Semiclassical Transition State Theory Research Articles

The role of torsional motion on the properties of propiolic acid and its H/D isotopic analogs: A density functional study using SCTST and a full anharmonic VPT2 model

The conformational isomerization of propiolic acid and its H/D isotopic counterparts are studied by using high-level quantum chemistry in conjugation with semiclassical transition state theory and second order vibrational perturbation theory. The electronic structure calculations were carried at DFT and MP2 levels of theory. The vibrational anharmonicity coefficients including the fully coupled vibrational modes of the reaction coordinate of the transition state, used in semiclassical transition state theory, are computed at hybrid functional B3LYP in conjugation with aug-cc-pVTZ and SNSD basis sets. The corresponding solutions give rate as well as the equilibrium constants between the isomers and the isotopic analogs.

First-principles investigation of quantum mechanical effects on the diffusion of hydrogen in iron and nickel

The diffusion coefficients of interstitial hydrogen in bulk Fe and Ni crystals have been calculated over a wide range of temperatures employing first-principles methods based on density functional theory. Quantum mechanical effects have been included by means of the semiclassical transition state theory and the small-polaron model of Flynn and Stoneham. Our results show that to include such effects is crucial for a quantitative simulation of H diffusion in bcc Fe even at room temperature, while in the case of fcc Ni this is less important. The comparison with other theoretical approaches as well as with experimental studies emphasizes the main advantages of the present approach: it is quantitatively accurate and computationally efficient.

Reduced-Dimensionality Semiclassical Transition State Theory: Application to Hydrogen Atom Abstraction and Exchange Reactions of Hydrocarbons

Quantum mechanical methods for calculating rate constants are often intractable for reactions involving many atoms. Semiclassical transition state theory (SCTST) offers computational advantages over these methods but nonetheless scales exponentially with the number of degrees of freedom (DOFs) of the system. Here we present a method with more favorable scaling, reduced-dimensionality SCTST (RD SCTST), that treats only a subset of DOFs of the system explicitly. We apply it to three H abstraction and exchange reactions for which two-dimensional potential energy surfaces (PESs) have previously been constructed and evaluated using RD quantum scattering calculations. We differentiated these PESs to calculate harmonic frequencies and anharmonic constants, which were then used to calculate cumulative reaction probabilities and rate constants by RD SCTST. This method yielded rate constants in good agreement with quantum scattering results. Notably, it performed well for a heavy-light-heavy reaction, even though it does not explicitly account for corner-cutting effects. Recent extensions to SCTST that improve its treatment of deep tunneling were also evaluated within the reduced-dimensionality framework. The success of RD SCTST in this study suggests its potential applicability to larger systems.

Stabilization of the Simplest Criegee Intermediate from the Reaction between Ozone and Ethylene: A High-Level Quantum Chemical and Kinetic Analysis of Ozonolysis.

The fraction of the collisionally stabilized Criegee species CH2OO produced from the ozonolysis of ethylene is calculated using a two-dimensional (E, J)-grained master equation technique and semiclassical transition-state theory based on the potential energy surface obtained from high-accuracy quantum chemical calculations. Our calculated yield of 42 ± 6% for the stabilized CH2OO agrees well, within experimental error, with available (indirect) experimental results. Inclusion of angular momentum in the master equation is found to play an essential role in bringing the theoretical results into agreement with the experiment. Additionally, yields of HO and HO2 radical products are predicted to be 13 ± 6% and 17 ± 6%, respectively. In the kinetic simulation, the HO radical product is produced mostly from the stepwise decomposition mechanism of primary ozonide rather than from dissociation of hot CH2OO.

Theoretical studies on the kinetics of hydrogen abstraction reactions of H and CH3 radicals from CH3OCH3 and some of their H/D isotopologues.

The hydrogen abstraction reactions by H and CH3 radicals from CH3OCH3 and some of their H/D isotopologues are studied by semiclassical transition state theory. Many high-level density functional, ab initio, and combinatory quantum chemical methods, including B3LYP, BB1K, MP2, MP4, CCSD(T), CBS-Q, and G4 methods, are employed to compute the energies and rovibrational properties of the stationary points for the title reactions. Xij vibrational anharmonicity coefficients, used in semiclassical transition state theory, are computed at the B3LYP, BB1K, and MP2 levels of theory. Thermal rate coefficients and kinetic isotope effects are computed over the temperature range from 200 to 2500 K and compared with available experimental data. The computed rate constants for the title reactions are represented as the equation k(T) = ATn exp[−E(T + T0)/(T2 + T02)].

