Rate-controlling Transition States Research Articles

Activity and stability of alloyed NiCo catalyst for the dry reforming of methane: A combined DFT and microkinetic modeling study

Dry reforming of methane (DRM) takes the greenhouse gas methane and carbon dioxide as reactants to produce syngas, showing positive effect on the ecological environment and energy conversion. Although pristine Ni and Co catalysts show high activity during this process, they are easily deactivated. Ni catalysts tend to deposit carbon, while Co catalysts would be oxidized. Compared with Ni, the formation of a one to one ratio NiCo alloy generally shows higher catalyst reactivity. However, there are still contradictions regarding the stability of this alloy catalyst. In this work, we used a combination of density functional theory calculations and microkinetic simulations to understand how the surface structure of the alloy affects the activity and stability of the catalyst. Possible terminations of NiCo alloys were considered and compared regarding the reaction rates, coverage of surface species and rate controlling transition states. Based on these results and those reported in our previous work, understandings on experimental observations can be obtained.

Identification of a Selectivity Descriptor for Propane Dehydrogenation through Density Functional and Microkinetic Analysis on Pure Pd and Pd Alloys

First principles periodic density functional theory (DFT) calculations, in conjunction with detailed microkinetic modeling and experimental characterization, are employed to elucidate the structure sensitivity and identify key selectivity descriptors for nonoxidative propane dehydrogenation (PDH) on intermetallic alloys. A comprehensive theoretical treatment of 1:1 PdIn surfaces demonstrates that the Pd-terminated steps have 5 orders of magnitude higher rates than do the (110) terraces, with nearly complete selectivity to propylene formation. Pure Pd steps and terraces, in contrast, have considerably lower propylene selectivity and higher coverages of adsorbed intermediates, suggesting that Pd may experience more coking and reduced lifetimes compared to the alloys. A degree of rate and selectivity control analysis on the optimized microkinetic model demonstrates that propane C–H bond scission to yield 1-propyl is the most kinetically relevant step for propylene formation, while the C–C bond breaking barriers are important for byproduct formation. From these analyses, a simplified rate expression is derived for the step surface of the alloy, leading to the identification of a selectivity descriptor expressed in terms of effective free energy barriers of the rate controlling transition states, propane C–H bond breaking, and propyne C–C bond breaking. This descriptor is subsequently generalized to evaluate the propylene production selectivities for a series of Pd-containing alloys. The results show enhanced agreement with experimentally measured selectivity trends compared to traditional selectivity descriptors, suggesting a general strategy for identification of highly selective, nonoxidative PDH alloy catalysts.

Thermodynamically consistent forward and reverse degrees of rate control in reversible reactions

The net rate of a composite reaction is the difference between the forward and reverse reaction rates, which are kinetically distinct despite sharing elementary reaction steps and therefore have different rate-controlling transition states and species. Thus, degrees of rate control defined to identify rate-controlling transition states and species for the net rate confound contributions from the forward and reverse reactions. Herein, the forward and reverse degrees of rate control are defined to independently quantify the extent that species and transition states control the forward and reverse rates in reversible reactions. These degrees of rate control are defined as the relative change in the forward and reverse reaction rates per kBT decrease in the standard-state molecular free energies of transition states and species, and they are related to experimentally measurable quantities such as steady-state fractional coverages, reaction orders, and energies and entropies of activation of the forward and reverse reaction rates. The forward/reverse degrees of rate control represent stoichiometric coefficients for species and transition states in an equilibrium between the initial states and transition states of the apparent rate-controlling steps of forward and reverse overall reactions. At equilibrium, the apparent transition states for the forward reaction and reverse reaction converge, and thus the forward and reverse rate-controlling steps combine to form a single apparent rate-controlling step. This apparent rate-controlling step is comprised of an apparent initial state, transition state, and final state, where the apparent final state of the forward reaction is the apparent initial state of the reverse reaction. The apparent rate-controlling step behaves identically to an elementary step reaction at equilibrium with a pseudo-mass-action rate function given by the transition-state-theory (TST) form rate function (Foley and Bhan, 2020) with a stoichiometric number equal to the affinity-averaged stoichiometric number, σ¯. The ratio of the forward and reverse TST-form rate functions is identical to the overall thermodynamic equilibrium relation, consistent with the principles of microscopic reversibility and detailed balance at equilibrium.

