Accurate Rate Coefficients Research Articles

High-pressure methane oxidation behind reflected shock waves

Experiments on CH 4 oxidation behind reflected shock waves were conducted at elevated pressures, and the results compared to a detailed kinetics model. Mixtures of CH 4 and O 2 dilute in either argon or nitrogen were studied over a wide range of stoichiometry (=0.5–4.0), bath gas dilution (90.0–99.5%), pressure (9–480 atm), and temperature (1410–2040 K), corresponding to total concentrations from 5.6×10 −5 to 3.6×10 −3 mol/cm 3 . Reaction progress was monitored using narrow-line laser absorption of OH at 306 nm, infrared emission of CH 4 near 3.4 μm, and pressure measurements. The measured species time-histories and pressure traces were assembled into an extensive database of characteristic reaction times, peak OH mole fractions, and ignition delay times that can be used for comparisons with detailed kinetics mechanisms. The chemical kinetics model utilized in the present comparisons is the latest GRI mechanism, GRI-Mech 1.2. As a whole, agreement between the model predictions and the experimental measurements is good, particularly for ignition delay times. However, based on the results of certain CH 4 profiles, improvements in the model for high-pressure, fuel-rich conditions are needed. Sensitivity and species contribution analyses were used to identify the most important reactions at pressures up to 500 atm, some of which require more accurate rate coefficients. As pressure increases, the CH 3 removal pathways are altered, the CH 3 formation pathways remain the same, and reactions involving HO 2 become important.

Conditions for the Determination of Precise and Accurate Free-Radical Propagation Rate Coefficients from Pulsed-Laser-Made Polymer

A revision of the long known mathematical representation of the chain length distribution of polymer resulting from pulsed-laser-initiated free-radical polymerization of Aleksandrov, Genkin, Kitai, Smirnova, and Sokolov revealed that it vividly reflects some very essential characteristics of the underlying kinetics, which have so far been largely overlooked. In particular, with respect to an experimental determination of the propagation rate coefficient k p , it was found that this representation suggests the measurement of the chain lengths at maxima or at low molecular weight side inflection points of pulsed initiation originating structures within chain length distributions of pulsed-laser-made polymer, depending on whether sufficiently high or low concentrations of radicals are being produced per initiating laser pulse, respectively. This suggestion was verified for pulsed laser polymerizations of styrene and methyl methacrylate, at which values of k p (styrene) = 92 L mol -1 s -1 and k p (methyl methacrylate) = 359 L mol -1 s -1 were obtained for a temperature of 25 °C.

Calculations of interstellar radiative association rates including tunnelling: the strange case of C2H + 2 + H2

Both the radiative association reaction and the ion–molecule reaction between the reactants C2H+2 and H2 occur appreciably at temperatures under 100 K and must be included in models of interstellar and circumstellar chemistry. In this paper, we consider the mechanism of the association reaction to form C2H+4. Ab initio quantum chemical calculations have been undertaken to determine the pathway of minimum potential energy. This pathway is distinct from another pathway we have calculated for the ion–molecule reaction, which forms C2H+3+ H. For the association channel, our ab initio calculations show that there is a small entrance channel barrier under which low-temperature reactants must tunnel to access the deep potential well associated with C2H+4. Other than redissociation into reactants, the C2H+4 reaction complex can dissociate only to the classical (higher energy) form of C2H+3+ H; this channel is endothermic and does not occur at low temperatures, enhancing the prospect that the C2H+4 complex can be stabilized by collision with a third body or via emission of a photon. Phase space calculations extended to include tunnelling for both the formation and redissociation of the C2H+4 complex do not reproduce low-temperature experimental measurements of the rate of the association channel. Rather, a phase space calculation in which it is assumed that the entrance channel barrier does not exist is in agreement with most of the experimental data. It is likely, however, that a small barrier does exist. Accurate radiative association rate coefficients, largely unaffected by the existence of such a small barrier, are tabulated in the temperature range 2–80 K.

Calculation of thermal rate coefficients from the quantum flux autocorrelation function: Converged results and variational quantum transition state theory for O+HD↔OD+H and O+HD↔OH+D

The thermal rate coefficients for the title reactions with zero total angular momentum are calculated by an ℒ 2 basis-set evaluation of the flux autocorrelation function. We use three dividing surfaces, each one separating one arrangement from the other two. The rate coefficients for O+HD↔OD+H or OH+D are converged to within 1.2% over the temperature range 300–1000 K and to within 2.4% at 200 K. The rate coefficients for the reactions H+OD↔D+OH are converged to within 22% at 1000 K and upper bounds to these rate coefficients are given for the temperature range 200–800 K. Flux autocorrelation functions and rate coefficients are calculated for different positions of the dividing surface to show that the computed rate coefficient is stable with respect to varying this position. Rate coefficients are also calculated by a variational version of quantum mechanical transition state theory and the results are compared to the accurate rate coefficients obtained from flux autocorrelation function theory.

