Calculation Of Reaction Rate Constants Research Articles

Density Functional Theory Analysis of Elementary Reactions in NOx Reduction on Rh Surfaces and Rh Clusters

The reduction of NOx is crucial for reducing air pollution from vehicle exhaust. In the presence of Rh-based catalysts, the dissociation of NO and the formation of N2O and N2 constitute the important elementary steps of NOx reduction. The present study used density functional theory (DFT) to investigate the catalytic performances of the Rh(111) surface and Rh55 and Rh147 clusters toward these elementary reactions. The NO dissociation reaction was found to have minimum activation barriers (Ea) of 0.63, 0.68, and 1.25 eV on Rh55, Rh147, and Rh(111), respectively. Therefore, it is the fastest on small Rh clusters. In contrast, the N2 formation reaction is relatively inefficient on small clusters, with corresponding Ea values of 2.14, 1.79, and 1.71 eV. Because of the stronger binding of N atoms to the Rh clusters than to the Rh surface, N2 formation through the recombination of N atoms has a higher Ea value on Rh clusters. The calculated reaction rate constants confirmed that small Rh clusters are less react...

Hydrogen Abstraction from Hydrocarbons by NH2.

This contribution investigates thermokinetic parameters of bimolecular gas-phase reactions involving the amine (NH2) radical and a large number of saturated and unsaturated hydrocarbons. These reactions play an important role in combustion and pyrolysis of nitrogen-rich fuels, most notably biomass. Computations performed at the CBS-QB3 level and based on the conventional transition-state theory yield potential-energy surfaces and reaction rate constants, accounting for tunnelling effects and the presence of hindered rotors. In an analogy to other H abstraction systems, we demonstrate only a small influence of variational effects on the rate constants for selected reaction. The studied reactions cover the abstraction of hydrogen atoms by the NH2 radical from the C-H bonds in C1-C4 species, and four C5 hydrocarbons of 2-methylbutane, 2-methyl-1-butene, 3-methyl-1-butene, 3-methyl-2-butene, and 3-methyl-1-butyne. For the abstraction of H from methane, in the temperature windows 300-500 and 1600-2000 K, the calculated reaction rate constants concur with the available experimental measurements, i.e., kcalculated/kexperimetal = 0.3-2.5 and 1.1-1.4, and the previous theoretical estimates. Abstraction of H atom from ethane attains the ratio of kcalculated/kexperimetal equal to 0.10-1.2 and 1.3-1.5 over the temperature windows of available experimental measurements, i.e., 300-900 K and 1500-2000 K, respectively. For the remaining alkanes (propane and n-butane), the average kexperimental/kcalculated ratio remains 2.6 and 1.3 over the temperature range of experimental data. Also, comparing the calculated standard enthalpy of reaction (ΔrH°298) with the available experimental measurements for alkanes, we found the mean unsigned error of computations as 3.7 kJ mol-1. This agreement provides an accuracy benchmark of our methodology, affording the estimation of the unreported kinetic parameters for H abstractions from alkenes and alkynes. On the basis of the Evans-Polanyi plots, calculated bond dissociation enthalpies (BDHs) correlate linearly with the standard enthalpy of activation (Δ⧧H°298), allowing estimation of the enthalpy barrier for reaction of NH2 with other hydrocarbons in future work. Finally, we develop six sets of the generalized Arrhenius rate parameters for H abstractions from different C-H bond types. These parameters extend the application of the present results to any noncyclic hydrocarbon interacting with the NH2 radical.

다성분 반응 이동 모델링을 이용한 트리클로로에틸렌(TCE)으로 오염된 지하수에서의 자연저감 평가

To properly manage and remediate groundwater contaminated with chlorinated hydrocarbons such as trichloroethylene (TCE), it is necessary to assess natural attenuation processes of contaminants in the aquifer along with investigation of contamination history and aquifer characterization. This study evaluated natural attenuation processes of TCE at an industrial site in Korea by delineating hydrogeochemical characteristics along the flow path of contaminated groundwater, by calculating reaction rate constants for TCE and its degradation products, and by using geochemical and reactive transport modeling. The monitoring data showed that TCE tended to be transformed to cis-1,2-dichloroethene (cis-1,2-DCE) and further to vinyl chloride (VC) via microbial reductive dechlorination, although the degree was not too significant. According to our modeling results, the temporal and spatial distribution of the TCE plume suggested the dominant role of biodegradation in attenuation processes. This study can provide a useful method for assessing natural attenuation processes in the aquifer contaminated with chlorinated hydrocarbons and can be applied to other sites with similar hydrological, microbiological, and geochemical settings.

