Combining Transition State Theory Research Articles

In-depth mechanistic and kinetic investigation of sonochemically mediated atom transfer radical polymerization using modeling approach

Mechano/sonochemically mediated reversible deactivation radical polymerization has attracted great attention because of the novel electron transfer regulation process and high-efficient process intensification on mass transfer. Herein, a multi-scale modeling strategy combining quantum chemical calculation and kinetic modeling was developed for sonochemically induced electron transfer controlled atom transfer radical polymerization (SET-ATRP) to study the complicated SET process and its effects on polymerization. At the molecular scale, density functional theory (DFT) calculations were used to acquire the electron characteristic and structure–reactivity of the reactants, intermediates and products during SET process, which provides guideline to figure out the underlying mechanism. Results showed that DMSO•• generated under ultrasonication could react with free Me6TREN to induce electron transfer for the reduction of CuIIBr/L+ to produce CuI/L+, which is the key step for a successful polymerization. The corresponding elementary reaction rate coefficients were calculated by thermodynamic formulae combining transition state theory and Marcus theory. At the micro-scale, kinetic modeling based on method of moment was established to account for the role of SET process in regulating polymerization. Good agreements between the simulation results and experimental data confirmed the reliability of the as-developed multi-scale modeling strategy. More Me6TREN and CuIIBr/L+ resulted in more electron transfer and faster polymerization rate. This work provides an in-depth mechanism insights and kinetic understanding for SET-ATRP, which has a promising potential to promote its progress of application.

Theoretical investigations on the kinetics of dimethoxymethane with peroxy radicals

The reaction kinetics of dimethoxymethane (DMM) towards H atom abstraction by hydroperoxy and methyl peroxy radicals were investigated using the G4 composite method. All the studied reactions were found to be endothermic and non-spontaneous in nature. Canonical Variational Transition State Theory in combination with Small Curvature Tunneling corrections were adopted to calculate the rate coefficients in the temperature range of 400–1500 K. The Arrhenius expressions for the reaction of DMM with CH3OO and HO2 radicals were obtained as ktotal = 1.50 × 10−12 exp (−8159/T) and ktotal = 4.40 × 10−12 exp (−7251/T) cm3 molecule−1 s−1 respectively.

Theoretical Study of Radical-Molecule Reactions with Negative Activation Energies in Combustion: Hydroxyl Radical Addition to Alkenes.

Many of the radical–molecule reactions are nonelementary reactions with negative activation energies, which usually proceed through two steps. They exist extensively in the atmospheric chemistry and hydrocarbon fuel combustion, so they are extensively studied both theoretically and experimentally. At the same time, various models, such as a two transition state model, a steady-state model, an equilibrium-state model, and a direct elementary dynamics model are proposed to get the kinetic parameters for the overall reaction. In this paper, a conversion temperature TC1 is defined as the temperature at which the standard molar Gibbs free energy change of the formation of the reaction complex is equal to zero, and it is found that when T ≫ TC1, the direct elementary dynamics model with an inclusion of the tunneling correction of the second step reaction is applicable to calculate the overall reaction rate constants for this kind of reaction system. The reaction class of hydroxyl radical addition to alkenes is chosen as the objects of this study, five reactions are chosen as the representative for the reaction class, and their single-point energies are calculated using the method of CCSD(T)/CBS, and it is shown that the highest conversion temperature for the five reactions is 139.89 K, far below the usual initial low-temperature (550 K) oxidation chemistry of hydrocarbon fuels; therefore, the steady-state approximation method is applicable. All geometry optimizations are performed at the BH&HLYP/6-311+G(d,p) level, and the result shows that the geometric parameters in the reaction centers are conserved; hence, the isodesmic reaction method is applicable to this reaction class. To validate the accuracy of this scheme, a comparison of electronic energy difference at the BH&HLYP/6-311+G(d,p) level and the corrected electronic energy difference with the electronic energy difference at the CCSD(T)/CBS level is performed for the five representative reactions, and it is shown that the maximum absolute deviation of electronic energy difference can be reduced from 2.54 kcal·mol–1 before correction to 0.58 kcal·mol–1 after correction, indicating that the isodesmic reaction method is applicable for the accurate calculation of the kinetic parameters for large-size molecular systems with a negative activation energy reaction. The overall rate constants for 44 reactions of the reaction class of hydroxyl radical addition to alkenes are calculated using the transition-state theory in combination with the isodesmic correction scheme, and high-pressure limit rate rules for the reaction class are developed. In addition, the thermodynamic parameter is calculated and the results indicate that our dynamics model is applicable for our studied reaction class. A chemical kinetic modeling and sensitivity analysis using the calculated kinetic data is performed for the combustion of ethene, and the results indicate the studied reaction is important for the low-to-medium temperature combustion modeling of ethene.