Hydrogen Abstraction Reaction of Hydroxyl Radical with 1,1-Dibromoethane and 1,2-Dibromoethane Studied by Using Semi-Classical Transition State Theory

The hydrogen abstraction reaction by OH radical from CH2BrCH2Br (R1) and CH₃CHBr2 (R2) is investigated theoretically by semi-classical transition state theory. The stationary points for both reactions are located by using ωB97X-D and KMLYP density functional methods along with cc-pVTZ basis. Single-point energy calculations are performed at the QCISD(T) and CCSD(T) levels of theory with different basis sets. The results show that the activation energies are very sensitive to effects of electron correlation and basis set. In order to correct basis set effects on the calculated energetic, a correction factor (CF) is determined from the energy difference between the MP2/cc-pVTZ and MP2/aug-cc-pVTZ levels. xij vibrational anharmonicity coefficients, needed for semi-classical transition state theory, are calculated at the KMLYP/cc-pVTZ level of theory. Thermal rate coefficients are computed over the temperature range from 200 to 3000 K and they are shown to be in accordance with available experimental data. The computed rate constants for the reactions R1 and R2 are fitted to the equation k(T)=A T^n exp[-E(T+T_0 )/(T^2+ T_0^2 ) ].

Relatively Selective Production of the Simplest Criegee Intermediate in a CH4/O2 Electric Discharge: Kinetic Analysis of a Plausible Mechanism.

High -accuracy coupled cluster methods in combination with microcanonical semiclassical transition state theory are used to investigate a plausible formation mechanism of the simplest Criegee intermediate in a CH4/O2 discharge experiment. Our results suggest that the Criegee intermediate is produced in a three-step process: (i) production of methyl radical by cleavage of a C-H bond of CH4; (ii) association of methyl radical with molecular oxygen to form a vibrationally excited methyl peroxy, which is in a rapid microequilibrium with the reactants; and finally, (iii) H-abstraction of CH3OO by O2, which results in the formation of cool CH2OO, which has insufficient internal energy to rearrange to dioxirane.

Theoretical Kinetics Studies on the Reaction of CF3CF═CF2 with Hydroxyl Radical

The potential energy surface for the reaction of hexafluoropropene with hydroxyl radical is explored by using BB1K density functional method. Single-point energy calculations are performed at CBS-Q level of theory. Semiclassical transition state theory and a modified strong collision/RRKM model are employed to calculate the thermal rate coefficients for the formation of major products as a function of temperature and pressure. It is revealed from the computed rate constants that the major product channels at low temperatures and high pressures are the formation of the primary adducts formed through OH addition to the double bond of CF3═CFCF2. At high temperatures and low pressures, however, many products arising from unimolecular decomposition of the chemically activated intermediates become important. P9A (CF3CFCOF + HF) and P7B (CF3COCF2 + HF) are dominant products at elevated temperatures. Semiclassical transition state theory is used to compute the overall high-pressure rate constants over the temperature range of 200-1500 K. The computed rate constants are in accordance with the available experimental data.

Theoretical/experimental comparison of deep tunneling decay of quasi-bound H(D)OCO to H(D) + CO₂.

The measured H(D)OCO survival fractions of the photoelectron-photofragment coincidence experiments by the Continetti group are qualitatively reproduced by tunneling calculations to H(D) + CO2 on several recent ab initio potential energy surfaces for the HOCO system. The tunneling calculations involve effective one-dimensional barriers based on steepest descent paths computed on each potential energy surface. The resulting tunneling probabilities are converted into H(D)OCO survival fractions using a model developed by the Continetti group in which every oscillation of the H(D)-OCO stretch provides an opportunity to tunnel. Four different potential energy surfaces are examined with the best qualitative agreement with experiment occurring for the PIP-NN surface based on UCCSD(T)-F12a/AVTZ electronic structure calculations and also a partial surface constructed for this study based on CASPT2/AVDZ electronic structure calculations. These two surfaces differ in barrier height by 1.6 kcal/mol but when matched at the saddle point have an almost identical shape along their reaction paths. The PIP surface is a less accurate fit to a smaller ab initio data set than that used for PIP-NN and its computed survival fractions are somewhat inferior to PIP-NN. The LTSH potential energy surface is the oldest surface examined and is qualitatively incompatible with experiment. This surface also has a small discontinuity that is easily repaired. On each surface, four different approximate tunneling methods are compared but only the small curvature tunneling method and the improved semiclassical transition state method produce useful results on all four surfaces. The results of these two methods are generally comparable and in qualitative agreement with experiment on the PIP-NN and CASPT2 surfaces. The original semiclassical transition state theory method produces qualitatively incorrect tunneling probabilities on all surfaces except the PIP. The Eckart tunneling method uses the least amount of information about the reaction path and produces too high a tunneling probability on PIP-NN surface, leading to survival fractions that peak at half their measured values.

