Outer Transition State Research Articles

Canonical Unified Statistical Rate Constants Using a High-Level Composite Coupled Cluster Energy Scheme for the CH4 + CH Reaction

We report an ab initio study on the kinetics and chemical dynamics of the CH4 + CH reaction using a coupled cluster based composite scheme that includes unrestricted coupled cluster singles and doubles with perturbative connected triples method, UCCSD(T), energies extrapolated to the complete basis set limit, in addition to core-valence, higher-order correlation, and relativistic corrections. With this protocol, the reaction enthalpies for the two main reaction channels, C2H4 + H and CH2 + CH3, are reproduced with an absolute deviation of 0.04 kcal mol–1 relative to experimental data. At the UCCSD(T)/complete basis set (CBS) level of theory, the formation of the C2H5 intermediate is barrierless, in contrast with the low submerged barrier (–1.87 kcal -mol–1 relative to the reactants) found at the UCCSD(T)/augmented correlation-consistent polarized double-zeta (aug-cc-pVDZ) level of theory. With the correlation-consistent polarized triple-zeta (cc-pVTZ) basis set, we describe structural variations for the reaction bottleneck along the reaction path, finding at least three canonical variational transition states for the temperature range from 20 to 800 K. The thermal rates were obtained via the canonical unified statistical theory (CUS), using the canonical variational transition state theory (VTST) for the inner-transition state and long-range transition state theory (LRTST) for the outer-transition state. Our calculations agree with literature measurements and show inverse Arrhenius behavior, as observed experimentally. At 298 K, the computed rate constant is 2.65 × 10–10 cm3 molecule–1 s−1 and reported experimental measurements range from 2.5 × 10−12 to 3.0 × 10–10 cm3 molecule–1 s−1. Our theoretical study represents an improvement on previous computational investigations and highlights that even relatively simple gas-phase reactions can require high levels of theory to be modeled accurately.

Association of Cl with C2H2 by unified variable-reaction-coordinate and reaction-path variational transition-state theory

Barrierless unimolecular association reactions are prominent in atmospheric and combustion mechanisms but are challenging for both experiment and kinetics theory. A key datum for understanding the pressure dependence of association and dissociation reactions is the high-pressure limit, but this is often available experimentally only by extrapolation. Here we calculate the high-pressure limit for the addition of a chlorine atom to acetylene molecule (Cl + C2H2→C2H2Cl). This reaction has outer and inner transition states in series; the outer transition state is barrierless, and it is necessary to use different theoretical frameworks to treat the two kinds of transition state. Here we study the reaction in the high-pressure limit using multifaceted variable-reaction-coordinate variational transition-state theory (VRC-VTST) at the outer transition state and reaction-path variational transition state theory (RP-VTST) at the inner turning point; then we combine the results with the canonical unified statistical (CUS) theory. The calculations are based on a density functional validated against the W3X-L method, which is based on coupled cluster theory with single, double, and triple excitations and a quasiperturbative treatment of connected quadruple excitations [CCSDT(Q)], and the computed rate constants are in good agreement with some of the experimental results. The chlorovinyl (C2H2Cl) adduct has two isomers that are equilibrium structures of a double-well C≡C-H bending potential. Two procedures are used to calculate the vibrational partition function of chlorovinyl; one treats the two isomers separately and the other solves the anharmonic energy levels of the double well. We use these results to calculate the standard-state free energy and equilibrium constant of the reaction.

Theoretical studies on the kinetics of the hydrogen-abstraction reactions from 1,3,5-trioxane and 1,4-dioxane by OH radicals

Theoretical investigations have been performed on the kinetics of bimolecular hydrogen-abstraction reactions of 1,3,5-trioxane and 1,4-dioxane cyclic ethers with OH radicals. Hydrogen abstraction from both axial and equatorial positions of 1,3,5-trioxane and 1,4-dioxane was considered. Optimization of the structures, and the calculation of energies, vibrational frequencies and moments of inertia for all the stationary points including reactants, hydrogen-bonded complexes, transition states and products were carried out using density functional theory at the M06-2X level together with the MG3S basis set. Single-point energy calculations on the optimized points were obtained at the CBS-QB3 level. The calculations show that the title reactions proceed through relatively strong hydrogen-bonded complexes due to the hydrogen bonding between the OH radicals and the oxygen atoms of the cyclic ethers. A two-transition state model (an inner tight transition state and an outer loose transition state) was employed to compute the hydrogen-abstraction rate coefficients. The rate coefficients were also computed using conventional transition state theory considering a tight transition state for the purpose of comparison. It was found that when the reactions proceed via inner transition states with relative energies higher than the reactants, the computed rate coefficients are underestimated by conventional transition state theory.

