Quantum instanton evaluation of the thermal rate constants and kinetic isotope effects for SiH4+H-->SiH3+H2 reaction in full Cartesian space

The quantum instanton calculations of thermal rate constants for the gas-phase reaction SiH4+H-->SiH3+H2 and its deuterated analogs are presented, using an analytical potential energy surface. The quantum instanton approximation is manipulated by full dimensionality in Cartesian coordinate path integral Monte Carlo approach, thereby taking explicitly into account the effects of the whole rotation, the vibrotational coupling, and anharmonicity of the reaction system. The rates and kinetic isotope effects obtained for the temperature range of 200-1000 K show good agreements with available experimental data, which give support to the accuracy of the underlying potential surface used. In order to investigate the sole quantum effect to the rates, the authors also derive the classical limit of the quantum instanton and find that it can be exactly expressed as the classical variation transition state theory. Comparing the quantum quantities with their classical analogs in the quantum instanton formula, the authors demonstrate that the quantum correction of the prefactor is more important than that of the activation energy at the transition state.     

On the efficient path integral evaluation of thermal rate constants within the quantum instanton approximation

We present an efficient path integral approach for evaluating thermal rate constants within the quantum instanton (QI) approximation that was recently introduced to overcome the quantitative deficiencies of the earlier semiclassical instanton approach [Miller, Zhao, Ceotto, and Yang, J. Chem. Phys. 119, 1329 (2003)]. Since the QI rate constant is determined solely by properties of the (quantum) Boltzmann operator (specifically, by the zero time properties of the flux-flux and delta-delta correlation functions), it can be evaluated by well-established techniques of imaginary time path integrals even for quite complex chemical reactions. Here we present a series of statistical estimators for relevant quantities which can be evaluated straightforwardly with any nonlinear reaction coordinates and general Hamiltonians in Cartesian space. To facilitate the search for the optimal dividing surfaces required by the QI approximation, we introduce a two-dimensional quantum free energy surface associated with the delta-delta correlation function and describe how an adaptive umbrella sampling can be used effectively to construct such a free energy surface. The overall computational procedure is illustrated by the application to a hydrogen exchange reaction in gas phase, which shows excellent agreement of the QI rates with those obtained from quantum scattering calculations.     

Ab initio rate constants from hyperspherical quantum scattering: application to H + CH4 --> H2 + CH3

A general and practical procedure is described for calculating rate constants for chemical reactions using a minimal number of ab initio calculations and quantum-dynamical computations. The method exploits a smooth interpolating functional developed in the hyperspherical representation. This functional is built from two Morse functions and depends on a relatively small number of parameters with respect to conventional functionals developed to date. Thus only a small number of ab initio points needs to be computed. The method is applied to the H + CH4 --> H2 + CH3 reaction. The quantum scattering calculations are performed treating explicitly the bonds being broken and formed. All the degrees of freedom except the breaking and forming bonds are optimized ab initio and harmonic vibrational frequencies and zero-point energies for them are calculated at the MP2(full) level with a cc-pVTZ basis set. Single point energies are calculated at a higher level of theory with the same basis set, namely CCSD(T, full). We report state-to-state cross sections and thermal rate constants for the title reaction and make comparisons with previous results. The calculated rate constants are in good agreement with experiments.     

Accurate potential energy surface and quantum reaction rate calculations for the H+CH4-->H2+CH3 reaction

Calculations for the cumulative reaction probability N(E) (for J=0) and the thermal rate constant k(T) of the H+CH(4)-->H(2)+CH(3) reaction are presented. Accurate electronic structure calculations and a converged Shepard-interpolation approach are used to construct a potential energy surface which is specifically designed to allow the precise calculation of k(T) and N(E). Accurate quantum dynamics calculations employing flux correlation functions and multiconfigurational time-dependent Hartree wave packet propagation compute N(E) and k(T) based on this potential energy surface. The present work describes in detail the various convergence test performed to investigate the accuracy of the calculations at each step. These tests demonstrate the predictive power of the present calculations. In addition, approximate approaches for reaction rate calculations are discussed. A quite accurate approximation can be obtained from a potential energy surface which includes only interpolation points on the minimum energy path.     