Modeling the effects of cosolvents on biodiesel production

In this study, a mathematical model is developed for predicting the effect of cosolvents on the biodiesel production, by taking into account the fact that the process consists of two liquid phases. The proposed model consists of a detailed chemical kinetic reaction mechanism and the phase equilibrium of the two phases. The experimental data for estimating the reaction rate constants consists of 1580 dynamic concentration data related to cosolvent-free systems. Then, the calculated reaction rate constants are used to model the biodiesel production process in systems containing cosolvents to investigate the cosolvent effects on the process. The average absolute relative deviation of 1.0% for all the experimental data points is a testament to the accuracy of the predictive model. Hence, the model was used to investigate the effect of methanol to oil ratio, the ratio of cosolvent to methanol, and the amount of catalyst on the biodiesel production rate and yield, in the presence of cosolvents tetrahydrofuran and diethyl ether. According to the results, the use of cosolvent leads to increase the reaction rates. In the other words, the process time is reduced; however, the final yield of biodiesel does not change. Comparison between two cosolvents shows that diethyl ether is more appropriate than tetrahydrofuran, because, in the use of diethyl ether, less cosolvent to methanol ratio is needed. Also, the effect of catalyst concentration is similar to the effect cosolvent.

Reaction rates and kinetic isotope effects of H2 + OH → H2O + H.

We calculated reaction rate constants including atom tunneling of the reaction of dihydrogen with the hydroxy radical down to a temperature of 50 K. Instanton theory and canonical variational theory with microcanonical optimized multidimensional tunneling were applied using a fitted potential energy surface [J. Chen et al., J. Chem. Phys. 138, 154301 (2013)]. All possible protium/deuterium isotopologues were considered. Atom tunneling increases at about 250 K (200 K for deuterium transfer). Even at 50 K the rate constants of all isotopologues remain in the interval 4 ⋅ 10(-20) to 4 ⋅ 10(-17) cm(3) s(-1), demonstrating that even deuterated versions of the title reaction are possibly relevant to astrochemical processes in molecular clouds. The transferred hydrogen atom dominates the kinetic isotope effect at all temperatures.

Ab Initio Calculation of Rate Constants for Molecule-Surface Reactions with Chemical Accuracy.

The ab initio prediction of reaction rate constants for systems with hundreds of atoms with an accuracy that is comparable to experiment is a challenge for computational quantum chemistry. We present a divide‐and‐conquer strategy that departs from the potential energy surfaces obtained by standard density functional theory with inclusion of dispersion. The energies of the reactant and transition structures are refined by wavefunction‐type calculations for the reaction site. Thermal effects and entropies are calculated from vibrational partition functions, and the anharmonic frequencies are calculated separately for each vibrational mode. This method is applied to a key reaction of an industrially relevant catalytic process, the methylation of small alkenes over zeolites. The calculated reaction rate constants (free energies), pre‐exponential factors (entropies), and enthalpy barriers show that our computational strategy yields results that agree with experiment within chemical accuracy limits (less than one order of magnitude).

Ab Initio Calculation of Rate Constants for Molecule–Surface Reactions with Chemical Accuracy

AbstractThe ab initio prediction of reaction rate constants for systems with hundreds of atoms with an accuracy that is comparable to experiment is a challenge for computational quantum chemistry. We present a divide‐and‐conquer strategy that departs from the potential energy surfaces obtained by standard density functional theory with inclusion of dispersion. The energies of the reactant and transition structures are refined by wavefunction‐type calculations for the reaction site. Thermal effects and entropies are calculated from vibrational partition functions, and the anharmonic frequencies are calculated separately for each vibrational mode. This method is applied to a key reaction of an industrially relevant catalytic process, the methylation of small alkenes over zeolites. The calculated reaction rate constants (free energies), pre‐exponential factors (entropies), and enthalpy barriers show that our computational strategy yields results that agree with experiment within chemical accuracy limits (less than one order of magnitude).