A theoretical study of the addition of CH2OO to hydroxymethyl hydroperoxide and its implications on SO3 formation in the atmosphere.

The reaction of hydroxymethyl hydroperoxide (HMHP, HOCH2OOH) with the simplest Criegee intermediate, CH2OO, has been examined using quantum chemical methods with transition state theory. Geometry optimization and IRC calculations were performed using the M06-2X, MN15-L, and B2PLYP-D3 functionals in conjunction with the aug-cc-pVTZ basis set. Single point energy calculations using QCISD(T) and BD(T) with the same basis set have been performed to determine the energy of reactants, reactive complexes, transition states, and products. Rate coefficients have been obtained using variational transition state theory. The addition of CH2OO on the three different oxygen atoms in HMHP has been considered and the ether oxide forming channel, CH2OO + HOCH2OOH → HOCH2O(O)CH2OOH (channel 2), is the most favorable. The best computed standard enthalpy of reaction (ΔH) and zero-point corrected barrier height are -20.02 and -6.33 kcal mol-1, respectively. The reaction barrier is negative and our results suggest that both the inner and outer transition states contribute to the corresponding overall reactive flux in the tropospheric temperature range (220 K to 320 K). A two-transition state model has been used to obtain reliable rate coefficients at the high-pressure limit. The pressure-dependent rate coefficient calculations using the SS-QRRK theory have shown that this channel is pressure-dependent. Moreover, our investigation has shown that the ether oxide formed may rapidly react with SO2 at 298 K to form SO3, which can, in turn, react with water to form atmospheric H2SO4. A similar calculation has been conducted for the reaction of HMHP with OH, suggesting that the titled reaction may be a significant sink of HMHP. Therefore, the reaction between CH2OO and HOCH2OOH could be an indirect source for generating atmospheric H2SO4, which is crucial to the formation of clouds, and it might relieve global warming.

Experimental and Computational Studies of Unimolecular 1,1-HX (X = F, Cl) Elimination Reactions of C2D5CHFCl: Role of Carbene:HF and HCl Adducts in the Exit Channel of RCHFCl and RCHCl2 Reactions.

The gas-phase unimolecular reactions of C2D5CHFCl molecules with 94 kcal mol-1 of vibrational energy have been studied by the chemical-activation experimental technique and by electronic-structure computations. Products from the reaction of C2D5CHFCl molecules, formed by the recombination of C2D5 and CHFCl radicals in a room temperature bath gas, were measured by gas chromatography-mass spectrometry. The 2,1-DCl (81%) and 1,1-HCl (17%) elimination reactions are the principal processes, but 2,1-DF and 1,1-HF elimination reactions also are observed. Comparison of experimental rate constants to calculated statistical rate constants provides threshold energies. The potential surfaces associated with C2D5(F)C: + HCl and C2D5(Cl)C: + HF reactions are of special interest because hydrogen-bonded adducts with HCl and HF with dissociation energies of 6.4 and 9.3 kcal mol-1, respectively, are predicted by calculations. The relationship between the geometries and threshold energies of transition states for 1,1-HCl elimination and carbene:HCl adducts is complex, and previous studies of related molecules, such as CD3CHFCl, CD2ClCHFCl, C2D5CHCl2, and halogenated methanes are included in the computational analysis. Extensive calculations for CH3CHFCl as a model for 1,1-HCl reactions illustrate properties of the exit-channel potential energy surface. Since the 1,1-HCl transition state is submerged relative to dissociation of the adduct, inner and outer transition states should be considered for analysis of rate constants describing 1,1-HCl elimination and addition reactions of carbenes to HCl.