The decomposition mechanism of C4F7N-Cu gas mixtures

C4F7N is one of the most remarkable replacements for SF6, and its decomposition mechanism has a great influence on insulating performance and environmental properties. It is noteworthy that discharges or high temperature also evaporates metal electrodes (e.g., Cu) in the equipment, and the generated metal gases interact with C4F7N and thus affect the C4F7N decomposition mechanism, but the decomposition mechanism is still not clear. In this paper, therefore, the B3LYP method in conjunction with 6-311G(d, p) basis set (for C, N, and F atoms) and Lanl2DZ basis set (for Cu atom) combining transition state theory is used to study the decomposition mechanism of C4F7N-Cu mixtures. 31 reactions are determined in decomposition pathways of C4F7N-Cu mixtures, and their potential energy surface as well as reaction mechanisms are obtained. The rate constants over 300 K–3500 K relevant to the insulation breakdown temperature are calculated based on the above calculations, and dominant reactions in different temperature regions are selected. The results show that (R14) C4F7N + Cu → CF3CFCN + CF2CuF plays a major role in the decomposition of C4F7N-Cu mixtures below 1500 K, while (R1) C4F7N + Cu → TSa1 → CuCN + C3F7 and (R21) C4F7N + Cu → TSc1 → CF3CF(CN)CF2 + CuF are dominant above 1500 K; (R23) CF3CF(CN)CF2 + Cu → CF2(Cu)C(F)CN + CF3 is the most important reaction leading to the generation of CF3 below 1500 K with the overwhelming rate constant, but other reactions also generating CF3 are dominant above 1500 K.

Strain rate effect on dislocation climb mechanism via self-interstitials

The climb mechanism of an edge-dislocation is investigated by combining Transition State Theory and potential energy surface searching technique (an atomistic modeling framework named as ABC-T). As common point defects, self-interstitial-atoms (SIAs) and their agglomeration around dislocations in ‘clouds’ have complex and significant impact on the onset of metal plasticity. Reproducing atomic details of the interactions between SIAs and dislocations in a dynamic scenario is crucial for understanding the dynamic strain aging, and also the irradiation hardening. In order to describe the kinetics of SIA clouds in the vicinity of an edge dislocation, we choose a single SIA bi-dumbbell in body-centered-cubic (BCC) Fe in this study. The bi-dumbbell is absorbed completely to form a jog pair in our simulations at realistic laboratory strain rate. While at higher strain rate dislocation pinning with a stop-and-go manner is induced by incomplete absorption. As a transition state before the jog pair, a defect attaches to dislocation line and requires much higher activation energy than the thermal energy at room temperature to further evolve. Although more realistic picture of this interaction needs free energy calculation and dynamics trajectory to confirm different evolution pathways, our results offer a direct qualitative comparison between strain rates revealing the intrinsic difficulty of dislocation climb.

Reaction pathway and H/D kinetic isotope effects of the triple proton transfer in a 7‐hydroxyquinoline‐methanol complex in the ground state: A computational approach

AbstractMultiple proton transfer (PT) is an essential process in long‐range proton transport such as proton relay in enzymes. 7‐Hydroxyquinoline (7HQ) undergoes alcohol‐mediated PT in both the excited and ground states, and this system has been investigated as a biomimetic model. In the present study, the reaction pathway of triple PT in a 7HQ‐methanol cluster, 7HQ·(MeOH)2, in the ground state has been investigated using density functional theory calculations to clarify the reaction mechanism and the origin of the experimentally observed kinetic isotope effect (KIE). The PT takes place in an asynchronous concerted fashion, in which the oxygen atom in 7HQ first accepts a proton from the directly hydrogen‐bonded MeOH. The rate constants and primary H/D KIEs have been estimated with canonical variational transition state theory in combination with the small curvature tunneling approximation. The tunneling effect on the PT rate is significant, and the KIE is much greater than 1 at room temperature. The rule of the geometric mean for the KIEs breaks down because of the asynchronicity in the motions of 3 protons and tunneling effect. In addition, the rate constant is smaller, the KIE is larger, and the activation energy is higher compared with the experimental values in heptane solution, suggesting that the PT dynamics in solution is governed by not only the intrinsic PT process but also thermal fluctuation of the solute and solvent molecules, which plays an important role in the configurational change of the 7HQ·(MeOH)2 complex.