Rate constants calculation of hydrogen abstraction reactions CH3CHBr + HBr and CH3CBr2 + HBr

Dual‐level direct dynamics method is used to study the kinetic properties of the hydrogen abstraction reactions of CH₃CHBr + HBr → CH₃CH₂Br + Br (R1) and CH₃CBr₂ + HBr → CH₃CHBr₂ + Br (R2). Optimized geometries and frequencies of all the stationary points and extra points along the minimum‐energy path are obtained at the MPW1K/6‐311+G(d,p), MPW1K/ma‐TZVP, and BMK/6‐311+G(d,p) levels. Two complexes with energies less than that of the reactants are located in the entrance of each reaction at the MPW1K/6‐311+G(d,p) and MPW1K/ma‐TZVP levels, respectively. The energy profiles are further refined with the interpolated single‐point energies method at the G2M(RCC5)//MPW1K/6‐311+G(d,p) level of theory. By the improved canonical variational transition‐state theory with the small‐curvature tunneling correction (SCT), the rate constants are evaluated over a wide temperature range of 200–2000 K. Our calculations have shown that the radical reactivity decreases from CH₃CHBr to CH₃CBr₂. Finally, the total rate constants are fitted by two modified Arrhenius expression. © 2012 Wiley Periodicals, Inc.     

H原子与CH3NH2抽氢反应的动力学计算

用QC ISD(T)/6-311 G(3DF,3PD)/MP2/6-311G(D,P)方法研究了H原子与CH3NH2的抽氢反应过程。该反应包含两个反应通道:H分别从CH3基团(R1)和NH2(R2)基团上抽氢。R1势垒比R2势垒低3.42kJ/mol,表明R1是主反应通道。在从头算的基础上,用变分过渡态理论(CVT)加小曲率隧道效应(SCT)研究了各反应温度范围为200~4000K内的速率常数,所得结果与实验值符合的很好。动力计算表明,在所研究的温度范围内,变分效应对速率常数的计算影响不大,而在低温范围内,隧道效应起了很重要的作用。     

Reflected shock tube studies of high-temperature rate constants for OH + CH4 --> CH3 + H2O and CH3 + NO2 --> CH3O + NO

The reflected shock tube technique with multipass absorption spectrometric detection of OH radicals at 308 nm has been used to study the reactions OH + CH(4) --> CH(3) + H(2)O and CH(3) + NO(2) --> CH(3)O + NO. Over the temperature range 840-2025 K, the rate constants for the first reaction can be represented by the Arrhenius expression k = (9.52 +/- 1.62) x 10(-11) exp[(-4134 +/- 222 K)/T] cm(3) molecule(-1) s(-1). Since this reaction is important in both combustion and atmospheric chemistry, there have been many prior investigations with a variety of techniques. The present results extend the temperature range by 500 K and have been combined with the most accurate earlier studies to derive an evaluation over the extended temperature range 195-2025 K. A three-parameter expression describes the rate behavior over this temperature range, k = (1.66 x 10(-18))T(2.182) exp[(-1231 K)/T] cm(3) molecule(-1) s(-1). Previous theoretical studies are discussed, and the present evaluation is compared to earlier theoretical estimates. Since CH(3) radicals are a product of the reaction and could cause secondary perturbations in rate constant determinations, the second reaction was studied by OH radical production from the fast reactions CH(3)O --> CH(2)O + H and H + NO(2) --> OH + NO. The measured rate constant is 2.26 x 10(-11) cm(3) molecule(-1) s(-1) and is not dependent on temperature from 233 to 1700 K within experimental error.     

Kinetics of the hydrogen abstraction *CH3 + alkane --> CH4 + alkyl reaction class: an application of the reaction class transition state theory

Kinetics of the hydrogen abstraction reaction (*)CH(3) + CH(4) --> CH(4) + (*)CH(3) is studied by a direct dynamics method. Thermal rate constants in the temperature range of 300-2500 K are evaluated by the canonical variational transition state theory (CVT) incorporating corrections from tunneling using the multidimensional semiclassical small-curvature tunneling (SCT) method and from the hindered rotations. These results are used in conjunction with the Reaction Class Transition State Theory/Linear Energy Relationship (RC-TST/LER) to predict thermal rate constants of any reaction in the hydrogen abstraction class of (*)CH(3) + alkanes. Our analyses indicate that less than 40% systematic errors on the average exist in the predicted rate constants using the RC-TST/LER method while comparing to explicit rate calculations the differences are less than 100% or a factor of 2 on the average.     

