One-dimensional Master Equation Research Articles

Paving the way to the synthesis of PAHs in dark molecular clouds: The formation of cyclopentadienyl radical (c-C5H5)

Context. The interest of astrophysicists and astrochemists in studying polycyclic aromatic hydrocarbons (PAHs) has grown since their assignment to previously unidentified IR emission bands of dust grains. Although observations show that PAHs are present in the interstellar medium (ISM), there is still no consensus about their formation. PAH formation has been studied following two approaches: bottom-up (i.e. through the association of smaller hydrocarbons) and top-down (via the photo-dissociation or hydrogenation of larger-structures). The recent detection of simple aromatic rings in the TMC-1 molecular cloud seems to suggest the bottom-up scenario is favoured. Aims. We study the reaction between the propargyl (C3H3) radical and the vinyl radical (C2H3) under interstellar conditions, providing new kinetic parameters for the formation of PAH precursors. Methods. We used high-level quantum-chemical calculations to describe the reaction mechanism between these two radicals. We calculated the rate constant of the individual product channels in the temperature range 10–400 K and at 1 × 10−7 atm by solving the one-dimensional master equation to quantitatively understand whether this reaction is viable in the ISM. Results. Our results show that this reaction is likely to occur even in the low-density (~104 cm−3) and low-temperature (~10 K) conditions of molecular dark clouds. The main product is the cyclopentadienyl radical (C5H5). The unsaturated open-chain hydrocarbon C5H5 in the trans (trans-C5H5) and cis conformations (cis-C5H5) are also formed, but to a lesser extent. Conclusions. Our results show that the reaction of vinyl radical with propargyl radical is efficient under interstellar conditions and yields the cyclopentadienyl radical, which could be an important precursor for the formation of more complex polycyclic hydrocarbons (e.g. indene) and simple PAHs (e.g. naphthalene) in molecular dark clouds.

Investigation of Methylcyclopentadiene Reactivity: Abstraction Reactions and Methylcyclopentadienyl Radical Unimolecular Decomposition.

Understanding the reactivities of methylcyclopentadiene and the methylcyclopentadienyl radical is important in order to improve our comprehension of the chemical kinetics leading to the formation, decomposition, and growth of the first aromatic ring, as it has been shown that five-membered-ring species are important intermediates in the reaction kinetics of aromatic species. In this work, the rate constants of some key H-abstraction reactions from methylcyclopentadiene to produce the methylcyclopentadienyl radical and the formation of fulvene and benzene from the latter are theoretically determined. Rate constants are evaluated using the ab initio transition state theory-based master equation approach, determining structures and Hessians of all stationary points at the ωB97X-D/aug-cc-pVTZ level, energies at the CCSD(T) level extrapolated to the complete basis set limit, RRKM rate constants using conventional and variational transition state theory, and phenomenological rate constants through the solution of the one-dimensional master equation. Variational corrections are determined in both internal and Cartesian coordinates, and it is found that the choice of the coordinate system can impact the accuracy of the calculated rate constants by up to a factor of 4 for H-abstraction reactions and 2 for the unimolecular decomposition of the methylcyclopentadienyl radical. The calculated rate constants are in good agreement with the available literature data. Prompt dissociation of methylcyclopentadienyl radicals accessed following H-abstraction from methylcyclopentadiene was also investigated, and the corresponding rate constants were determined; the results show that prompt dissociation plays a key role under combustion conditions. Finally, lumping of theoretically derived rate constants to account for methylcyclopentadiene ⇄ methylcyclopentadienyl tautomerism allowed the derivation of a simplified set of rate constants suitable to be inserted into kinetic mechanisms.

