rate-determining steps, but rather rate-determining states. We also include a study on the effect of reactant and product concentrations. In the energetic span approximation, only the reactants or products that are located between the TDI and TDTS accelerate or inhibit the reaction. In this manner, the energetic span model creates a direct link between experimental quantities and theoretical results. The versatility of the energetic span model is demonstrated with several catalytic cycles of organometallic reactions.

Kinetic-Quantum Chemical Model for Catalytic Cycles: The Haber−Bosch Process and the Effect of Reagent Concentration

A combined kinetic-quantum chemical model is developed with the goal of estimating in a straightforward way the turnover frequency (TOF) of catalytic cycles, based on the state energies obtained by quantum chemical calculations. We describe how the apparent activation energy of the whole cycle, so-called energetic span (delta E), is influenced by the energy levels of two species: the TOF determining transition state (TDTS) and the TOF determining intermediate (TDI). Because these key species need not be adjoining states, we conclude that for catalysis there are no rate-determining steps, only rate determining states. In addition, we add here the influence of reactants concentrations. And, finally, the model is applied to the Haber-Bosch process of ammonia synthesis, for which we show how to calculate which catalyst will be the most effective under specific reagents conditions.

Automatic analysis of computed catalytic cycles

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.

Spin‐component‐scaled double hybrids: An extensive search for the best fifth‐rung functionals blending DFT and perturbation theory

Following up on an earlier preliminary communication (Kozuch and Martin, Phys. Chem. Chem. Phys. 2011, 13, 20104), we report here in detail on an extensive search for the most accurate spin‐component‐scaled double hybrid functionals [of which conventional double hybrids (DHs) are a special case]. Such fifth‐rung functionals approach the performance of composite ab initio methods such as G3 theory at a fraction of their computational cost, and with analytical derivatives available. In this article, we provide a critical analysis of the variables and components that maximize the accuracy of DHs. These include the selection of the exchange and correlation functionals, the coefficients of each component [density functional theory (DFT), exact exchange, and perturbative correlation in both the same spin and opposite spin terms], and the addition of an ad‐hoc dispersion correction; we have termed these parametrizations “DSD‐DFT” (Dispersion corrected, Spin‐component scaled, Double‐hybrid DFT). Somewhat surprisingly, the quality of DSD‐DFT is only mildly dependent on the underlying DFT exchange and correlation components, with even DSD‐LDA yielding respectable performance. Simple, nonempirical GGAs appear to work best, whereas meta‐GGAs offer no advantage (with the notable exception of B95c). The best correlation components appear to be, in that order, B95c, P86, and PBEc, while essentially any good GGA exchange yields nearly identical results. On further validation with a wider variety of thermochemical, weak interaction, kinetic, and spectroscopic benchmarks, we find that the best functionals are, roughly in that order, DSD‐PBEhB95, DSD‐PBEP86, DSD‐PBEPW91, and DSD‐PBEPBE. In addition, DSD‐PBEP86 and DSD‐PBEPBE can be used without source code modifications in a wider variety of electronic structure codes. Sample job decks for several commonly used such codes are supplied as electronic Supporting Information. Copyright

The many faces of halogen bonding: a review of theoretical models and methods

Halogen bonds, the formally noncovalent interactions where the halogen acts as a Lewis acid, have brought several controversies to the theoretical world regarding its nature and components, e.g., charge transfer (CT), electrostatics, dispersion, and polarization. The debate on whether all characteristics are accounted for by electrostatics is examined, highlighting the importance of the CT and repulsive interactions. A number of strongly halogen‐bonded complexes are as covalent as metal–ligand coordination bonds. Different levels of computational methods are reviewed with the objective of finding the best accuracy/cost ratios. The unusual electronic anisotropy of the halogen donor and its interaction with a Lewis base demand specific calculation schemes. From the wave‐function theory methods, only the ones with empirical corrections (spin‐component‐scaled MP2 or CCSD, and MP2.5) are suitable when CCSD(T) is unattainable. Density functional theory functionals with a high amount of exact exchange are fast and reliable methods for halogen bonds, but double hybrids are more robust if other types of interactions are involved. Molecular mechanics methods can be useful, but only when specific corrections are added to compensate for the inability of such methods to describe CT. The most common method introduces a virtual site with a partial positive charge to account for the quantum chemical effect of the halogen bond. This methodology has been successfully applied to study protein–ligand interactions for drug design. WIREs Comput Mol Sci 2014, 4:523–540. doi: 10.1002/wcms.1189

A refinement of everyday thinking: the energetic span model for kinetic assessment of catalytic cycles

The energetic span model is a bridge connecting the kinetic outcome of experimental and theoretical catalysis. It proves the utility of working with Gibbs energies (E‐representation) instead of the rate constants (k‐representation), in line with the assertion saying that ‘there are no rate‐determining steps, but rate‐determining states’. With this model the turnover frequency (TOF), turnover number (TON) and the kinetic determining factors can be obtained from the reaction profile of a computed catalytic cycle. In this way, it is possible to examine, explain, and predict the efficiency of a catalyst. The effect of concentrations, different pathways, preactivation and deactivation, and the comparison of catalysts and reactants are analyzed with several examples from the literature. In addition, the AUTOF program (excel version) is presented, allowing the fast and simple analysis of theoretically calculated catalytic reactions.

Synthetic and Predictive Approach to Unsymmetrical Biphenols by Iron-Catalyzed Chelated Radical–Anion Oxidative Coupling

An iron-catalyzed oxidative unsymmetrical biphenol coupling in 1,1,1,3,3,3-hexafluoropropan-2-ol that proceeds via a chelated radical-anion coupling mechanism was developed. Based on mechanistic studies, electrochemical methods, and density functional theory calculations, we suggest a general model that enables prediction of the feasibility of cross-coupling for a given pair of phenols.

Calculations on tunneling in the reactions of noradamantyl carbenes.

Noradamantylchlorocarbene has been found experimentally to undergo ring expansion to 2-chloroadamantene at cryogenic temperatures. The rate constant, calculated with inclusion of small-curvature tunneling, is within a factor of 2 of the rate constant measured at 9 K in a nitrogen matrix. Our calculations predict that noradamantylfluorocarbene will not be found to rearrange under these conditions. The rate constant for carbon tunneling in the ring expansion of noradamantylmethylcarbene (1d) to 2-methyladamantene at T </~ 10 K is calculated to be lower by more than 8 orders of magnitude than the rate constant for formation of 3-vinylnoradamantane from 1d by hydrogen migration.

How Can Theory Predict the Selectivity of Palladium‐Catalyzed Cross‐Coupling of Pristine Aromatic Molecules?

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.

Selective Aerobic Oxidation of Methylarenes to Benzaldehydes Catalyzed by N -Hydroxyphthalimide and Cobalt(II) Acetate in Hexafluoropropan-2-ol

Efficient and highly selective catalytic conditions for the aerobic autoxidation of methylarenes to benzaldehydes, based on N-hydroxyphthalimide (NHPI) and cobalt(II) acetate in 1,1,1,3,3,3-hexafluoropropan-2-ol (HFIP), were developed. The sustainable conditions enable a multigram scale preparation of benzaldehyde derivatives in high efficiency and with excellent chemoselectivity (up to 99 % conversion and 98 % selectivity).