Degrees of Rate Control at Non(pseudo)steady-State Conditions

The degrees of rate control enable identification of rate-controlling transition states and species during (pseudo)steady-state reaction. We demonstrate a method for identifying rate-controlling tr...

Cleaning Up Mechanistic Debris Generated by Twister Ribozymes Using Computational RNA Enzymology.

The catalytic properties of RNA have been a subject of fascination and intense research since their discovery over 30 years ago. Very recently, several classes of nucleolytic ribozymes have emerged and been characterized structurally. Among these, the twister ribozyme has been center-stage, and a topic of debate about its architecture and mechanism owing to conflicting interpretations of different crystal structures, and in some cases conflicting interpretations of the same functional data. In the present work, we attempt to clean up the mechanistic "debris" generated by twister ribozymes using a comprehensive computational RNA enzymology approach aimed to provide a unified interpretation of existing structural and functional data. Simulations in the crystalline environment and in solution provide insight into the origins of observed differences in crystal structures, and coalesce on a common active site architecture, and dynamical ensemble in solution. We use GPU-accelerated free energy methods with enhanced sampling to ascertain microscopic nucleobase pK a values of the implicated general acid and base, from which predicted activity-pH profiles can be compared directly with experiments. Next, ab initio quantum mechanical/molecular mechanical (QM/MM) simulations with full dynamic solvation under periodic boundary conditions are used to determine mechanistic pathways through multi-dimensional free energy landscapes for the reaction. We then characterize the rate-controlling transition state, and make predictions about kinetic isotope effects and linear free energy relations. Computational mutagenesis is performed to explain the origin of rate effects caused by chemical modifications and make experimentally testable predictions. Finally, we provide evidence that helps to resolve conflicting issues related to the role of metal ions in catalysis. Throughout each stage, we highlight how a conserved L-platform structural motif, to- gether with a key L-anchor residue, forms the characteristic active site scaffold enabling each of the catalytic strategies to come together not only for the twister ribozyme, but the majority of the known small nucleolytic ribozyme classes.

Theoretical study of the mechanism of 2,5-diketopiperazine formation during pyrolysis of proline

ABSTRACT In biomass pyrolysis reactions, the wide range of products obtained (some of them environmentally harmful) usually depends on the temperature and the content of amino acids, this fact results in general interest in studying the involved mechanisms of reaction which, in many cases, are poorly understood. In this work, the mechanism of formation of 2,5-diketopiperazine upon pyrolysis of proline at 300°C was theoretically studied by means of DFT calculations (B97XD/6-311G(d,p)). All transition states and minimum energy structures involved were optimised, and thermodynamic parameters were theoretically estimated. A mechanism of four steps was proposed, and the most influential step was analysed by using the reaction force formalism, and an analysis of geometrical parameters, charge distributions and bond orders. Results show that the transition state correspond to a dehydration process, and its preceding intermediate, are the most important rate-controlling states of the overall reaction. Reaction force analysis shows a high dominance of geometrical rearrangements (75% of the activation energy), while charge transfer was not an important factor for the analysed reaction step. Finally, from the bond order analysis, it was determined that the rate-controlling transition state is early formed and that the process is asynchronous.

The Degree of Rate Control: A Powerful Tool for Catalysis Research

The “degree of rate control” (DRC) is a mathematical approach for analyzing multistep reaction mechanisms that has proven very useful in catalysis research. It identifies the “rate-controlling transition states and intermediates” (i.e., those whose DRCs are large in magnitude). Even in mechanisms with over 30 intermediates and transition states, these are generally just a few distinct chemical species whose energies, if they could be independently changed, would achieve a faster net reaction rate to the product of interest. For example, when there is a single “rate-determining step”, the DRC for its transition state (TS) is 1, which means (by definition) that if this TS’s energy could be decreased by kBT (where kB is Boltzmann’s constant and T is temperature), the net rate would increase by a factor of e. Because the (relative) energies of these key adsorbed intermediates and transition states can be adjusted by modifying the catalyst or solvent, or even a reactant’s molecular structure, the DRC values pr...

Electrophilic Aromatic Substitution: New Insights into an Old Class of Reactions.