Decomposition and isomerization of 1-pentanol radicals and the pyrolysis of 1-pentanol

Stable species and saddle points on the C5H11O potential energy surface relevant for 1-pentanol pyrolysis and combustion have been determined starting from the terminal adduct of the OH + 1-pentene reaction. A large number of stationary points were explored automatically with the KinBot software at the M06-2X/6-311++G(d,p) level. The kinetically relevant stationary points have been further characterized using UCCSD(T)-F12a/cc-pVTZ-F12//M06-2X/6-311++G(d,p) quantum chemistry calculations. The entrance channel consists of a barrierless outer transition state leading into a van der Waals well followed by a submerged saddle point, overall described with an effective two-transition-state model. The master equation has been solved to obtain pressure- and temperature-dependent rate coefficients for all reactions on the potential energy surface in the 300–2500 K temperature range and 0.01–100 atm pressure range. The newly obtained rate coefficients have been implemented in a kinetic model for the thermal decomposition of 1-pentanol diluted in a nitrogen stream. We measured the conversion of major species using gas chromatography with a flame ionization detector, and two-dimensional gas chromatography with time-of-flight mass spectrometric and flame ionization detectors in the effluent of a flow reactor at 0.17 MPa between 913 and 1023 K. Comparison of the simulated versus the experimental data acquired in this work shows that the reactions found by KinBot, for which earlier only poor estimates existed, are of significant importance to correctly describe conversion and product selectivities. It proves to be possible to generate adequate chemical models automatically provided that the underlying high-level ab initio data is computationally affordable.

Phase space barriers and dividing surfaces in the absence of critical points of the potential energy: Application to roaming in ozone.

We examine the phase space structures that govern reaction dynamics in the absence of critical points on the potential energy surface. We show that in the vicinity of hyperbolic invariant tori, it is possible to define phase space dividing surfaces that are analogous to the dividing surfaces governing transition from reactants to products near a critical point of the potential energy surface. We investigate the problem of capture of an atom by a diatomic molecule and show that a normally hyperbolic invariant manifold exists at large atom-diatom distances, away from any critical points on the potential. This normally hyperbolic invariant manifold is the anchor for the construction of a dividing surface in phase space, which defines the outer or loose transition state governing capture dynamics. We present an algorithm for sampling an approximate capture dividing surface, and apply our methods to the recombination of the ozone molecule. We treat both 2 and 3 degrees of freedom models with zero total angular momentum. We have located the normally hyperbolic invariant manifold from which the orbiting (outer) transition state is constructed. This forms the basis for our analysis of trajectories for ozone in general, but with particular emphasis on the roaming trajectories.

Enhancing Effects of Salt Formation on Catalytic Activity and Enantioselectivity for Asymmetric Hydrogenation of Isoquinolinium Salts by Dinuclear Halide-Bridged Iridium Complexes Bearing Chiral Diphosphine Ligands

Invited for the cover of this issue is the group of Kazushi Mashima at Osaka University. The image depicts a novel six-membered outer sphere transition state—the substrate and product are represented by locomotives with a six-membered rail, and chiral induction by a signal. Read the full text of the article at 10.1002/chem.201405408.

Predictive Theory for the Addition and Insertion Kinetics of 1CH2 Reacting with Unsaturated Hydrocarbons

The reactions of singlet methylene, (1)CH2, with unsaturated hydrocarbons are of considerable significance to the formation and growth of polycyclic aromatic hydrocarbons (PAHs). In this work, we employ high level ab initio transition state theory to predict the high pressure rate coefficient for singlet methylene reacting with acetylene (C2H2), ethylene (C2H4), propyne (CH3CCH), propene (CH3CHCH2), allene (CH2CCH2), 1,3-butadiene (CH2CHCHCH2), 2-butyne (CH3CCCH3), and benzene (C6H6). Both addition and insertion channels are found to contribute significantly to the kinetics, with the insertion kinetics of increasing importance for larger hydrocarbons due to the increasing number of CH bonds and increasingly attractive interactions. We treat the addition kinetics with direct CASPT2 based variable-reaction-coordinate transition state theory. One-dimensional corrections to the CASPT2 interaction energies are obtained from geometry relaxation calculations and CCSD(T)/CBS evaluations. The insertion kinetics is treated with traditional variational TST methods employing CCSD(T)/CBS energies obtained along the CASPT2/cc-pVTZ distinguished coordinate reaction paths. The overall rate constant and branching fractions are obtained from a multiple transition state model that accounts for the physical distinction between tight inner and loose outer transition states. The predicted rate constants, which cover the range from 200 to 2000 K, are found to be in excellent agreement with the available experimental data, with a maximum observed discrepancy of about 40%.