Enzymatic Kinetic Isotope Effects from First-Principles Path Sampling Calculations.

In this study, we develop and test a method to determine the rate of particle transfer and kinetic isotope effects in enzymatic reactions, specifically yeast alcohol dehydrogenase (YADH), from first-principles. Transition path sampling (TPS) and normal mode centroid dynamics (CMD) are used to simulate these enzymatic reactions without knowledge of their reaction coordinates and with the inclusion of quantum effects, such as zero-point energy and tunneling, on the transferring particle. Though previous studies have used TPS to calculate reaction rate constants in various model and real systems, it has not been applied to a system as large as YADH. The calculated primary H/D kinetic isotope effect agrees with previously reported experimental results, within experimental error. The kinetic isotope effects calculated with this method correspond to the kinetic isotope effect of the transfer event itself. The results reported here show that the kinetic isotope effects calculated from first-principles, purely for barrier passage, can be used to predict experimental kinetic isotope effects in enzymatic systems.

S-shooting: a Bennett-Chandler-like method for the computation of rate constants from committor trajectories.

Mechanisms of rare transitions between long-lived stable states are often analyzed in terms of commitment probabilities, determined from swarms of short molecular dynamics trajectories. Here, we present a computer simulation method to determine rate constants from such short trajectories combined with free energy calculations. The method, akin to the Bennett-Chandler approach for the calculation of reaction rate constants, requires the definition of a valid reaction coordinate and can be applied to both under- and overdamped dynamics. We verify the correctness of the algorithm using a one-dimensional random walker in a double-well potential and demonstrate its applicability to complex transitions in condensed systems by calculating cavitation rates for water at negative pressures.

Formation of dibenzofuran, dibenzo-p-dioxin and their hydroxylated derivatives from catechol.

We present, in this study, mechanistic and kinetic accounts of the formation of dibenzofuran (DF), dibenzo-p-dioxin (DD) and their hydroxylated derivatives (OHs-DF/OHs-DD) from the catechol (CT) molecule, as a model compound for phenolic constituents in biomass. Self-condensation of two CT molecules produces predominantly a DD molecule via open- and closed-shell corridors. Coupling modes involving the o-semiquinone radical and the CT molecule (o-SQ/CT) generate two direct structural blocks for the formation of OHs-DF/OHs-DD structures, ether-type intermediates and di-keto moieties. The calculated reaction rate constants indicate that the fate of ether-type intermediates is to make hydroxylated diphenyl ethers rather than to undergo cyclisation reactions leading to the formation of preDF structures. Unimolecular loss of a H or OH moiety from a pivotal carbon in these hydroxylated diphenyl ethers then produces hydroxylated and non-hydroxylated DD molecules. Formation of OHs-DF initiated by o(C)-o(C) cross-linkages involving o-SQ/o-SQ and o-SQ/CT reactions incurs very similar reaction and activation enthalpies encountered in the formation of chlorinated DFs from chlorophenols.

Reactions of HO2 with n-propylbenzene and its phenylpropyl radicals

Abstraction of an H atom from the propyl side chain by hydroperoxyl radicals (HO2) constitutes a central reaction in the low-temperature oxidation of n-propylbenzene (nPB). Herein, we calculate reaction rate constants for H abstraction from primary, secondary and benzylic sites in nPB. Rate of abstraction of a benzylic H atom dominates that of a secondary H atom with negligible abstraction of the primary H atom at T⩾600K. We present the reaction enthalpies for 1-phenyl-1-propyl (R1), 1-phenyl-2-propyl (R2) and 1-phenyl-3-propyl (R3) radicals, and compare the computed reaction rate constants and bond dissociation enthalpies with analogous scarce literature values. Addition of HO2 radicals to radical sites in R1, R2 and R3 proceeds in a highly exothermic process and results in the formation of HO2–phenylpropyl adducts. Mapped potential energy surfaces illustrate all plausible exit channels of the three HO2–phenylpropyl adducts. Master equation calculations for the three phenylpropyl+HO2 reactions indicate that direct O–OH bond fission and water elimination control the fate of the adducts leading to the formation of ketonic-type structures. Results from this study should be useful to update kinetic models for the low-temperature oxidation of alkylbenzenes in general.