Theoretical study on isomerization, decomposition and ring-closure reaction kinetics of methyl pentanoate radicals

A comprehensive study on the isomerization, decomposition and ring-closure reaction kinetics, as well as thermodynamic properties of methyl pentanoate radicals were carried out in this work. The M06–2X/cc-pVTZ level of theory was employed to optimize geometries and analyze frequencies for all the stationary points on the potential energy surfaces. The CCSD(T) method with two basis sets, cc-pVDZ and cc-pVTZ, was used to calculate single point energies, which were further extrapolated to the complete basis set (CBS) limit to construct the potential energy surfaces. The energy calculation results indicated that isomerization of δ-R to α-R, decomposition of γ-R to CH2C(=O)OCH3 and propene, and ring-closure reaction of δ-R to 1-methoxycyclopentanoxyl radical are the most energetically favored reactions among the studied isomerization, decomposition and ring-closure reaction channels, respectively. High pressure limit, and temperature and pressure dependent rate coefficients were determined by solving the one-dimensional energy-dependent master equations with Tsinghua University Minnesota Master Equation program (TUMME). The rate coefficients and branching ratios were found to be significantly affected by temperature and pressure. The decomposition reactions yielding small unsaturated esters or small ester radicals dominate at high temperatures, while the isomerization reactions proceeding via five- and six-membered ring saddle points, as well as the ring-closure reactions play more important roles at low temperatures. Significant discrepancies are observed between the theoretically calculated rate coefficients and estimated results. The thermochemical properties of methyl pentanoate radicals were calculated using isodesmic reaction method and atomization method together with the multistructural torsional anharmonicity partition functions. This study provides accurate kinetic and thermodynamic data on methyl pentanoate radicals, which are expected to advance our understanding of combustion chemistry of methyl pentanoate and larger methyl esters.

Thermal Decomposition of CH3O: A Curious Case of Pressure-Dependent Tunneling Effects.

The thermal unimolecular decomposition of a methoxy radical (CH3O), a key intermediate in the combustion of methane, methanol, and other hydrocarbons, was studied using high-level coupled-cluster calculations, followed by E,J-resolved master equation analyses. The experimental results available for a wide range of temperature and pressure are in striking agreement with the calculations. In line with a previous theoretical study that used a one-dimensional master equation, the tunneling correction is found to exhibit a marked pressure dependence, being the largest at low pressure. This curious effect on the tunneling enhancement also affects the calculated kinetic isotope effect, which falls initially with pressure but is predicted to rise again at high pressures. These findings serve to reconcile a set of conflicting results regarding the importance of tunneling in this prototype unimolecular reaction and also motivate further experimental investigation. This study also exemplifies how changes in the energy redistribution due to collisions manifest in the tunneling rates.

Hierarchical Study of the Reactions of Hydrogen Atoms with Alkenes: A Theoretical Study of the Reactions of Hydrogen Atoms with C2-C4 Alkenes.

The present study complements our previous studies of the reactions of hydrogen atoms with C5 alkene species including 1- and 2-pentene and the branched isomers (2-methyl-1-butene, 2-methyl-2-butene, and 3-methyl-1-butene), by studying the reactions of hydrogen atoms with C2–C4 alkenes (ethylene, propene, 1- and 2-butene, and isobutene). The aim of the current work is to develop a hierarchical set of rate constants for Ḣ atom addition reactions to C2–C5 alkenes, both linear and branched, which can be used in the development of chemical kinetic models. High-pressure limiting and pressure-dependent rate constants are calculated using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory and a one-dimensional master equation (ME). Rate constant recommendations for Ḣ atom addition and abstraction reactions in addition to alkyl radical decomposition reactions are also proposed and provide a useful tool for use in mechanisms of larger alkenes for which calculations do not exist. Additionally, validation of our theoretical results with single-pulse shock-tube pyrolysis experiments is carried out. An improvement in species mole fraction predictions for alkene pyrolysis is observed, showing the relevance of the present study.

Two-Dimensional Master Equation Modeling of Some Multichannel Unimolecular Reactions.