Experimental and Theoretical Study of the Kinetics and Mechanism of the Reaction of OH Radicals with Dimethyl Ether

The reaction of OH with dimethyl ether (CH3OCH3) has been studied from 195 to 850 K using laser flash photolysis coupled to laser induced fluorescence detection of OH radicals. The rate coefficient from this work can be parametrized by the modified Arrhenius expression k = (1.23 ± 0.46) × 10(-12) (T/298)(2.05±0.23) exp((257 ± 107)/T) cm(3) molecule(-1) s(-1). Including other recent literature data (923-1423 K) gives a modified Arrhenius expression of k1 = (1.54 ± 0.48) × 10(-12) (T/298 K)(1.89±0.16) exp((184 ± 112)/T) cm(3) molecule(-1) s(-1) over the range 195-1423 K. Various isotopomeric combinations of the reaction have also been investigated with deuteration of dimethyl ether leading to a normal isotope effect. Deuteration of the hydroxyl group leads to a small inverse isotope effect. To gain insight into the reaction mechanisms and to support the experimental work, theoretical studies have also been undertaken calculating the energies and structures of the transition states and complexes using high level ab initio methods. The calculations also identify pre- and post-reaction complexes. The calculations show that the pre-reaction complex has a binding energy of ~22 kJ mol(-1). Stabilization into the complex could influence the kinetics of the reaction, especially at low temperatures (<300 K), but there is no direct evidence of this occurring under the experimental conditions of this study. The experimental data have been modeled using the recently developed MESMER (master equation solver for multi energy well reactions) code; the calculated rate coefficients lie within 16% of the experimental values over the temperature range 200-1400 K with a model based on a single transition state. This model also qualitatively reproduces the observed isotope effects, agreeing closely above ~600 K but overestimating them at low temperatures. The low temperature differences may derive from an inadequate treatment of tunnelling and/or from an enhanced role of an outer transition state leading to the pre-reaction complex.

Gas-phase reaction between calcium monocation and fluoromethane: Analysis of the potential energy hypersurface and kinetics calculations

The gas-phase reaction between calcium monocation and fluoromethane: Ca(+)+CH(3)F-->CaF(+)+CH(3) was theoretically analyzed. The potential energy hypersurface was explored by using density functional theory methodology with different functionals and Pople's, Dunning's, Ahlrichs', and Stuttgart-Dresden basis sets. Kinetics calculations (energy and total angular momentum resolved microcanonical variational/conventional theory) were accomplished. The theoretically predicted range for the global kinetic rate constant values at 295 K (7.2x10(-11)-5.9x10(-10) cm(3) molecule(-1) s(-1)) agrees reasonably well with the experimental value at the same temperature [(2.6+/-0.8)x10(-10) cm(3) molecule(-1) s(-1)]. Explicit consideration of a two transition state model, where the formation of a weakly bounded prereactive complex is preceded by an outer transition state (entrance channel) and followed by an inner transition state connecting with a second intermediate that finally leads to products, is mandatory. Experimental observations on the correlation, or lack of correlation, between reaction rate constants and second ionization energies of the metal might well be rationalized in terms of this two transition state model.