Quantum dynamics of the abstraction reaction of H with cyclopropane.

The dynamics of the abstraction reaction of H atoms with the cyclopropane molecule is studied using quantum mechanical scattering theory. The quantum scattering calculations are performed in hyperspherical coordinates with a two-dimensional (2D) potential energy surface. The ab initio energy calculations are carried out with CCSD(T)-F12a/cc-pVTZ-F12 level of theory with the geometry and frequency calculations at the MP2/cc-pVTZ level. The contribution to the potential energy surface from the spectator modes is included as the projected zero-point energy correction to the ab initio energy. The 2D surface is fitted with a 29-parameter double Morse potential. An R-matrix propagation scheme is carried out to solve the close-coupled equations. The adiabatic energy barrier and reaction enthalpy are compared with high level computational calculations as well as experimental data. The calculated reaction rate constants shows very good agreement when compared with the experimental data, especially at lower temperature highlighting the importance of quantum tunnelling. The reaction probabilities are also presented and discussed. The special features of performing quantum dynamics calculation on the chemical reaction of a cyclic molecule are discussed.

Conformations of disulfide-intact and -reduced lysozyme ions probed by proton-transfer reactions at various temperatures.

Proton-transfer reactions of disulfide-intact and -reduced lysozyme ions (7+ through 14+) to 2,6-dimethylpyridine were examined in the gas phase using tandem mass spectrometry with electrospray ionization. By changing temperature of a collision cell from 280 to 460 K, temperature dependence of reaction rate constants and branching fractions was measured. Absolute reaction rate constants for the protein ions of specific charge states were determined from intensities of parent and product ions in the mass spectra. Remarkable change was observed for the rate constants and distribution of product ions. The rate constants for disulfide-intact ions changed more drastically with change of charge states and temperature than those for disulfide-reduced ions. Observed branching fractions for parent and product ions were represented by calculated reaction rate constants with a scheme of sequential process. The reaction rate constants are closely related to conformation changes with change of temperature, which are profoundly influenced by amputation of disulfide bonds.

High-Temperature Measurements of the Reactions of OH with Ethylamine and Dimethylamine

The overall rate constants of hydroxyl radicals (OH) with ethylamine (EA: CH3CH2NH2) and dimethylamine (DMA: CH3NHCH3) were investigated behind reflected shock waves using UV laser absorption of OH radicals near 306.7 nm. tert-Butyl hydroperoxide (TBHP) was used as the fast source of OH at elevated temperatures. Test gas mixtures of individual amines and TBHP, diluted in argon, were shock-heated to temperatures from 901 to 1368 K at pressures near 1.2 atm. The overall rate constants were determined by fitting the measured OH time-histories with the computed profiles using a detailed mechanism developed by Lucassen et al. (Combust. Flame 2012, 159, 2254-2279). Over the temperature range studied, the measured rate constants can be expressed as kEA+OH = 1.10 × 10(7)·T(1.93) exp(1450/T) cm(3) mol(-1) s(-1), and kDMA+OH = 2.26 × 10(4)·T(2.69) exp(1797/T) cm(3) mol(-1) s(-1). Detailed error analyses were performed to estimate the overall uncertainties of the measured reaction rate constants, and the estimated (2σ) uncertainties were found to be ±31% at 901 K and ±22% at 1368 K for kEA+OH, and ±29% at 925 K and ±21% at 1307 K for kDMA+OH. Variational transition state theory was used to compute the H-abstraction rates by OH for ethylamine and dimethylamine, with the potential energy surface, geometries, frequencies, and electronic energies calculated by Galano and Alvarez-Idaboy (J. Chem. Theory Comput. 2008, 4, 322-327) at CCSD(T)/6-311++G(2d,2p) level of theory. The calculated reaction rate constants are in good agreement with the experimental data.

