TOF-determining Transition State Research Articles

Theoretical study of the mechanism for the cycle reaction of N<sub>2</sub>O and CH<sub>4</sub> catalyzed by Fe<sup>+</sup>(<sup>6</sup>D) to yield CH<sub>3</sub>OH

The mechanism of the gas phase reaction between N₂O and CH₄ catalyzed by Fe⁺(⁶D) to yield CH₃OH has been investigated on the B3LYP and CCSD(T) levels. The potential energy surfaces (PESs) were characterized in detail using molecular orbital theory and natural bonding orbital (NBO). Crossing points between the different potential energy surfaces and the possibility of spin inversion were discussed based on calculation of spin-orbit coupling (SOC). The energetic span model developed by Kozuch was corrected in order to deal with non-adiabatic reactions. Finally, we calculated the turnover frequency (TOF) of the catalytic cycle and found the TOF determining transition state (TDTS) and the TOF determining intermediate (TDI) using the treated energetic span model.

Theoretical investigations of spin–orbit coupling and kinetics in reaction NO2 with CO catalyzed by gas phase bare Ir+

The potential energy surface (PES) corresponding to the reaction NO2(2A1) with CO(1∑+) catalyzed by Ir+ has been investigated by using density functional theory (DFT). Minimum energy crossing points (MECPs) on the potential energy surfaces are located by using the methods of Harvey et al. The possible spin inversion processes are discussed by means of spin–orbit coupling (SOC) calculations. As a result, the values of the SOC constants at 4/2MECP1 and 5/3MECP2 are 617 and 1187cm−1, respectively. The latter is found to be the energetically favored channel. The energetic span (δE) model coined by Kozuch was applied in this cycle to obtain some kinetic information. The turnover frequency (TOF) determining transition state (TDTS) and TOF determining intermediate (TDI) were confirmed, and the TOF was calculated by the AUTOF program at different temperatures.

Theoretical studies on the reaction of NO2 with CO catalyzed by bare Os+ cations and its kinetic information

The potential energy surface crossings for reaction between NO2(2A1) and CO(1∑+) catalyzed by Os+ have been investigated using the density functional theory (DFT). Minimum-energy crossing points (MECPs) between the potential energy surfaces and the possible spin inversion process are discussed by means of spin–orbit coupling (SOC) calculations. The latter is found to be the energetically favored channel. The energetic span (δE) model has been applied in this cycle to obtain some kinetic information. TDTS (TOF-determining transition state) and the TDI (TOF-determining intermediate) were confirmed, and TOF (E-representation) was calculated at different temperatures.

DFT and Experimental Studies on the PtX2/X–-Catalyzed Olefin Hydroamination: Effect of Halogen, Amine Basicity, and Olefin on Activity, Regioselectivity, and Catalyst Deactivation

A DFT/B3LYP study with inclusion of solvent and temperature effects has probed the olefin activation mechanism for the intermolecular hydroamination of ethylene and 1-hexene by aniline derivatives catalyzed by the PtX2/X– system on the basis of a variety of experimental results, including new experiments on catalyst deactivation. For ethylene and aniline, the calculated ΔG‡cycle between the resting state [PtX3(C2H4)]−, 1X, and the TOF-determining transition state of the C–H reductive elimination from [PtX3(H)(CH2CH2NHPh)]−, TS2X, is slightly smaller for X = Br than for Cl or I. The ΔG‡cycle decreases as the aniline basicity decreases. For the slightly less efficient hydroamination of 1-hexene, ΔG‡cycle is greater than that for the hydroamination of ethylene, with a preference for the Markovnikov addition, in agreement with experiment and with essentially equivalent ΔG‡cycle values for the Br and I systems. In general, the results of the calculations are in agreement with the experimental observation. A clear-cut comparison of trends is hampered by the small energy differences and by the possibility, proven in certain cases, that the reaction parameters under investigation affect the catalyst degradation rate in addition to its intrinsic activity. Extrapolation of the computational study to the fluoride system suggests that this should be even more active. However, experimental studies show that this is not the case. The reason for this anomaly has been traced to the basicity of the fluoride ion, which triggers more rapid catalyst decomposition. A bonding analysis of 1X indicates a significant push–pull π interaction between the C2H4 and the trans-F ligand.

Theoretical Investigation for the Cycle Reaction of N2O (x1∑+) with CO (1∑+) Catalyzed by IrOn+ (n = 1, 2) and Utilizing the Energy Span Model to Study Its Kinetic Information

The mechanisms of the reactions between N(2)O and CO catalyzed by IrO(n)(+) (n = 1, 2) have been investigated using B3LYP and CCSD(T) levels of theory. Spin inversion among three reaction profiles corresponding to the quintet, triplet, and singlet multiplicities was discussed by using spin-orbit coupling (SOC) calculations. The probability of electron hopping in the vicinity of the (MECP) has been calculated by the Landau-Zener-type model. The single P(1)(ISC) and double P(2)(ISC) passes estimated at MECP1(#) (SOC = 198.61 cm(-1)) are approximately 0.11 and 0.20, respectively. Important analysis and explanations were done using molecular orbital theory and natural bonding orbital (NBO). The energetic span (δE) model coined by Kozuch was applied in this cycle. The turnover frequency (TOF)-determining transition state (TDTS) and TDI (TOF-determining intermediate) were confirmed. Finally, TOF(IrO(+))/TOF(IrO(2)(+)) = 0.38 at 298 K.

Theoretical views on the cycle reaction of N 2O ( 1Σ +) + NH 3 ( 1A 1) + O 2[formula omitted] catalyzed by Fe + and utilizing the energy span model to study its kinetic information

The gas-phase Fe +-mediated cycle reaction N 2O ( 1Σ +) + NH 3 ( 1A 1) + O 2 1 Σ g + → N 2 1 Σ g + + H 2O ( 1A 1) + cis-HNO 2 ( 1A′) on both sextet and quartet potential energy surfaces (PESs) has been theoretically investigated using density functional theory. Spin inversion between sextet and quartet potential energy surfaces was discussed by using spin–orbit coupling (SOC) calculations. The crossing points and the corresponding minimum energy crossing points have been explored. The probability of hopping in the vicinity of the crossing has been calculated by the Landau–Zener-type model. The energetic span ( δE) model has been applied in this cycle to obtain some kinetic information. TOF ( E-representation) was calculated at different temperatures. TDTS (TOF-determining transition state) and TDI (TOF-determining intermediate) were confirmed. Finally, the minimum energy reaction path was found.

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.

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 Ohm's 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 Eyring's 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.