Quantum capture, adiabatic channel, and classical trajectory study of the high pressure rate constant of the reaction H+O2→HO2 between 0 and 5000K

Limiting high pressure rate constants for the recombination reaction H+O(2)-->HO(2) are modeled between 0 and 5000 K on an ab initio potential. Quantum capture theory is employed for the temperature range from 0 to about 1 K, while classical trajectory calculations are suitable for covering temperatures above about 200 K. The intermediate temperature range is analyzed by adiabatic channel capture theory. The system is characterized by transition-state switching from outer transition states in the long-range-C(6)R(6) potential to inner transition states in the range of a "shoulder" of the potential. The limiting high pressure rate constants from the trajectory calculations are sufficient for comparison with the experimental data which are available over the range from 300 to 900 K. Specific rate constants k(E,J) for HO(2) dissociation are also given and analyzed with respect to internal consistency with capture cross sections.

A Two Transition State Model for Radical−Molecule Reactions: Applications to Isomeric Branching in the OH−Isoprene Reaction

A two transition state model is applied to the prediction of the isomeric branching in the addition of hydroxyl radical to isoprene. The outer transition state is treated with phase space theory fitted to long-range transition state theory calculations on an electrostatic potential energy surface. High-level quantum chemical estimates are applied to the treatment of the inner transition state. A one-dimensional master equation based on an analytic reduction from two-dimensions for a particular statistical assumption about the rotational part of the energy transfer kernel is employed in the calculation of the pressure dependence of the addition process. We find that an accurate treatment of the two separate transition state regions, at the energy and angular momentum resolved level, is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is shown to occur at about 275 K, with significant effects from both transition states over the 30-500 K temperature range. Modest adjustments in the ab initio predicted inner saddle point energies yield predictions that are in quantitative agreement with the available high-pressure limit experimental observations and qualitative agreement with those in the falloff regime. The theoretically predicted capture rate is reproduced to within 10% by the expression [1.71 x 10(-10)(T/298)(-2.58) exp(-608.6/RT) + 5.47 x 10(-11)(T/298)-1.78 exp(-97.3/RT); with R = 1.987 and T in K] cm3 molecule(-1) s(-1) over the 30-500 K range. A 300 K branching ratio of 0.67:0.02:0.02:0.29 was determined for formation of the four possible OH-isoprene adduct isomers 1, 2, 3, and 4, respectively, and was found to be relatively insensitive to temperature. An Arrhenius activation energy of -0.77 kcal/mol was determined for the high-pressure addition rate constants around 300 K.

A Two Transition State Model for Radical−Molecule Reactions: A Case Study of the Addition of OH to C2H4

A two transition state model is applied to the study of the addition of hydroxyl radical to ethylene. This reaction serves as a prototypical example of a radical-molecule reaction with a negative activation energy in the high-pressure limit. The model incorporates variational treatments of both inner and outer transition states. The outer transition state is treated with a recently derived long-range transition state theory approach focusing on the longest-ranged term in the potential. High-level quantum chemical estimates are incorporated in a variational transition state theory treatment of the inner transition state. Anharmonic effects in the inner transition state region are explored with direct phase space integration. A two-dimensional master equation is employed in treating the pressure dependence of the addition process. An accurate treatment of the two separate transition state regions at the energy and angular momentum resolved level is essential to the prediction of the temperature dependence of the addition rate. The transition from a dominant outer transition state to a dominant inner transition state is predicted to occur at about 130 K, with significant effects from both transition states over the 10 to 400 K temperature range. Modest adjustment in the ab initio predicted inner saddle point energy yields theoretical predictions which are in quantitative agreement with the available experimental observations. The theoretically predicted capture rate is reproduced to within 10% by the expression [4.93 x 10(-12) (T/298)(-2.488) exp(-107.9/RT) + 3.33 x 10(-12) (T/298)(0.451) exp(117.6/RT); with R = 1.987 and T in K] cm3 molecules(-1) s(-1) over the 10-600 K range.