Direct dynamics study on the hydrogen abstraction reaction CH2O + HO2 --> CHO + H2O2

We present a direct ab initio dynamics study on the hydrogen abstraction reaction CH2O + HO2 --> CHO + H2O2, which is predicted to have four possible reaction channels caused by different attacking orientations of HO2 radical to CH2O. The structures and frequencies at the stationary points and the points along the minimum energy paths (MEPs) of the four reaction channels are calculated at the B3LYP/cc-pVTZ level of theory. Energetic information of stationary points and the points along the MEPs is further refined by means of some single-point multilevel energy calculations (HL). The rate constants of these channels are calculated using the improved canonical variational transition-state theory with the small-curvature tunneling correction (ICVT/SCT) method. The calculated results show that, in the whole temperature range, the more favorable reaction channels are Channels 1 and 3. The total ICVT/SCT rate constants of the four channels at the HL//B3LYP/cc-pVTZ level of theory are in good agreement with the available experiment data over the measured temperature ranges, and the corresponding three-parameter expression is k(ICVT/SCT) = 3.13 x 10(-20) T(2.70) exp(-11.52/RT) cm3 mole(-1) s(-1) in the temperature range of 250-3000 K. Additionally, the flexibility of the dihedral angle of H2O2 is also discussed to explain the different experimental values.     

Test of the quantum instanton approximation for thermal rate constants for some collinear reactions

Two variants of the recently developed quantum instanton (QI) model for calculating thermal rate constants of chemical reactions are applied to several collinear atom-diatom reactions with various skew angles. The results show that the original QI version of the model is consistently more accurate than the "simplest" quantum instanton version (both being applied here with one "dividing surface") and thus to be preferred. Also, for these examples (as with other earlier applications) the QI results agree well with the correct quantum rates (to within approximately 20% or better) for all temperatures >200 K, except for situations where dynamical corrections to transition state theory (i.e., "re-crossing" dynamics) are evident. (Since re-crossing effects are substantially reduced in higher dimensionality, this is not a cause for serious concern.) A procedure is also described which facilitates use of the METROPOLIS algorithm for evaluating all quantities that appear in the QI rate expression by Monte Carlo path integral methods.     

High-temperature rate constants for CH3OH + Kr --> products, OH + CH3OH --> products, OH + (CH3)(2)CO --> CH2COCH3 + H2O, and OH + CH3 --> CH) + H2O

The reflected shock tube technique with multipass absorption spectrometric detection of OH radicals at 308 nm (corresponding to a total path length of approximately 4.9 m) has been used to study the dissociation of methanol between 1591 and 2865 K. Rate constants for two product channels [CH3OH + Kr --> CH3 + OH + Kr (1) and CH3OH + Kr --> 1CH2 + H2O + Kr (2)] were determined. During the course of the study, it was necessary to determine several other rate constants that contributed to the profile fits. These include OH + CH3OH --> products, OH + (CH3)2CO --> CH2COCH3 + H2O, and OH + CH3 --> 1,3CH2 + H2O. The derived expressions, in units of cm(3) molecule(-1) s(-1), are k(1) = 9.33 x 10(-9) exp(-30857 K/T) for 1591-2287 K, k(2) = 3.27 x 10(-10) exp(-25946 K/T) for 1734-2287 K, kOH+CH3OH = 2.96 x 10-16T1.4434 exp(-57 K/T) for 210-1710 K, k(OH+(CH3)(2)CO) = (7.3 +/- 0.7) x 10(-12) for 1178-1299 K and k(OH+CH3) = (1.3 +/- 0.2) x 10(-11) for 1000-1200 K. With these values along with other well-established rate constants, a mechanism was used to obtain profile fits that agreed with experiment to within <+/-10%. The values obtained for reactions 1 and 2 are compared with earlier determinations and also with new theoretical calculations that are presented in the preceding article in this issue. These new calculations are in good agreement with the present data for both (1) and (2) and also for OH + CH3 --> products.     

Direct dynamic study on the hydrogen abstraction reaction CH3CN + OH-->CH2CN + H2O

The reaction of acetonitrile with hydroxyl has been studied using the direct ab initio dynamics methods. The geometries, vibrational frequencies of the stationary points, as well as the minimum energy paths were computed at the BHandHLYP and MP2 levels of theory with the 6-311G(d, p) basis set. The energies were further refined at the PMP4/6-311+G(2df, 2pd) and QCISD(T)/6-311+G(2df, 2pd) levels of theory based on the structures optimized at BHandHLYP/6-311G(d, p) and MP2/6-311G(d, p) levels of theory. The Polyrate 8.2 program was employed to predict the thermal rate constants using the canonical variational transition state theory incorporating a small-curvature tunneling correction. The computed rate constants are in good agreement with the available experimental data.     