Diffusion coefficients of alloying elements in dilute Mg alloys: A comprehensive first-principles study

First-principles calculations based on density functional theory have been used to calculate the temperature-dependent dilute tracer diffusion coefficients for 47 substitutional alloying elements in hexagonal closed packed (hcp) Mg by combining transition state theory and an 8-frequency model. The minimum energy pathways and the saddle point configurations during solute migration are calculated with the climbing image nudged elastic band method. Vibrational properties are obtained using the quasi-harmonic Debye model with inputs from first-principles calculations. An improved generalized gradient approximation of PBEsol is used in the present first-principles calculations, which is able to well describe both vacancy formation energies and vibrational properties. It is found that the solute diffusion coefficients in hcp Mg are roughly inversely proportional to the bulk modulus of the dilute alloys, which reflects the solutes' bonding to Mg. Transition metal elements with d electrons show strong interactions with Mg and have large diffusion activation energies. Correlation effects are not negligible for solutes Ca, Na, Sr, Se, Te, and Y, in which the direct solute migration barriers are much smaller than the solvent (Mg) migration barriers. Calculated diffusion coefficients are in remarkable agreement with available experimental data in the literature.

Data set for diffusion coefficients of alloying elements in dilute Mg alloys from first-principles.

Diffusion coefficients of alloying elements in Mg are critical for the development of new Mg alloys for lightweight applications. Here we present the data set of the temperature-dependent dilute tracer diffusion coefficients for 47 substitutional alloying elements in hexagonal closed packed (hcp) Mg calculated from first-principles calculations based on density functional theory (DFT) by combining transition state theory and an 8-frequency model. Benchmark for the DFT calculations and systematic comparison with experimental diffusion data are also presented. The data set refers to “Diffusion coefficients of alloying elements in dilute Mg alloys: A comprehensive first-principles study” by Zhou et al. [1].

Hybrid density-functional theory calculations of near-edge x-ray absorption fine-structure spectra: Applications on benzonitrile in gas phase

The experimental $\mathrm{N}(1s)$ near-edge x-ray-absorption fine-structure spectrum of the benzonitrile molecule in the gas phase shows well separated double peaks with different vibrational profiles. Hybrid density-functional theory calculations reveal that such a separation is a result of the conjugation effect on the nitrogen $2p$ orbitals and the double spectral peaks can be assigned as the $\mathrm{N}(1s)\ensuremath{-}\ensuremath{\pi}*$ out-of-plane and in-plane resonances. The vibrational profiles have been analyzed using a combined transition state theory and linear coupling model. Each profile consists of two different vibrational progressions corresponding to stretching modes and a broad continuum of bending excited states. The use of transition state theory allows identifying the dynamics of the N $1s$ core excitation. It is found that upon core excitations the $\mathrm{C}\mathrm{N}$ bond of the benzonitrile molecule can go from initial linear to final bent structures through different paths. The calculated spectrum is in excellent agreement with experiment.

Theory of atomic defects and diffusion in ordered compounds, and application to B2-FeAl

By means of a generalized grandcanonical approach the relations between the effective formation energies, entropies and volumes of atomic defects in ordered compounds and the parameters characterizing the microscopic properties of the single defects are derived, whereby the microscopic parameters are calculated by the ab initio electron theory. The migration energies for several possible self-diffusion paths are determined by the transition-state theory in combination with the ab initio electron theory. Results are obtained for B2-Fe x Al 1− x at or close to stoichiometry, and they are compared with experimental data.

Diffusion in Metals and Intermetallic Compounds: The Impact of AB-INITIO Calculations

ABSTRACTBy means of statistical mechanics the relations between the effective formation energies, entropies and volumes of atomic defects in ordered compounds which may be obtained experimentally and the parameters characterizing the microscopic properties of the single defects are derived, and the microscopic parameters are determined by the ab-initio electron theory. In a second step, the migration energies for possible self-diffusion paths are calculated by the transition-state theory in combination with the ab-initio electron theory. Results are reported for B2-FeAl and for Fe3Al, Ni3Sb and Fe3Si with D03 structure, and the impact of the calculations on the interpretation of experimental data is discussed.

Combining transition-state theory with quasiclassical trajectory calculations. Part 5.—Canonical calculations on the reaction: F + H2(v= 0)→ HF(v′)+ H

The dynamics of the reaction, F + H2(v=0)→ HF(v′)+H, occurring at 300 and 1000 K have been examined by the combined TST (transition-state theory)–QCT (quasiclassical trajectory) method which has been developed in earlier papers. In the TST–QCT method, the transition state is determined by finding pods (periodic orbiting dividing surfaces) on fixed-angle potential-energy surfaces for which the action over one cycle of the pods motion is (v+½)h. The complete transition state is defined by joining these pods together, and its phase space is sampled to select starting points for quasiclassical tranjectories, ‘forwards’ towards products and ‘backwards’ towards reagents. The results are compared with those from standard QCT calculations on the same modified LEPS surface (known as Muckerman 5), using of TST to estimate absolute rate constants from our results. Our calculations demonstrate that motion from separated F + H2(v= 0) to the transition state is highly vibrationally adiabatic and the calculated product vibrational energy distribution is in excellent agreement with that derived from standard QCT calculations. The advantages and limitations of the combined TST–QCT method as applied to canonical bimolecular reactions of species in defined vibrational states are discussed.