Multichannel thermal decomposition reactions of n-propyl radicals, 1-pentyl radicals, and toluene are investigated by solving a two-dimensional master equation formulated as a function of total energy (E) and angular momentum (J). The primary aim of this study is to elucidate the role of angular momentum in the kinetics of multichannel unimolecular reactions. The collisional transition processes of the reactants colliding with argon are characterized based on the classical trajectory calculations and implemented in the master equation. The rate constants calculated by using the two-dimensional master equation are compared with those of one-dimensional master equations. The consequence of the explicit treatment of angular momentum depends on the J dependence of the microscopic rate constants and is particularly emphasized in the thermal decomposition of toluene, for which the C-H and C-C bond fission channels are considered. The centrifugal effect is insignificant in the energetically favored C-H bond fission but is substantial in the energetically higher C-C bond fission, which causes rotational channel switching of the microscopic rate constants. The proper treatment of the J-dependent channel coupling effect, weak collisional transfer of J, and initial-J-dependent collisional energy transfer are found to be essential for predicting the branching fractions at low pressures.

The kinetics and dynamics of the multichannel multiwell reaction of CO(1Σ+) with OH(2Π): theoretical investigation

The kinetics and mechanism of the gas-phase reaction between carbon monoxide and hydroxyl radical have been theoretically investigated on the lowest potential energy surface. The dynamics of the reaction of CO(1Σ+) with OH(2Π) is studied by stochastic one-dimensional chemical master equation (CEM) simulation method. The role of the energized intermediates on the kinetics of the reaction was investigated by determination the fraction of different intermediates and products at the early stages of the reaction. The temperature dependence of the rate constants of the each individual channels of the reaction over a wide range of temperature (200–2000 K) was studied. The calculated rate constants from the CEM simulation were compared with those obtained from the RRKM–SSA [Rice–Ramsperger–Kassel–Marcus (RRKM) theory and Steady State Approximation (SSA)] method based on strong collision assumption. At lower temperatures, the calculated RRKM–SSA rate constant was found to be twice of the calculated by CEM, although the results are in good agreement with experimental values.

Theoretical, Experimental, and Modeling Study of the Reaction of Hydrogen Atoms with 1- and 2-Pentene.

Alkyl radicals are prominent in combustion chemistry as they are formed by hydrocarbon decomposition or from a radical attack on hydrocarbons. Accurate determinations of the thermochemistry and kinetics of their unimolecular isomerization and decomposition reactions and related addition reactions of alkenes are therefore important in simulating the combustion chemistry of virtually all hydrocarbon fuels. In this work, a comprehensive potential energy surface (PES) for Ḣ-atom addition to and abstraction from 1- and 2-pentene, and the subsequent C-C and C-H β-scission reactions, and H-atom transfer reactions has been considered. Thermochemical values for the species on the Ċ5H11 PES were calculated as a function of temperature (298-2000 K), with enthalpies of formation determined using a network of isodesmic reactions. High-pressure limiting and pressure-dependent rate constants were calculated using the Rice-Ramsperger-Kassel-Marcus theory coupled with a one-dimensional master equation. As a validation of our theoretical results, hydrogen atomic resonance absorption spectrometry experiments were performed on the Ḣ-atom addition and abstraction reactions of 1- and 2-pentene. By incorporating our calculations into a detailed chemical kinetic model (AramcoMech 3.0), excellent agreement with these experiments is observed. The theoretical results are further validated via a comprehensive series of simulations of literature data. Our a priori model is found to reproduce important absolute species concentrations and product ratios reported therein.

Theoretical Study on the Dynamics and Kinetics of the Reaction of CH2OH with OH.