Microscopic rate coefficients in reactions with flexible transition states: Analysis of the transitional-mode sum of states

Expressions are derived for the energy- and angular-momentum-resolved transitional-mode sum of states, WTM(E,J), for flexible transition states in unimolecular, recombination, or bimolecular collision–complex-forming reactions. The expressions are derived classically by evaluation of the phase-space volume integral. The phase-space integral is so arranged that the total available momentum-space volume, Φ(E,J,q), for a frozen configuration q is first evaluated. Accurate analytic expressions for Φ(E,J,q) are obtained for all relevant pairwise combinations of atom, linear, spherical-top, symmetric-top, and asymmetric-top fragments in flexible transition states. The analytic expressions for Φ(E,J,q) indicate clearly the conditions under which the common method of imposing angular momentum conservation, which assumes that J≊L (L being the orbital angular momentum), will fail. WTM(E,J) is then obtained by integration of Φ(E,J,q) over configuration space. Exact evaluation of the integral over configuration space involves at most a five-dimensional numerical integral. Accurate analytical expressions for WTM(E,J) are derived for model potentials which admit sufficient flexibility for the fitting of more-accurate potentials. These expressions enable the calculation of accurate microscopic rate coefficients k(E,J) by microcanonical variational Rice–Ramsperger–Kassel–Marcus (RRKM) theory at little more computational expense than a standard RRKM calculation.

General classical variational treatment of the rates of bimolecular exchange and unimolecular reactions involving three bodies

The classical variational theory of chemical reaction rates gives the rate as the equilibrium flux of systems through a trial surface in the phase space of the reaction system. The surface divides the phase space into reactant and product regions and is varied to obtain a least upper bound for the rate of product formation. For bimolecular reactions of the type A+BC→AB+C and the high pressure limit of unimolecular reactions of the type ABC→products, we have derived expressions which give the canonical and microcanonical rate coefficients for the most general dividing surface defined by internal configuration space coordinates. For bimolecular reactions, we have also derived an expression for the energy dependent mean reaction cross section for the most general dividing surface. Expressions for the rate coefficients and mean reaction cross section for any of the more restricted formulations of the dividing surface used in earlier work, and more flexible ones, can be obtained by the substitution of two terms in the appropriate general equation; namely, the partial derivatives of the function that defines the surface with respect to the internal coordinates that define the surface. For example, the flexibility of the surface can be improved systematically by introducing terms in a power series expansion of the surface. The application of a simplex algorithm to determine the coefficients (variational parameters) in an expansion of the surface that includes terms up to the second and third order may give a surface which is close to the best one possible. The minimization procedure corresponds to a search of the potential-energy function for a reaction coordinate that satisfies the variational condition. The variationally determined dividing surface identifies regions of configuration space in which the potential energy must be accurate in order to obtain accurate classical rate coefficients. Thecalculus of variations was applied to the general equations for the rate coefficients to obtain differential equations which give the best dividing surface defined by internal coordinates for the canonical and microcanonical formulations of transition state theory. The corresponding rate coefficients or mean reaction cross section are as close as possible to convergence with the results of classical trajectory calculations. The flux can thus be minimized completely by obtaining a numerical solution for the differential equations which define the best surface or nearly minimized for a series approximation to the best surface. Computational studies are required to determine the more tractable method. By using an appropriate generating function, the procedure described in this work can be extended to reactions involving more than three bodies. The variationally determined dividing surface, reaction coordinate, and reaction surface Hamiltonian could provide a basis for a semiclassical theory of reaction rates.

Recombination of Neon-Like and Adjacent Ions in Plasmas

The neon-like and sodium-like ions of medium Z elements, chromium and nickel are identified as abundant or strongly radiating species in the transport dominated region of the JET plasma. Also in plasma produced by laser ablation of multilayer targets stimulated emission has been identified from neon-like selenium. For both observations accurate theoretical electronic recombination rate coefficients contribute to spectral interpretation, to unambiguous separation of diffusive and atomic processes in impurity transport and to derivation of metal concentrations from VUV lines.A new calculation is presented of recombination of fluorine-like, neon-like and sodium-like ions of chromium, iron, nickel and selenium. Radiative recombination and dielectronic recombination rates to angularly resolved energy levels of both low and high principal quantum number are determined using combination of multiconfiguration perturbation theory and Correspondence Principle techniques. The modifying effects of collisional redistribution in finite density plasma are evaluated and effective net recombination coefficients and effective recombination coefficients to excited levels leading to radiative emission obtained.The theoretical radial distribution of nickel ions across the JET torus is obtained by combining the recombination results with a transport model.