The classic SEAr mechanism of electrophilic aromatic substitution (EAS) reactions described in textbooks, monographs, and reviews comprises the obligatory formation of arenium ion intermediates (σ complexes) in a two-stage process. Our findings from several studies of EAS reactions challenge the generality of this mechanistic paradigm. This Account focuses on recent computational and experimental results for three types of EAS reactions: halogenation with molecular chlorine and bromine, nitration by mixed acid (mixture of nitric and sulfuric acids), and sulfonation with SO3. Our combined computational and experimental investigation of the chlorination of anisole with molecular chlorine in CCl4 found that addition-elimination pathways compete with the direct substitution processes. Detailed NMR investigation of the course of experimental anisole chlorination at varying temperatures revealed the formation of addition byproducts. Moreover, in the absence of Lewis acid catalysis, the direct halogenation processes do not involve arenium ion intermediates but instead proceed via concerted single transition states. We also obtained analogous results for the chlorination and bromination of several arenes in nonpolar solvents. We explored by theoretical computations and experimental spectroscopic studies the classic reaction of benzene nitration by mixed acid. The structure of the first intermediate in this process has been a subject of contradicting views. We have reported clear experimental UV/vis spectroscopic evidence for the formation of the first intermediate in this reaction. Our broader theoretical modeling of the process considers the effects of the medium as a bulk solvent but also the specific interactions of a H2SO4 solvent molecule with intermediates and transition states along the reaction path. In harmony with the obtained spectroscopic data, our computational results reveal that the structure of the initial π complex precludes the possibility of electronic charge transfer from the benzene π system to the nitronium unit. In contrast to usual interpretations, our computational results provide compelling evidence that in nonpolar, noncomplexing media and in the absence of catalysts, the mechanism of aromatic sulfonation with sulfur trioxide is concerted and does not involve the conventional σ-complex (Wheland) intermediates. Stable under such conditions, (SO3)2 dimers react with benzene much more readily than monomeric sulfur trioxide. In polar (complexing) media, the reaction follows the classic two-stage SEAr mechanism. Still, the rate-controlling transition state involves two SO3 molecules. The reactivity and regioselectivity in EAS reactions that follow the classic mechanistic scheme are quantified using a theoretically evaluated quantity, the electrophile affinity (Eα), which measures the stabilization energy associated with the formation of arenium ions. Examples of applications are provided.

The potential energy surface of OH anion reaction with CH3OOH: Theoretical investigations

Removing ROOH in the atmosphere is important because they can lead to the redistribution of HOx and ROx radicals, which regulate the oxidation capacity of the atmosphere. The MP2 method and the B3LYP and PBE0 DFT functionals, with 6-31++G∗∗ and aug-cc-pVDZ basis sets were employed to determine the geometries, reaction paths and mechanisms of OH−+CH3OOH reaction. Single point energy calculations were carried out at CCSD(T)/aug-cc-pVDZ level of theory served as benchmark. Although B3LYP energies gives the best agreement to the benchmark, it failed to locate TS1. PBE0/6-311+G(d,p) is chosen as an appropriate method for the dynamics simulations. Four product channels are observed, where CH3OO−+H2O and H2O+CH2O+HO− are competitive due to the similar barrier height, and H2O+CH2(OH)O− is the most exothermic product, and in contrast, CH3OH+HOO− is the least feasible one. The PES results are not consistent with the experimental observation where product H2O+CH2(OH)O− is not found, which might attribute to a “rough” landscape of PES after passing a rate controlling transition state, implying a non-IRC behavior for this reaction.

Assessment of metal-assisted nucleophile activation in the hepatitis delta virus ribozyme from molecular simulation and 3D-RISM.

The hepatitis delta virus ribozyme is an efficient catalyst of RNA 2′-O-transphosphorylation and has emerged as a key experimental system for identifying and characterizing fundamental features of RNA catalysis. Recent structural and biochemical data have led to a proposed mechanistic model whereby an active site Mg2+ ion facilitates deprotonation of the O2′ nucleophile, and a protonated cytosine residue (C75) acts as an acid to donate a proton to the O5′ leaving group as noted in a previous study. This model assumes that the active site Mg2+ ion forms an inner-sphere coordination with the O2′ nucleophile and a nonbridging oxygen of the scissile phosphate. These contacts, however, are not fully resolved in the crystal structure, and biochemical data are not able to unambiguously exclude other mechanistic models. In order to explore the feasibility of this model, we exhaustively mapped the free energy surfaces with different active site ion occupancies via quantum mechanical/molecular mechanical (QM/MM) simulations. We further incorporate a three-dimensional reference interaction site model for the solvated ion atmosphere that allows these calculations to consider not only the rate associated with the chemical steps, but also the probability of observing the system in the presumed active state with the Mg2+ ion bound. The QM/MM results predict that a pathway involving metal-assisted nucleophile activation is feasible based on the rate-controlling transition state barrier departing from the presumed metal-bound active state. However, QM/MM results for a similar pathway in the absence of Mg2+ are not consistent with experimental data, suggesting that a structural model in which the crystallographically determined Mg2+ is simply replaced with Na+ is likely incorrect. It should be emphasized, however, that these results hinge upon the assumption of the validity of the presumed Mg2+-bound starting state, which has not yet been definitively verified experimentally, nor explored in depth computationally. Thus, further experimental and theoretical study is needed such that a consensus view of the catalytic mechanism emerges.