Hydrogen abstraction reactions of hydroxyl radicals with 1,1,2,2-tetrachloroethane, 1,1,1,2-tetrachloroethane and pentachloroethane studied by using semi-classical transition state theory

The hydrogen abstraction reactions by OH radicals from CHCl2CHCl2 (R1), CH2ClCCl3 (R2) and C2HCl5 (R3) are investigated theoretically by semi-classical transition state theory. Many high-level density functional, ab initio and combinatory electronic structure calculation methods are used to evaluate the energies and ro-vibrational properties of the stationary points for the title reactions. xij vibrational anharmonicity coefficients, needed for semi-classical transition state theory, are calculated at the KMLYP/cc-pVTZ level of theory. Thermal rate coefficients are computed over the temperature range from 200 to 2000 K and compared with available experimental data. The computed rate constants for the reactions R1, R2 and R3 are fitted to the equation k(T) = ATnexp [ − E(T + T0)/(T2 + T20)].

Accurate ab Initio Thermal Rate Constants for Reaction of O(3P) with H2 and Isotopic Analogues

Semiclassical transition state theory, in combination with high accuracy quantum chemistry, is used to compute thermal rate constants from first principles for the O((3)P) + H2 reaction and its isotopic counterparts. In the temperature regime of 298-3500 K (which spans 8 orders of magnitude for rate constants), our theoretical results are in excellent agreement (within 5-15%) with all available experimental data from 298 to 2500 K but are somewhat too low (from 15 to 35%) at higher temperatures. Several possible reasons that might cause the degradation at high temperatures are discussed. Vibrational state-selected rate constants and their correlations with normal thermal rate constant are derived and are given in the Supporting Information.

Computational Replication of the Abnormal Secondary Kinetic Isotope Effects in a Hydride Transfer Reaction in Solution with a Motion Assisted H-Tunneling Model

We recently reported abnormal secondary deuterium kinetic isotope effects (2° KIEs) for hydride transfer reactions from alcohols to carbocations in acetonitrile (Chem. Comm. 2012, 48, 11337). Experimental 2° KIE values were found to be inflated on the 9-C position in the xanthylium cation but deflated on the β-C position in 2-propanol with respect to the values predicted by the semi-classical transition-state theory. No primary (1°) isotope effect on 2° KIEs was observed. Herein, the KIEs were replicated by the Marcus-like H-tunneling model that requires a longer donor–acceptor distance (DAD) in a lighter isotope transfer process. The 2° KIEs for a range of potential tunneling-ready-states (TRSs) of different DADs were calculated and fitted to the experiments to find the TRS structure. The observed no effect of 1° isotope on 2° KIEs is explained in terms of the less sterically hindered TRS structure so that the change in DAD due to the change in 1° isotope does not significantly affect the reorganization of the 2° isotope and hence the 2° KIE. The effect of 1° isotope on 2° KIEs may be expected to be more pronounced and thus observable in reactions occurring in restrictive environments such as the crowded and relatively rigid active site of enzymes.

Accurate Determination of Barrier Height and Kinetics for the F + H2O → HF + OH Reaction

The reaction energy and barrier height of the title reaction are investigated using two high-level ab initio protocols, namely Focal Point Analysis (FPA) and modified High Accuracy Extrapolated Ab Initio Thermochemistry (HEAT) methods. It is concluded from these calculations that despite some multireference character, dynamic electron correlation plays a dominant role near the reaction barrier. Thus, the coupled-cluster method with higher excitations than singles and doubles gives a better description than the multireference configuration interaction method for the barrier height. The FPA and HEAT classical barrier heights, including the spin-orbit and other corrections, are 1.919 and 2.007 kcal/mol, respectively. The rate constants and H/D kinetic isotope effect for the title reaction are determined by semiclassical transition-state theory based on the anharmonic potential energy surface near the saddle point, and the agreement with experiment is excellent. The rate constants are also computed using a quasi-classical trajectory method on a global potential energy surface scaled to the FPA barrier height and a similar level of agreement with experimental data is obtained.