Test of variational transition state theory with a large-curvature tunneling approximation against accurate quantal reaction probabilities and rate coefficients for three collinear reactions with large reaction-path curvature: Cl+HCl, Cl+DCl, and Cl+MuCl

The large-curvature ground-state model for the transmission coefficient of generalized transition state theory [presented in a previous paper by B. C. Garrett, D. G. Truhlar, A. F. Wagner, and T. H. Dunning, J. Chem. Phys. 78, 4400(1983)] is tested against accurate quantal calculations of the rate coefficients for collinear reactions with very large inertial effects, namely Cl+HCl→ClH+Cl, Cl+DCl→ClD+Cl, and Cl+MuCl→ClMu+Cl. The tests cover the temperature range 200–2400 K. The accurate rate calculations are based on reaction probabilities obtained by a new numerical method for solving Schrödinger’s equation in Delves’ coordinates. Improved canonical variational transition state theory predicts rate coefficients 5.0–18 times smaller than those predicted by conventional transition state theory for the H transfer; for the D transfer, the ratio is 2.0–3.4; and for Mu it is 22–2.8×107. The large-curvature model predicts transmission coefficients as large as 41, 8, and 206 for the H, D, and Mu-transfer cases at 200 K, decreasing to 1.2, 1.1, and 1.4 at 2400 K. Despite the large effect of variationally optimizing the transition state location and the large size of the tunneling effect and the wide variation of both effects with temperature, improved canonical variational transition state theory with large-curvature ground-state transmission coefficients (ICVT/LCG) is accurate within a factor of 1.7 over a temperature range of a factor of 8, 300–2400 K, for all three reactions. At 200 K, the ICVT/LCG model underestimates the rate coefficients, by factors of 2.3, 1.9, and 1.5 for H, D, and Mu, respectively.

Kinetic isotope effects in the Mu+H2 and Mu+D2 reactions: Accurate quantum calculations for the collinear reactions and variational transition state theory predictions for one and three dimensions

We consider three reactions: H+H2→H2+H; Mu+H2→MuH+H; Mu+D2 →MuD+D. We calculate accurate quantum mechanical reaction probabilities and thermal rate coefficients for all three reactions in collinear geometry using the Liu–Siegbahn–Truhlar–Horowitz (LSTH) accurate potential energy surface. These rate coefficients are used to test conventional transition state theory and the improved canonical variational theory with Marcus–Coltrin-path semiclassical adiabatic ground-state transmission coefficients (ICVT/MCPSAG). The ICVT/MCPSAG theory is found to be greatly superior and reasonably reliable. These conclusions are tested for sensitivity to variations in the potential energy surface by repeating the calculations for the less accurate Porter–Karplus surface. The conclusions are unaltered by this. The ICVT/MCPSAG theory and LSTH surface are then employed to predict the rate coefficients for all three reactions in three dimensions.

Rate of radiative recombination for some atoms and ions of the upper atmosphere

Accurate rate coefficients for the radiative recombination of a number of positive ions of the upper atmosphere are computed by the detailed balance method in the temperature range 200–4000 K. Simple expressions are also presented for their quick estimation.

Resonances in 1s-2s and 1s-2p collision strengths for electron impact excitation of hydrogenic ions

Accurate rate coefficients for the electron impact excitation of positive ions are required for the interpretation of the spectra of hot plasmas. In making calculations, account should be taken of resonances in collision strengths at energies which contribute to the rate coefficients. For 1s-2s and 1s-2p excitation of hydrogenic ions it is shown that (3l3l') resonances occur at energies close to the excitation thresholds. The effect of resonances of the type (3ln'l') with n'>or=3 is to increase rate coefficients by about 20% for 1s-2s and 10% for 1s-2p.

ChemInform Abstract: HYDROGEN ABSTRACTION BY FLUORINE ATOMS UNDER CONDITIONS OF THERMAL INITIATION, HYDROCARBONS AND FLUORINATED HYDROCARBONS

Modified nuclear recoil techniques have been used to obtain accurate relative bimolecular rate coefficients for thermally induced hydrogen abstraction reactions by atomic fluorine. New results are reported for 12 hydrocarbons and partially fluorinated hydrocarbons studied at 303°K.

Hydrogen abstraction by fluorine atoms under conditions of thermal initiation: Hydrocarbons and fluorinated hydrocarbons

AbstractModified nuclear recoil techniques have been used to obtain accurate relative bimolecular rate coefficients for thermally induced hydrogen abstraction reactions by atomic fluorine. New results are reported for 12 hydrocarbons and partially fluorinated hydrocarbons studied at 303°K.

Oxygen recombination in the tropical nightglow

In order to explain O I lines in the tropical nightglow, complete and reasonably accurate recombination and emission rate coefficients are used to construct a detailed radiative cascade model of a recombining oxygen plasma. Effective recombination coefficients are given for all low quantum number O I levels for the two limiting cases of zero and infinite optical depth of the resonance lines. The direct recombination coefficients for the S levels, and to a lesser extent the P levels, are significantly smaller than those previously quoted in the literature. The quantitative evaluation of radiative cascading in the optically thin limit predicts an order of magnitude lower intensity for the 1304-Å line than that predicted by a recently published optically thin model using an estimate of the cascade contributions to the intensity. However, the optically thick model, which is more realistic for the F2 region than the thin model, predicts a 1304-Å intensity in good agreement with observations of the 1304-Å line.