The stochastic one-dimensional chemical master equation (CME) simulation method was used to investigate the dynamics of the reaction of CH2OH with OH. A multiwell multichannel potential energy surface (PES) was constructed at the CCSD(T)/Aug-cc-pVTZ//CBS-QB3 and QCISD(T)/Aug-cc-pVTZ//CBS-QB3 levels of theory. The constructed PES consisted of three chemically activated intermediates and two van der Waals complexes. The fractional population analysis unraveled the role of the energized intermediates and van der Waals complexes in the early stages of this complex reaction. The CME calculations provided the phenomenological rate constants through analysis of the eigenvalues and eigenvectors of collision matrices while Leonard-Jones potential was used to model the collisions. The CME results indicated that CH2O and H2O were the major products, in accordance with the literature. Also, the findings declared the temperature and pressure independence of the reaction over a wide range of temperature (250 to 2400 K) and pressure (0.1 to 7 atm). Furthermore, the efficiency of tunneling on the hydrogen transfer isomerization reaction of trans-HCOH to CH2O was confirmed over the temperature range of 250 to 3000 K. The rate constants for different reaction channels are reported.

A theoretical study on the dynamics of gas-phase reaction of methyl cation with atomic oxygen

The dynamics and kinetics of the reaction of CH3+ cation with atomic oxygen in its lowest triplet and singlet states in the presence of N2 molecules as the bath gas is theoretically investigated. The potential energies over both surfaces at the CCSD(T)/aug-cc-pVTZ level of theory are explored. Both singlet and triplet surfaces characterize by barrierless initiation step. The entrance channel to form the energized adducts are governed by the capture probability once the centrifugal barrier is surmounted. Multiwell-multichannel mechanisms are found for both singlet and triplet potential energy surfaces. One-dimensional chemical master equation is solved to explore the dynamics and kinetics of the title reaction. The fractional populations of the stationary points as function of time are analyzed to determine the role of the energized intermediates on the dynamics of the title reaction. No significant temperature or pressure dependence for the title reaction was observed over a wide range of temperature (300–3000 K) and pressure (0.1–4.5 atm). The results indicate cis and trans-HCOH+, CH2O+, and H atom are the major products for both surfaces. CVT method was used to explore the importance of tunneling in hydrogen transfer isomerization reactions of CH2O+ to trans-HCOH+ and HOC+ to HCO+ using small-curvature approximation.

Reaction Dynamics of O((3)P) + Propyne: II. Primary Products, Branching Ratios, and Role of Intersystem Crossing from Ab Initio Coupled Triplet/Singlet Potential Energy Surfaces and Statistical Calculations.

The mechanism of the O((3)P) + CH3CCH reaction was investigated using a combined experimental/theoretical approach. Experimentally the reaction dynamics was studied using crossed molecular beams (CMB) with mass-spectrometric detection and time-of-flight analysis at 9.2 kcal/mol collision energy. Theoretically master equation (ME) simulations were performed on a potential energy surface (PES) determined using high-level ab initio electronic structure calculations. In this paper (II) the theoretical results are described and compared with experiments, while in paper (I) are reported and discussed the results of the experimental study. The PES was investigated by determining structures and vibrational frequencies of wells and transition states at the CASPT2/aug-cc-pVTZ level using a minimal active space. Energies were then determined at the CASPT2 level increasing systematically the active space and at the CCSD(T) level extrapolating to the complete basis set limit. Two separate portions of the triplet PES were investigated, as O((3)P) can add either on the terminal or the central carbon of the unsaturated propyne bond. Minimum energy crossing points (MECPs) between the triplet and singlet PESs were searched at the CASPT2 level. The calculated spin-orbit coupling constants between the T1 and S0 electronic surfaces were ∼25 cm(-1) for both PESs. The portions of the singlet PES that can be accessed from the MECPs were investigated at the same level of theory. The system reactivity was predicted integrating stochastically the one-dimensional ME using Rice-Ramsperger-Kassel-Marcus theory to determine rate constants on the full T1/S0 PESs, accounting explicitly for intersystem crossing (ISC) using the Landau-Zener model. The computational results are compared both with the branching ratios (BRs) determined experimentally in the companion paper (I) and with those estimated in a recent kinetic study at 298 K. The ME results allow to interpret the main system reactivity: CH3CCO + H and CH3 + HCCO are the major channels active on the triplet PES and are formed from the wells accessed after O addition to the terminal and central C, respectively; (1)CH3CH + CO and C2H3 + HCO are the major channels active on the singlet PES and are formed from the methylketene and acrolein wells after ISC. However, also a large number of minor channels (∼15) are active, so that the system reactivity is quite complicated. The comparison between computational and experimental BRs is quite good for the kinetic study, while some discrepancy with the CMB estimations suggests that dynamic non-ergodic effects may influence the system reactivity. Channel specific rate constants are calculated in the 300-2250 K and 1-30 bar temperature and pressure ranges. It is found that as the temperature increases the H abstraction reaction, whose contribution is negligible in the experimental conditions, increases in relevance, and the extent of ISC decreases from ∼80% at 300 K to less than 2% at 2250 K.