Mechanistic insights into RNA transphosphorylation from kinetic isotope effects and linear free energy relationships of model reactions.

Phosphoryl transfer reactions are ubiquitous in biology and the understanding of the mechanisms whereby these reactions are catalyzed by protein and RNA enzymes is central to reveal design principles for new therapeutics. Two of the most powerful experimental probes of chemical mechanism involve the analysis of linear free energy relations (LFERs) and the measurement of kinetic isotope effects (KIEs). These experimental data report directly on differences in bonding between the ground state and the rate-controlling transition state, which is the most critical point along the reaction free energy pathway. However, interpretation of LFER and KIE data in terms of transition-state structure and bonding optimally requires the use of theoretical models. In this work, we apply density-functional calculations to determine KIEs for a series of phosphoryl transfer reactions of direct relevance to the 2'-O-transphosphorylation that leads to cleavage of the phosphodiester backbone of RNA. We first examine a well-studied series of phosphate and phosphorothioate mono-, di- and triesters that are useful as mechanistic probes and for which KIEs have been measured. Close agreement is demonstrated between the calculated and measured KIEs, establishing the reliability of our quantum model calculations. Next, we examine a series of RNA transesterification model reactions with a wide range of leaving groups in order to provide a direct connection between observed Brønsted coefficients and KIEs with the structure and bonding in the transition state. These relations can be used for prediction or to aid in the interpretation of experimental data for similar non-enzymatic and enzymatic reactions. Finally, we apply these relations to RNA phosphoryl transfer catalyzed by ribonuclease A, and demonstrate the reaction coordinate-KIE correlation is reasonably preserved. A prediction of the secondary deuterium KIE in this reaction is also provided. These results demonstrate the utility of building up knowledge of mechanism through the systematic study of model systems to provide insight into more complex biological systems such as phosphoryl transfer enzymes and ribozymes.

Gas-Phase Chemical Dynamics Simulations on the Bifurcating Pathway of the Pimaradienyl Cation Rearrangement: Role of Enzymatic Steering in Abietic Acid Biosynthesis.

The biosynthesis of abietadiene is the first biosynthetically relevant process shown to involve a potential energy surface with a bifurcating reaction pathway. Herein, we use gas-phase, enzyme-free direct dynamics simulations to study the behavior of the key reaction (bifurcating) step, which is conversion of the C20 pimaradienyl cation to the abietadienyl cation. In a previous study (J. Am. Chem. Soc.2011, 133, 8335), a truncated C10 model was used to investigate this reaction. The current work finds that the complete C20 pimaradienyl cation gives reaction dynamics similar to that reported for the truncated C10 model. We find that in the absence of the enzyme, the C20 abietadienyl cation is generated in almost equal quantity (1.3:1) as an unobserved (in nature) seven-membered ring product. These simulations allude to a need for abietadiene synthase to steer the reaction to avoid generation of the seven-membered ring product. The methodology of post-transition state chemical dynamics simulations is also considered. The trajectories are initiated at the rate-controlling transition state (TS) separating the pimaradienyl and abietadienyl cations. Accurate results are expected for the short-time direct motion from this TS toward the abietadienyl cation. However, the dynamics may be less accurate for describing the unimolecular reactions that occur in moving toward the pimaradienyl cation, due to the unphysical flow of zero-point energy.