Low-Temperature Mechanisms for the Formation of Substituted Azanaphthalenes through Consecutive CN and C2H Additions to Styrene and N-Methylenebenzenamine: A Theoretical Study

Ab initio G3(MP2,CC)/B3LYP/6-311G** calculations of potential energy surfaces (PESs) for the reactions of cyano and ethynyl radicals with styrene and N-methylenebenzenamine have been performed to investigate a possible formation mechanism of the prototype nitrogen-containing polycyclic aromatic compounds: (substituted) 1- and 2-azanaphthalenes. The computed PESs and molecular parameters have been used for RRKM and RRKM-Master Equation calculations of reaction rate constants and product branching ratios under single-collision conditions and at pressures from 3 to 10(-6) mbar and temperatures of 90-200 K relevant to the organic aerosol formation regions in the stratosphere of a Saturn's moon Titan. The results show that ethynyl-substituted 1- and 2-azanaphthalenes can be produced by consecutive CN and C2H additions to styrene or by two C2H additions to N-methylenebenzenamine. All CN and C2H radical addition complexes are formed in the entrance channels without barriers, and the reactions are computed to be exothermic, with all intermediates and transition states along the favorable pathways residing lower in energy than the respective initial reactants. The reactions are completed by dissociation of chemically activated radical intermediates via H losses, so that collisional stabilization of the intermediates is not required to form the final products. These features make the proposed mechanism viable even at very low temperatures and under single-collision conditions and especially significant for astrochemical environments. In Titan's stratosphere, collisional stabilization of the initial CN + styrene reaction adducts may be significant, but substantial amounts of 2-vinylbenzonitrile and 2-ethynyl-N-methylenebenzenamine can still be produced and then react with C2H to form substituted azanaphthalenes.

Model-Based Experimental Design to Estimate Kinetic Parameters of the Enzymatic Hydrolysis of Lignocellulose

A model-based nonlinear optimum experimental design technique has been implemented to estimate the kinetic parameters of the lignocellulose enzymatic hydrolysis process, mainly focused on the calculation of reaction rate constants and activation energy parameters. Analysis of the reaction was based on the mechanism of simultaneous consecutive enzymatic reactions of cellulose and hemicellulose to produce sugar-rich syrups. A mathematical model was developed as a set of ordinary differential equations (ODEs). To enhance the parameter estimation process, a control variable that directly affects the response of the system (temperature) was included to predict the state variable profiles over a broad experimental range. To determine the optimal profiles for the temperature gradient, optimal control problems were set up and solved numerically. A comparison between model prediction profiles and experimental data was performed to adjust kinetic parameter estimation to real process features. The results show that nonlinear optimum experiments enhance the quality of the estimates because of the optimality criterion included in the objective function and because the embedded nonlinear behavior is explicitly addressed.

Calculation of chemical reaction rate constants using on-the-fly high level electronic structure computations with account of multidimensional tunneling

The semiclassical instanton approach to the calculation of reaction rate constants at arbitrary temperatures in multiatomic systems is combined with high-level ab initio calculations of reactive potential energy surface (PES). The number of required ab initio calculations weakly depends on system size and allows on-the-fly evaluations of PES with high accuracy. The approach can be efficiently parallelized and provides a practical way of calculating quantum reaction rate constants with account of nuclear quantum effects such as multidimensional tunneling and zero point energies, which are rigorously incorporated in the theory. An algorithm for the search of instanton trajectories is explained. Application of the approach is illustrated for H + H(2) → H(2) + H and D + D(2) → D(2) + D bimolecular reactions in the wide temperature range with on-the-fly evaluation of PES at the ab initio full configuration interaction (FCI), coupled-cluster single double (CCSD), and single and double excitation configuration interaction (CISD) levels.