Combining transition-state theory with quasiclassical trajectory calculations. Part 6.—Microcanonical calculations on the reaction: F + H2(v= 0)→ HF(v′)+ H

Procedures are described for applying the combined TST (transition-state theory)–QCT (quasiclassical trajectory) method to reactions occurring at constant collision energy rather than at constant temperature, as in earlier papers, and results for the reaction F+H2(v= 0)→ HF(v′)+H are reported. In the TST–QCT method, the transition state is defined by joining together pods (periodic orbiting dividing surfaces) on fixed-angle potential-energy surfaces for which the action over one cycle of the pods motion is (v+1/2)h. The phase space of the transition state is then sampled by appropriate pseudorandom techniques to provide starting points for pairs of quasiclassical trajectories, ‘forward’ towards products and ‘backward’ towards reagents. In applying the TST–QCT method to microcanonical systems, the energies associated with reaction coordinate, bending and overall rotational motions in the transition state are selected using correlations between these motions and those in the separated reagents which were previously established from trajectories run back from the transition state. The results of our calculations on F+H2(v= 0) are compared with those from the extensive, conventional QCT study of Muckerman on the same potential-energy surface (Muckerman 5). As with canonical calculation using the combined TST–QCT method, there is excellent agreement between the two sets of results.

Combining transition state theory with quasiclassical trajectory calculations. III. Applications to the three-dimensional H + H 2(ν) reaction

A new method is described of using quasiclassical trajectories to study the dynamics of elementary reactions in three dimensions. Trajectories are initiated in the phase space of suitably chosen transition state and run forwards and backwards in time from the same starting point to simulate a complete collision. The transition state for a given vibrational level ν is determined by first finding pods (periodic orbiting dividing surfaces) on fixed-angle potential energy surfaces for which the action over one cycle of the pods motion is (ν + 1 2 ) h. The complete transition is then defined by joining these pods together. Methods are described for pseudo-randomly sampling the phase space of these transition states. Results for collisions of H + H 2(ν) with ν = 0–5 and 9 on the accurate Liu-Siegbahn-Truhlar-Horowitz surface are presented and compared with the results of conventional quasiclassical trajectory studies that have already been reported in the literature. Absolute values of rate constants are obtained using the adiabatic reactive sudden version of the transition state theory. Comparisons of our combined method with conventional techniques are encouraging and there is a considerable saving in computer time resulting from the elimination of trajectories which do not reach the strong interaction zone. Only slight differences are found when the energy of the transition state bending motion is set equal to its zero-point quantum value rather than selected from a classical Boltzmann distribution.

Combining transition state theory with quasiclassical trajectory calculations: application to the nitrogen exchange reaction N+N 2( v)

The dynamics of collisions between N atoms and vibrationally excited N 2( v⩽ 15) have been studied using a new method in which quasiclassical trajectories are initiated at suitably chosen transition states. The transition state for a particular vibrational level v is determined by first finding PODSs (periodic orbiting dividing surfaces) on fixed-angle potential energy surfaces for which the action over one cycle of the PODS motion is ( v+ 1 2 ) h. The complete transition state is defined by joining these PODSs together and its phase space is sampled pseudorandomly to select starting points for quasiclassical trajectories. The results of the calculations are compared with those from conventional quasiclassical trajectory calculations on the same LEPS potential energy surface, using the adiabatic reactive sudden version of transition state theory to estimate absolute rate constants from our results. The agreement is good and the combined method brings about a great saving in computing time by eliminating trajectories which do not reach the strong interaction zone.

Combining transition state theory with quasiclassical trajectory calculations. Part 1.—Collinear collisions

Quasiclassical trajectory calculations of two kinds have been performed on collinear reactive collisions involving three atoms: i.e. A + BC → AB + C. In the first set of calculations, trajectories are initiated with A and BC (v= 0) well-separated. In the second, a normal mode analysis is carried out at the saddlepoint on the potential energy surface and the line (S*) orthogonal to the reaction coordinate is defined. Trajectories are then run “forward” and “backward” from points on S*, with the system initially being assigned zero-point energy associated with the motion along this line and corresponding to the “real” frequency in standard transition state theory. Results are compared for all 8 combinations of L(1 a.m.u.) and H(35 a.m.u.) atoms on three different potential energy surfaces, as well as for F + H2 and H + F2. On surfaces with early barriers, motion between the separated reagents and the transition state exhibits a high degree of vibrational adiabaticity and the reaction probabilities and patterns of energy disposal from the two sets of calculation are very similar. The implications of these results for standard transition state theory and for increasing the effectiveness of full-scale quasiclassical trajectory calculations are discussed.