A theoretical study on the dynamics of the gas phase reaction of NH2(2B1) with HO2(2A″)

Quasi-classical trajectory calculations and stochastic one-dimensional chemical master equation simulation methods are used to study the dynamics of the reaction of amidogen radical [NH2(2B1)] with hydroperoxyl radical [HO2(2A″)] on the lowest singlet electronic state. The title complex reaction takes place on a multi-well multichannel potential energy surface consisting of three deep potential wells and one van der Waals complex. In quasi-classical trajectory calculations a new analytical potential energy surface based on CCSD(T)/aug-cc-pVTZ//MPW1K/6-31+G(d,p) ab initio method was driven and used to study the dynamics of the title reaction. In quasi-classical trajectory calculations, the reactive cross sections and reaction probabilities are determined for 200–2000 K relative translational energies to calculate the rate constants. The same ab initio method was used to have the necessary data for solving the one-dimensional chemical master equation to calculate the rate constants of different channels. In solving the master equation, the Lennard-Jones potential model was used to form the collision between the collider gases. The fractional populations of different intermediates and products in the early stages of the reaction were examined to determine the role of the energized intermediates and the van der Waals complex on the dynamics of the title reaction. Although the calculated total rate constants from both methods are in good agreement with the reported experimental values in the literature, the quasi-classical trajectory simulation predicts the formation of NH2O + OH as the major channel in the title reaction in accordance with the previous studies (Sumathi and Peyerimhoff, Chem. Phys. Lett., 263:742–748, 1996), while the stochastic master equation simulation predicts the formation of HNO + H2O as the major products.

Theoretical Study on the Dynamics of the Reaction of HNO((1)A') with HO2((2)A″).

We used stochastic one-dimensional chemical master equation (CME) simulation to gain insight into the dynamics of the reaction of HNO((1)A') with HO2((2)A″). The reaction takes place over a multiwell, multichannel potential energy surface that is based on the computations at the CBS-QB3 level of theory. The calculated multipath potential energy surface consists of three potential wells and three van der Waals complexes. In solving the master equation, the Lennard-Jones potential is used to model the collision between the collider gases. The fractional population of different intermediates and products in the early stages of the reaction is examined to determine the role of the energized intermediates and van der Waals complexes on the kinetics of the title reaction. The major products of the title reaction at lower temperatures are OH, HNO2, HNOH, and O2(X(3)Σg(-)). The temperature- and pressure-dependence of the reaction over a wide range of temperature (300-3000 K) and pressure (0.1-2000 Torr) are studied. No sign of pressure dependence was being observed for the title reaction over the stated range of pressure. The calculated rate constants from the CME simulation are compared with those obtained from the RRKM-SSA method that is based on strong collision assumption. Our results indicate that the strong collision assumption increases the calculated rate constant for the formation of the main products (HNO2 + OH) by a factor of 2 at 300 K and 1 atm pressure, compared to the results of CME simulation, although the results are in good agreement at higher temperatures.