Product branching ratios in photodissociation of phenyl radical: A theoretical ab initio/Rice–Ramsperger–Kassel–Marcus study

Ab initio CCSD(T)/CBS//B3LYP/6-311G** calculations of the potential energy surface for possible dissociation channels of the phenyl radical are combined with microcanonical Rice-Ramsperger-Kassel-Marcus calculations of reaction rate constants in order to predict statistical product branching ratios in photodissociation of c-C(6)H(5) at various wavelengths. The results indicate that at 248 nm the photodissociation process is dominated by the production of ortho-benzyne via direct elimination of a hydrogen atom from the phenyl radical. At 193 nm, the statistical branching ratios are computed to be 63.4%, 21.1%, and 14.4% for the o-C(6)H(4) + H, l-C(6)H(4) ((Z)-hexa-3-ene-1,5-diyne) + H, and n-C(4)H(3) + C(2)H(2) products, respectively, in a contradiction with recent experimental measurements, which showed C(4)H(3) + C(2)H(2) as the major product. Although two lower energy pathways to the i-C(4)H(3) + C(2)H(2) products are identified, they appeared to be kinetically unfavorable and the computed statistical branching ratio of i-C(4)H(3) + C(2)H(2) does not exceed 1%. To explain the disagreement with experiment, we optimized conical intersections between the ground and the first excited electronic states of C(6)H(5) and, based on their structures and energies, suggested the following photodissociation mechanism at 193 nm: c-C(6)H(5) 1 → absorption of a photon → electronically excited 1 → internal conversion to the lowest excited state → conversion to the ground electronic state via conical intersections at CI-2 or CI-3 → non-statistical decay of the vibrationally excited radical favoring the formation of the n-C(4)H(3) + C(2)H(2) products. This scenario can be attained if the intramolecular vibrational redistribution in the CI-2 or CI-3 structures in the ground electronic state is slower than their dissociation to n-C(4)H(3) + C(2)H(2) driven by the dynamical preference.

Unraveling the mechanism of the NO reduction by CO on gold based catalysts

Periodic density functional theory (DFT) calculations have been used to unravel the mechanism of the NO reduction by CO (NO+CO→N2+CO2) on clean and hydrogen covered gold based catalysts. The effects caused by the presence of low-coordinated atoms on the catalyst were taken into consideration by using the stepped Au(321) surface. A careful analysis of several reaction mechanisms was made and it is concluded that if hydrogen species are not available on the catalyst surface, the N–O bond cleavage will proceed through the ON2O and N2O intermediates while CO reacts directly with formed oxygen adatoms. If hydrogen species are available on the catalyst, the reaction will occur via the NOH and N2O intermediates. However, the reaction has to compete with a more favorable route, where NH3 instead of N2 is obtained after formation of NOH and NHxOH intermediates. The calculations agree also with the experimental observation of the NCO intermediate species which is formed without energy cost from combination of CO and N fragments. The NCO species is very probably a spectator at moderate temperatures since its evolution toward N2 and CO2 is less favorable than other possible routes studied in this work. Finally, calculated reaction rate constants at three different temperatures show that most of the reactions studied are only possible at moderately high temperature.

Theoretical study on the unimolecular decomposition of thiophenol

The potential energy surface for the unimolecular decomposition of thiophenol (C(6)H(5)SH) is mapped out at two theoretical levels; BB1K/GTlarge and QCISD(T)/6-311+G(2d,p)//MP2/6-31G(d,p). Calculated reaction rate constants at the high pressure limit indicate that the major initial channel is the formation of C(6)H(6)S at all temperatures. Above 1000 K, the contribution from direct fission of the S-H bond becomes important. Other decomposition channels, including expulsion of H(2) and H(2)S are of negligible importance. The formation of C(6)H(6)S is predicted to be strong-pressure dependent above 900 K. Further decomposition of C(6)H(6)S produces CS and C(5)H(6). Overall, despite the significant difference in bond dissociation, i.e., 8-9 kcal/mol between the S-H bond in thiophenol and the O-H bond in phenol, H migration at the ortho position in the two molecules represents the most accessible initial channel.