Channel Specific Rate Constants Relevant to the Thermal Decomposition of Disilane

Rate constants for the thermal dissociation of Si2H6 are predicted with a novel transition state model. The saddle points for dissociation on the Si2H6 potential energy surface are lower in energy than the corresponding separated products, as confirmed by high level ab initio quantum mechanical calculations. Thus, the dissociations of Si2H6 to produce SiH2 + SiH4 (R1) and H3SiSiH + H2 (R2) both proceed through tight inner transition states followed by loose outer transition states. The present "dual" transition state model couples variational phase space theory treatments of the outer transition states with ab initio based fixed harmonic vibrator treatments of the inner transition states to obtain effective numbers of states for the two transition states acting in series. It is found that, at least near room temperature, such a dual transition state model is generally required for the proper description of each of the dissociations. Only at quite high temperatures, i.e., above 2000 K for (R1) and 600 K for (R2), does a single fixed inner transition state provide an adequate description. Similarly, only at quite low temperatures (below 100 and 10 K for (R1) and (R2), respectively) does a single outer transition state provide an adequate description. Pressure dependent rate constants are obtained from solutions to the multichannel master equation. These calculations confirm that dissociation channel (R2) is negligible under conditions relevant to the thermal chemical vapor deposition (CVD) processes. Rate constants for the chemical activation reactions, SiH2 + SiH4 --> Si2H6 (R-1) and SiH2 + SiH4 --> H3SiSiH + H2 (R3), are also evaluated within the dual transition state model. It is found that reaction R3 is the dominant channel for low pressures and high temperatures, i.e., below 100 Torr for temperatures above 1100 K.

Treatment of the K-quantum number in unimolecular reaction theory: insights from product correlations.

The connection between the K-quantum number and product correlations in the barrierless unimolecular dissociation of symmetric-top molecules is explored to establish a qualitative diagnostic for the treatment of the K-rotor dynamics in unimolecular reaction theory. We find that fragment scalar and vector correlations can provide guidance in this matter, and the photodissociation dynamics of thermal NCNO to form CN and NO at several dissociation wavelengths are presented to demonstrate the utility of this approach. The "goodness" of the K-quantum number can be related to the amount of energy in the conserved vibrational modes at the inner transition state. On the basis of measured correlated vibrational distributions, the K-quantum number is found to be approximately conserved at the inner transition state for the photodissociation of NCNO at 514, 520, and 526 nm. The methodology, involving a comparison of product distributions from the photodissociation of jet and thermal ensembles at identical wavelengths, is general and may be applied to previously studied systems that dissociate along barrierless potential energy surfaces, CF(3)NO and CH(2)CO. In addition, vector correlations serve as a means to probe the K-mixing at the outer transition state, and measured v-j correlations in the photodissociation of thermal NCNO are presented.

How a Transition State Tightens: The Singlet Photodissociation of Ketene as a Test Case

The tightening of the transition state as energy increases above the dissociation threshold is studied for the dissociation of singlet ketene. Rate constants and quantum yields have been determined for the photodissociation of ketene to produce CH2(ã1A1)(0,0,0) + CO(X̃ 1Σ+)(v=1). At 57, 110, 200, 357, and 490 cm-1 above this threshold, vibrational branching ratios for the singlet products were measured and compared to theory. Above 100 cm-1, the experimental values are consistent with the separate statistical ensembles (SSE) and variational RRKM models. CO(v=1,J) photofragment excitation (PHOFEX) spectra were observed up to 300 cm-1 over the threshold for production of CO(v=1) and used to calculate the total yield of the state probed. The J dependence of these yields is statistical, consistent with the observed 1CH2 rotational distributions. Thus, the total CO(v=1) singlet yield and rate constant are determined as a continuous function of energy up to 300 cm-1. Rate constants are given accurately by phase space theory (PST) up to 35 ± 5 cm-1. The ab initio rate constants of Klippenstein, East, and Allen match the experimental rate constants from 10 to 6000 cm-1 well within experimental uncertainty without any adjustment of parameters for the unified statistical model of Miller. Thus the rate appears to be controlled by an inner transition state near 3 Å and the outer PST transition state acting in series with the outer transition state dominating for energies below 50 cm-1 and the inner for energies above a few hundred cm-1. From the measured rate constants, an experimental density of states is calculated to be 0.94 times the anharmonic ab initio density of states. This allows the degeneracy gt of the coupled triplet channels to be determined from the rates at the triplet threshold, gt = 1.0 ± 0.1. The vibrational branching ratios and product yields for the vibrationally excited triplet products were also estimated and found to be nearly constant over this energy region. These values are about 17% of those predicted for vibrationally adiabatic dynamics in the exit valley after passage through the triplet transition state.