A Shock Tube Study of H2 + OH → H2O + H Using OH Laser Absorption

ABSTRACTThe rate constant for the reaction of hydroxyl radicals (OH) with molecular hydrogen (H2) was measured behind reflected shock waves using UV laser absorption of OH radicals near 306.69 nm. Test gas mixtures of H2 and tert‐butyl hydroperoxide (TBHP) diluted in argon were shock‐heated to temperatures ranging from 902 to 1518 K at pressures of 1.15–1.52 atm. OH radicals were produced by rapid thermal decomposition of TBHP at high temperatures. The rate constant for the title reaction was inferred by best fitting the measured OH time histories with the simulated profiles from the comprehensive reaction mechanism of Wang et al. (USC‐Mech v2.0) (2007). The measured values can be expressed in the Arrhenius equation as k1(T) = 4.38 × 1013 exp(–3518/T) cm3 mol−1 s−1 over the temperature range studied. A detailed error analysis was performed to estimate the overall uncertainty of the title reaction, and the estimated (2 – σ) uncertainties were found to be ±17% at 972 and 1228 K. The present measurements are in excellent agreement with the previous experimental studies from Frank and Just (Ber Bunsen‐Ges Phys Chem 1985, 89, 181–187), Michael and Sutherland (J Phys Chem 1988, 92, 3853–3857), Davidson et al. (Symp (Int) Combust 1988, 22, 1877–1885), Oldenborg et al. (J Phys Chem 1992, 96, 8426–8430), and Krasnoperov and Michael (J Phys Chem A 2004, 108, 5643–5648).In addition, the measured rate constant is in close accord with the non‐Arrhenius expression from GRI‐Mech 3.0 (http://www.me.berkeley.edu/gri_mech/) and the theoretical calculation using semiclassical transition state theory from Nguyen et al. (Chem Phys Lett 2010, 499, 9–15).

HO + CO Reaction Rates and H/D Kinetic Isotope Effects: Master Equation Models with ab Initio SCTST Rate Constants

Ab initio microcanonical rate constants were computed using Semi-Classical Transition State Theory (SCTST) and used in two master equation formulations (1D, depending on active energy with centrifugal corrections, and 2D, depending on total energy and angular momentum) to compute temperature-dependent rate constants for the title reactions using a potential energy surface obtained by sophisticated ab initio calculations. The 2D master equation was used at the P = 0 and P = ∞ limits, while the 1D master equation with centrifugal corrections and an empirical energy transfer parameter could be used over the entire pressure range. Rate constants were computed for 75 K ≤ T ≤ 2500 K and 0 ≤ [He] ≤ 10(23) cm(-3). For all temperatures and pressures important for combustion and for the terrestrial atmosphere, the agreement with the experimental rate constants is very good, but at very high pressures and T ≤ 200 K, the theoretical rate constants are significantly smaller than the experimental values. This effect is possibly due to the presence in the experiments of dimers and prereactive complexes, which were not included in the model calculations. The computed H/D kinetic isotope effects are in acceptable agreement with experimental data, which show considerable scatter. Overall, the agreement between experimental and theoretical H/D kinetic isotope effects is much better than in previous work, and an assumption of non-RRKM behavior does not appear to be needed to reproduce experimental observations.

Reaction of HO with CO: Tunneling Is Indeed Important.

The potential energy surface and chemical kinetics for the reaction of HO with CO, which is an important process in both combustion and atmospheric chemistry, were computed using high-level ab initio quantum chemistry in conjunction with semiclassical transition state theory under the limiting cases of high and zero pressure. The reaction rate constants calculated from first principles agree extremely well with all available experimental data, which range in temperature over a domain that covers both combustion and terrestrial atmospheric chemistry. The role of quantum tunneling is confirmed to be extremely important, which supports recent work by Continetti and collaborators regarding the loss of hydrogen atoms from vibrationally excited states of HOCO. A sensitivity analysis has been carried out and serves as the basis for a plausible estimate of uncertainty in the calculations.