Charge-carrier relaxation in disordered organic semiconductors studied by dark injection: Experiment and modeling

Understanding of stationary charge transport in disordered organic semiconductors has matured during recent years. However, charge-carrier relaxation in nonstationary situations is still poorly understood. Such relaxation can be studied in dark injection experiments, in which the bias applied over an unilluminated organic semiconductor device is abruptly increased. The resulting transient current reveals both charge-carrier transport and relaxation characteristics. We performed such experiments on hole-only devices of a polyfluorene-based organic semiconductor. Modeling the dark injection by solving a one-dimensional master equation using the equilibrium carrier mobility leads to a too-slow current transient, since this approach does not account for carrier relaxation. Modeling by solving a three-dimensional time-dependent master equation does take into account all carrier transport and relaxation effects. With this modeling, the time scale of the current transient is found to be in agreement with experiment. With a disorder strength somewhat smaller than extracted from the temperature-dependent stationary current-voltage characteristics, also the shape of the experimental transients is well described.

Stochastic Dynamics for Passage Times and Diffusion Approximations for Finite Capacity Storage Models with Different Kinds of Barriers

In this article, we discuss a number of storage models of finite capacity with random inputs, random outputs, and linear release policy. They form a class of one-dimensional master equations with separable kernels. For this class of problems, the integral equations for first overflow or first emptiness can be transformed exactly into ordinary differential equations. Analysis is done with separable kernel. For all the stochastic models, two barriers are considered: one at X = 0 and the other at X = k, and the barriers are treated as absorbing or reflecting. The imbedding method is used to derive a third order differential equation. We consider first passage times for overflow without or with emptiness of the dam. We also study the passage times for first emptiness with and without overflows. The expected amount of overflows in a given time is also calculated. Finally, by suitable statistical features, all these models are converted into diffusion process with drift. Closed form solutions are obtained for all the problems in terms of Laplace transform functions. For the diffusion process with drift first passage time density is arrived at by treating X = 0 and X = k as absorbing barriers. One of the barriers as reflecting is also studied.

Feshbach projection-operator partitioning for quantum open systems: Stochastic approach

The dynamics of a state of interest coupled to a non-Markovian environment is studied by concatenating the non-Markovian quantum state diffusion equation and the Feshbach projection-operator partitioning technique. An exact one-dimensional stochastic master equation is derived as a general tool for controlling an arbitrary component of the system. We show that the exact one-dimensional stochastic master equation can be efficiently solved beyond the widely adapted second-order master equations. The generality and applicability of this hybrid approach is justified and exemplified by several coherence control problems concerning quantum state protection against leakage and decoherence.

Thermal rate constants of the pyrolysis of n-Heptane

Rate coefficients for straight chain alkane and free radical decomposition are important in combustion process. This work reports a theoretical study of the pyrolysis of n-Heptane. The barrier heights of the C−C fission reaction, β-scission reaction and H-atom abstraction reaction, as well as geometrical parameters of the reactants, products, and transition states involved in the decomposition of n-Heptane have been calculated at the CCSD(T)/6–311G( d,p)//B3LYP/6–311G( d,p) level. The temperature-dependent rate constants for individual reaction have been obtained in the temperature range of 200–3000 K using variational transition state theory and Rice–Ramsperger–Kassel–Marcus theory. The pressure dependence rate constants have been treated by one-dimensional master equation calculations at different pressure as well as high-pressure limit. In order to facilitate the use of the reaction rate constants for chemical kinetics modeling, all of the individual rate constants were fitted to a modified three-parameter Arrhenius expression: k( T) = AT n exp(− E b / RT) at various pressures. Some of the predicted rate constants are in reasonable agreement with the available experimental and previous theoretical results. The pyrolysis mechanism and RRKM-based rate constants presented in this paper may be used in high accuracy combustion modeling.