Including anharmonicity in the calculation of rate constants. II. The OH+H2-->H2O+H reaction

A recently developed method for calculating anharmonic vibrational energy levels at nonstationary points along a reaction path that is based on second-order perturbation theory in curvilinear coordinates is combined with variational transition state theory with semiclassical multidimensional tunneling approximations to calculate thermal rate constants for the title reaction. Two different potential energy surfaces were employed for these calculations, an improved version of the author's surface 5 and the WSLFH surface of Wu et al. [J. Chem. Phys. 113, 3150 (2000)]. We present detailed comparisons of rate constants computed for the two surfaces with and without anharmonicity and with various approximations for incorporating tunneling along the reaction path. The results for this system are quite sensitive to the surface employed, the choice of coordinates (curvilinear versus rectilinear), and the inclusion of anharmonicity. A comparison with experiment provides information on the accuracy of these surfaces.     

Ab initio rate constants from hyperspherical quantum scattering: application to H+C2H6 and H+CH3OH

The dynamics and kinetics of the abstraction reactions of H atoms with ethane and methanol have been studied using a quantum mechanical procedure. Bonds being broken and formed are treated with explicit hyperspherical quantum dynamics. The ab initio potential energy surfaces for these reactions have been developed from a minimal number of grid points (average of 48 points) and are given by analytical functionals. All the degrees of freedom except the breaking and forming bonds are optimized using the second order perturbation theory method with a correlation consistent polarized valence triple zeta basis set. Single point energies are calculated on the optimized geometries with the coupled cluster theory and the same basis set. The reaction of H with C2H6 is endothermic by 1.5 kcal/mol and has a vibrationally adiabatic barrier of 12 kcal/mol. The reaction of H with CH3OH presents two reactive channels: the methoxy and the hydroxymethyl channels. The former is endothermic by 0.24 kcal/mol and has a vibrationally adiabatic barrier of 13.29 kcal/mol, the latter reaction is exothermic by 7.87 kcal/mol and has a vibrationally adiabatic barrier of 8.56 kcal/mol. We report state-to-state and state-selected cross sections together with state-to-state rate constants for the title reactions. Thermal rate constants for these reactions exhibit large quantum tunneling effects when compared to conventional transition state theory results. For H+CH3OH, it is found that the CH2OH product is the dominant channel, and that the CH3O channel contributes just 2% at 500 K. For both reactions, rate constants are in good agreement with some measurements.     

Theoretical study of the complex-forming CH + H2 --> CH2 + H reaction

The complex-forming CH + H2 --> CH2 + H reaction is studied employing a recently developed global potential energy function. The reaction probability in the total angular momentum J = 0 limit is estimated with a four-atom quantum wave packet method and compared with classical trajectory and statistical theory results. The formation of complexes from different reactant internal states is also determined with wave packet calculations. While there is no barrier to reaction along the minimum energy path, we find that there are angular constraints to complex formation. Trajectory-based estimates of the low-pressure rate constants are made and compared with experimental results. We find that zero-point energy violation in the trajectories is a particularly severe problem for this reaction.     

A coupled states calculation of accurate quantum rate constants for H + H2

In this article we present the results of converged quantum reactivescattering calculations of thermal rate constants for H + H₂ using the Liu-Siegbahn-Truhlar-Horowitz (LSTH) potential energy surface. These calculations are based on the coupled states (CS) approximation wherein rotational states having different body fixed angular momentum projection quantum numbers are decoupled. By comparision with accurate coupled channel results on the Porter-Karplus No. 2 (PK2) potential surface, we estimate that the maximumerror in thermal rate constants arising from both this approximation and from other numerical approximations in the calculation is less than 25%. We also show that the sum over projection quantum numbers Ω associated with the CS calculation may be approximated quite accurately in terms of the Ω = 0 rate constants by assuming that the |Ω| > 0 rate constants differ from Ω = 0 by a shift in activation energy, which reflects the vibrationally adiabatic bending energy associated with each Ω. Comparison of the LSTH rate constants with experiment indicates average errors of 16% and 24% relative to the two modern measurementsof the rate constants for H + H₂. These errors are reduced to 18% and 9% if the CS rate constants are multiplied by exp(0.0065 eV/kT). The expected error (based on recent quantum structure calculations) associated with the 0.425 eV barrier of theLSTH potential surface is 0.0065 eV. Overall, the agreement of either the LSTH or modified LSTH rate constants with experiment is within the 32% maximum disagreement between the two experimental measurements at all butthe lowest temperature that has been studied. Comparison of our CS rate constants with the results from simpler theories is considered using both the LSTH and PK2 potential surfaces. The best overall agreement is with transition state theories that use accurate dynamical methods to calculate tunnelling factors. These include reduced dimensionality quantum dynamics methods and variational transition state theory using either the Marcus-Coltrin or least action ground-state tunnelling paths. Comparison with the results of quasiclassical trajectory calculations indicates substantial errors at low temperatures.     