Ab initio chemical kinetics for the reactions of N 2 with singlet and triplet C 2O radicals

The possible energy pathways for the reactions of N 2 with singlet and tripled C 2O have been investigated at the CCSD(T)/6-311+G(3df)//B3LYP/6-311+G(3df) level of theory. Our results show that the rate-controlling transition states for the formation of 3CNN + CO, NCO + CN and 3NCN + CO through triplet surface have 36.2, 57.7 and 60.5 kcal/mol barriers relative to the reactants 3C 2O + N 2. Formation of 1CNN + CO and 1NCN + CO via the singlet surface needs to overcome 43.7 and 66.9 kcal/mol barriers. The dominant products are 1,3CNN + CO and cyc- 1NCN + CO, their rate constants in cm 3 molecule −1 s −1 can be presented as k 1 ( 3CNN + CO) = 3.5 × 10 −11 exp(−36.8 kcal/mol/ RT), k 2 ( 1CNN + CO) ⩽ 2.9 × 10 −12 exp(−33.2 kcal/mol/ RT) and k 3 (cyc- 1NCN + CO) = 6.86 × 10 −20exp(−27.7 kcal/mol/ RT), which are significantly lower than those assumed in the literature. The rate constants for the formation of 3NCN + CO and NCO + CN are too small to be important due to their high exit barriers. The predicted heats of reaction for formation of products NCO + CN, 3CNN + CO and 3NCN + CO are 45.9, 18.1 and −10.7 kcal/mol, which agree excellently with the experimental values, 45.8, 17.7 and −10.7 kcal/mol. Our results imply that the reaction of C 2O with N 2 cannot compete with the CH + N 2 reaction for prompt-NO formation in hydrocarbon combustion.

Degree of Rate Control: How Much the Energies of Intermediates and Transition States Control Rates

For many decades, the concept of a "rate-determining step" has been of central importance in understanding chemical kinetics in multistep reaction mechanisms and using that understanding to advantage. Yet a rigorous method for identifying the rate-determining step in a reaction mechanism was only recently introduced, via the "degree of rate control" of elementary steps. By extending that idea, we argue that even more useful than identifying the rate-determining step is identifying the rate-controlling transition states and the rate-controlling intermediates. These identify a few distinct chemical species whose relative energies we could adjust to achieve a faster or slower net reaction rate. Their relative energies could be adjusted by a variety of practical approaches, such as adding or modifying a catalyst, modifying the solvent, or simply modifying a reactant's molecular structure to affect electronic or steric control on the relative energies of the key species. Since these key species are the ones whose relative energies most strongly influence the net reaction rate, they also identify the species whose energetics must be most accurately measured or calculated to achieve an accurate kinetic model for any reaction mechanism. Thus, it is very important to identify these rate-controlling transition states and rate-controlling intermediates for both applied and basic research. Here, we present a method for doing that.

Transesterification Thio Effects of Phosphate Diesters: Free Energy Barriers and Kinetic and Equilibrium Isotope Effects from Density-Functional Theory

Primary and secondary kinetic and equilibrium isotope effects are calculated with density-functional methods for the in-line dianionic methanolysis of the native (unsubstituted) and thio-substituted cyclic phosphates. These reactions represent reverse reaction models for RNA transesterification under alkaline conditions. The effect of solvent is treated with explicit (single and double) water molecules and self-consistently with an implicit (continuum) solvation model. Singly substituted reactions at the nonbridging O(P1) position and bridging O(2)('), O(3)('), and O(5)(') positions and a doubly substituted reaction at the O(P1) and O(P2) positions were considered. Aqueous free energy barriers are calculated, and the structures and bond orders of the rate-controlling transition states are characterized. The results are consistent with available experimental data and provide useful information for the interpretation of measured isotope and thio effects used to probe mechanism in phosphoryl transfer reactions catalyzed by enzymes and ribozymes.

Theoretical studies on the C 2H+O 2 reaction: mechanism for HCO+CO, HCCO+O and CH+CO 2 formation

The reaction of the ethynyl radical with molecular oxygen has been examined using density functional theory. Two major reaction routes are open to the chemically activated HCCOO adduct 1 : dissociation to HCCO+O 16 and formation of the thermodynamically most stable products HCO + CO 12 : HCCOO 1 → dioxirenyl 2 → oxyrenyloxy 3 → oxo-ketene 5 → HCO + CO 12 → H + 2CO 15 . The CCSD(T)/6-311++G(d,p)// B3LYP/6-311++G(d,p) energies of the respective rate controlling transition states, 1/16 and 1/2 , indicate that the route leading to H + CO + CO should dominate. Several other [C 2,H,O 2] isomers and other, minor pathways have also been characterised. The present study reveals this reaction to be a capture-limited association-elimination reaction with a high and pressure-independent rate coefficient.