Ab Initio Reaction Rate Constants Computed Using Semiclassical Transition-State Theory: HO + H2 → H2O + H and Isotopologues

A new algorithm [Nguyen, T. L.; Stanton, J. F.; Barker, J. R. Chem. Phys. Lett. 2010, 9, 499] for the semiclassical transition-state theory (SCTST) formulated by W. H. Miller and co-workers is used to compute rate constants for the isotopologues of the title reaction, with no empirical adjustments. The SCTST and relevant results from second-order vibrational perturbation theory (VPT2) are summarized. VPT2 is used at the CCSD(T) level of electronic structure theory to compute the anharmonicities of the fully coupled vibrational modes (including the reaction coordinate) of the transition structure. The anharmonicities are used in SCTST to compute the rate constants over the temperature range from 200 to 2500 K. The computed rate constants are compared to experimental data and theoretical calculations from the literature. The SCTST results for absolute rate constants and for both primary and secondary isotope effects are in excellent agreement with the experimental data for this reaction over the entire temperature range. The sensitivity of SCTST to various parameters is investigated by using a set of simplified models. The results show that multidimensional tunneling along the curved reaction path is important at low temperatures and the anharmonic coupling among the vibrational modes is important at high temperatures. The theoretical kinetics data are also presented as fitted empirical algebraic expressions.

A practical implementation of semi-classical transition state theory for polyatomics

An algorithm is described for computing rate constants with semi-classical transition state theory (SCTST) formulated by Miller and coworkers. SCTST incorporates non-separable coupling among all degrees of freedom and multi-dimensional quantum mechanical tunneling along the curved reaction path. The algorithm, which is practical for reactants containing dozens of atoms, predicts both microcanonical and canonical rate constants. In addition, the quantum chemistry code CFOUR has been extended to efficiently compute fully-coupled vibrational anharmonicities for transition states at the CCSD(T) level of theory. The new methods are demonstrated for the H 2 + OH reaction and the ‘tail-biting’ isomerization of acetylperoxyl radical.

Modeling Proton Jumps in HY Zeolite: Effects of Acid Site Heterogeneity

We have computed the total mean rate coefficient for proton transfer in bare H−Y zeolite, for comparison with NMR experiments and previous calculations. We computed proton-transfer energies using two-layer ONIOM calculations on an 8T−53T cluster, where xT indicates x tetrahedral atoms. Rate coefficients were computed using truncated harmonic semiclassical transition state theory. The zero-point energy (ZPE) corrected proton site energies in H−Y (FAU structure) were found to be O3 (0 kJ mol-1), O1 O2 (16.1 kJ mol-1), and O4 (17.5 kJ mol-1), in quantitative agreement with previous calculations and in qualitative agreement with neutron diffraction occupancies. A new local minimum denoted O2* (31.4 kJ mol-1 relative to O3) was located, with a proton bound to O2 but pointing into the sodalite cage. Transition states between each pair of minima were fully characterized, yielding ZPE corrected activation energies ranging from 35.5 to 123.4 kJ mol-1. No correlation was found between barrier height and local structure; we considered 10 structural parameters including ring size, T−O−T angle, and nonbonded oxygen distance. Total mean rate coefficients were found to exhibit a strong non-Arrhenius temperature dependence, with apparent activation energies in the range of ca. 60−100 kJ mol-1 at high temperature, and ca. 3 kJ mol-1 at low temperature. This low-temperature value reflects thermally assisted tunneling to a site with a slightly higher energy. NMR experiments by Sarv et al. and Ernst et al. report apparent activation energies of 61 and 78 kJ mol-1, respectively, extracted from temperature ranges 298−658 and 610−640 K. Our theoretically computed apparent activation energies for these temperature ranges are 72 and 79 kJ mol-1, respectively, in quite good agreement with experiment.

Anhydrous and Water-Assisted Proton Mobility in Phosphotungstic Acid

Nonlocal gradient-corrected density functional theoretical calculations were used to determine the energetics associated with proton migration in phosphotungstic acid. The activation energy for anhydrous proton hopping between two oxygen atoms on the exterior of the molecular Keggin unit was calculated to be 103.3 kJ mol(-1). The quantum-tunneling effect on the rate of proton movement was determined using semiclassical transition-state theory and was found to be a major contributor to the overall rate of proton movement at temperatures below approximately 350 K. The adsorption of water on an acidic proton decreases the activation barrier for hopping to 11.2 kJ mol(-1) by facilitating proton transfer along hydrogen bonds. The overall rate constant for proton hopping was determined as a function of temperature and water partial pressure. Small amounts of water greatly enhance the overall rate of proton movement.