Computational study on the reaction CH2CH2 + F --> CH2CHF + H

Previous ab initio studies on reactions involving radical addition to alkenes showed that such reactions are very sensitive to theoretical levels, and thus are difficult to deal with. This motivates us to theoretically reexamine the title reaction thoroughly, which has been studied only at several low levels of theory. In the present work, the geometry optimizations and energy calculations for all species involved in the title reaction were performed at several high levels of theory. The reaction mechanism of the title reaction is discussed at the CCSD(T)/aug-cc-pVDZ//CCSD/6-31G(d,p) theoretical level. According to our study, the fluorine addition to ethylene occurs via the formation of a prereaction complex with C2v symmetry, which is pointed out for the first time. The prereaction complex evolves into a fluoroethyl radical almost without a barrier, with an exothermicity of 41.49 kcal/mol. The fluoroethyl radical can further decompose into a hydrogen atom and fluoroethylene, with an energy release of 10.33 kcal/mol. Besides the direct departure of the hydrogen atom from the fluoroethyl radical, an indirect decomposition pathway may also be open, which has not been reported before. In addition, the formation of a fluoroethyl radical from a separate fluorine atom and ethylene is described pictorially via the molecular intrinsic characteristic contour (MICC) and the electron density mapped on it. Thereby, strong interpolarization and evident electron transfer between the fluorine atom and ethylene are observed as they approach each other. The transition structure for the fluorine addition to ethylene is clearly shown to be reactant-like. This provides new and intuitional insight into the title reaction.     

Dependence of the rate constants on the treatment of internal rotation modes: the reaction OH + CH3SH --> CH3S + H2O as an example

The title reaction has been used as an example to test the importance of using a hindered rotor treatment instead of a harmonic oscillator model for calculating vibrational partition functions corresponding to low-frequency internal rotation modes. First, a normal-mode analysis according to the Ayala and Schlegel's algorithm has been used to identify the internal rotation modes of methanethiol and the transition state structure. Then, after calculation of the energy barrier for each internal rotation, the corresponding hindered rotor partition functions have been calculated following the CW scheme of Chuang and Truhlar. The results show that the anharmonic treatment produces a rather modest improvement of the rate constants at room temperature or below.     

Low temperature quantum rate coefficient of the H + CH+ reaction

In this paper we report the first theoretical study of the title reaction. A global, single-valued model of the ground-state potential energy surface has been obtained by fitting to an extensive set of high-level ab initio calculations. The surface is found to be attractive apart from linear geometries where energy barriers appear due to conical intersections. This model was then used to calculate the reactive reactant state selected cross sections for collision energies ranging from threshold up to 4000 cm(-1). These calculations were performed using our version of the Baer's approach of the RIOSA-NIP method which is based on the use of a negative imaginary potential. We find that the reaction probability is extremely oscillatory as a function of kinetic energy as it is a case for insertion reactions with a low exoergicity. The resulting reaction rate coefficient is found to first increase slowly as a function of temperature up to a broad maximum around 20 K and then to decrease slowly when temperature keeps increasing.     

Crossed beams study of the reaction 1CH2+C2H2-->C3H3+H

The reaction of electronically excited singlet methylene (1CH2) with acetylene (C2H2) was studied using the method of crossed molecular beams at a mean collision energy of 3.0 kcal/mol. The angular and velocity distributions of the propargyl radical (C3H3) products were measured using single photon ionization (9.6 eV) at the advanced light source. The measured distributions indicate that the mechanism involves formation of a long-lived C3H4 complex followed by simple C-H bond fission producing C3H3+H. This work, which is the first crossed beams study of a reaction involving an electronically excited polyatomic molecule, demonstrates the feasibility of crossed molecular beam studies of reactions involving 1CH2.