Chemically activated reactions on the C7H5 energy surface: propargyl + diacetylene, i-C5H3 + acetylene, and n-C5H3 + acetylene

This study uses computational chemistry and statistical reaction rate theory to investigate the chemically activated reaction of diacetylene (butadiyne, C(4)H(2)) with the propargyl radical (C˙H(2)CCH) and the reaction of acetylene (C(2)H(2)) with the i-C(5)H(3) (CH(2)CCCC˙H) and n-C(5)H(3) (CHCC˙HCCH) radicals. A detailed G3SX-level C(7)H(5) energy surface demonstrates that the C(3)H(3) + C(4)H(2) and C(5)H(3) + C(2)H(2) addition reactions proceed with moderate barriers, on the order of 10 to 15 kcal mol(-1), and form activated open-chain C(7)H(5) species that can isomerize to the fulvenallenyl radical with the highest barrier still significantly below the entrance channel energy. Higher-energy pathways are available leading to other C(7)H(5) isomers and to a number of C(7)H(4) species + H. Rate constants in the large multiple-well (15) multiple-channel (30) chemically activated system are obtained from a stochastic solution of the one-dimensional master equation, with RRKM theory for microcanonical rate constants. The dominant products of the C(4)H(2) + C(3)H(3) reaction at combustion-relevant temperatures and pressures are i-C(5)H(3) + C(2)H(2) and CH(2)CCHCCCCH + H, along with several quenched C(7)H(5) intermediate species below 1500 K. The major products in the n-C(5)H(3) + C(2)H(2) reaction are i-C(5)H(3) + C(2)H(2) and a number of C(7)H(4) species + H, with C(7)H(5) radical stabilization at lower temperatures. The i-C(5)H(3) + C(2)H(2) reaction predominantly leads to C(7)H(4) + H and to stabilized C(7)H(5) products. The title reactions may play an important role in polycyclic aromatic hydrocarbon (PAH) formation in combustion systems. The C(7)H(5) potential energy surface developed here also provides insight into several other important reacting gas-phase systems relevant to combustion and astrochemistry, including C(2)H + the C(3)H(4) isomers propyne and allene, benzyne + CH, benzene + C((3)P), and C(7)H(5) radical decomposition, for which some preliminary analysis is presented.

Collisional Energy Transfer in Unimolecular Reactions: Direct Classical Trajectories for CH4 ⇄ CH3 + H in Helium

Direct classical trajectories are used to compute energy transfer parameters appropriate for use in master equation calculations for the CH4 <--> CH3 + H reaction in He at 300-2000 K. The quantum chemistry method used in the direct trajectory calculations is MP2/aug'-cc-pVDZ, which is validated against higher level ab initio calculations. The average energy transferred in deactivating collisions is shown to increase with the initial rotational excitation J' of CH4 and with the temperature of the bath gas T(bath). When thermally averaged over J', the resulting average downward energy transfer alpha is found to increase nearly linearly with T(bath) (alpha = 110T(bath)0.81 cm(-1)). The results of master equation calculations carried out using the single-exponential-down model and the computed values of alpha are compared with experimental results and recent recommendations. At elevated temperatures (>600 K), good agreement between the predicted and experimental rate coefficients is obtained. At room temperature, the computed rate coefficients are in good agreement with the experimental results if the two-dimensional (E, J) formulation of the master equation is used. Smaller values of alpha (by 25%) are necessary to fit the experimental data at room temperature using the one-dimensional (E) master equation. The present study, combined with previous ab initio transition state theory calculations for the CH3 + H capture rate, provides a complete first-principles characterization of the temperature and pressure dependent rate coefficients for this simple single-well system.

Master Equation and Control of an Open Quantum System with Leakage

Given a multilevel system coupled to a bath, we use a Feshbach P, Q partitioning technique to derive an exact trace-nonpreserving master equation for a subspace S_{i} of the system. The resultant equation properly treats the leakage effect from S_{i} into the remainder of the system space. Focusing on a second-order approximation, we show that a one-dimensional master equation is sufficient to study problems of quantum state storage and is a good approximation, or exact, for several analytical models. It allows a natural definition of a leakage function and its control and provides a general approach to study and control decoherence and leakage. Numerical calculations on an harmonic oscillator coupled to a room temperature harmonic bath show that the leakage can be suppressed by the pulse control technique without requiring ideal pulses.