RRKM Rate Research Articles

The Vinyl + NO Reaction: Determining the Products with Time-Resolved Fourier Transform Spectroscopy

We have studied the vinyl + NO reaction using time-resolved Fourier transform emission spectroscopy, complemented by electronic structure and microcanonical RRKM rate coefficient calculations. To unambiguously determine the reaction products, three precursors are used to produce the vinyl radical by laser photolysis: vinyl bromide, methyl vinyl ketone, and vinyl iodide. The emission spectra and theoretical calculations indicate that HCN + CH2O is the only significant product channel for the C2H3 + NO reaction near room temperature, in contradiction to several reports in the literature. Although CO emission is observed when vinyl bromide is used as the precursor, it arises from the reaction of NO with photofragments other than vinyl. This conclusion is supported by the absence of CO emission when vinyl iodide or methyl vinyl ketone is used. Prompt emission from vibrationally excited NO is evidence of the competition between back dissociation and isomerization of the initially formed nitrosoethylene adduct, consistent with previous work on the pressure dependence of this reaction. Our calculations indicate that production of products is dominated by the low energy portion of the energy distribution. The calculation also predicts an upper bound of 0.19% for the branching ratio of the H2CNH + CO channel, which is consistent with our experimental results.

Unimolecular Rate Constants for HX or DX Elimination (X = F, Cl) from Chemically Activated CF3CH2CH2Cl, C2H5CH2Cl, and C2D5CH2Cl: Threshold Energies for HF and HCl Elimination

Vibrationally activated CF(3)CH(2)CH(2)Cl molecules were prepared with 94 kcal mol(-1) of vibrational energy by the combination of CF(3)CH(2) and CH(2)Cl radicals and with 101 kcal mol(-1) of energy by the combination of CF(3) and CH(2)CH(2)Cl radicals at room temperature. The unimolecular rate constants for elimination of HCl from CF(3)CH(2)CH(2)Cl were 1.2 x 10(7) and 0.24 x 10(7) s(-1) with 101 and 94 kcal mol(-1), respectively. The product branching ratio, k(HCl)/k(HF), was 80 +/- 25. Activated CH(3)CH(2)CH(2)Cl and CD(3)CD(2)CH(2)Cl molecules with 90 kcal mol(-1) of energy were prepared by recombination of C(2)H(5) (or C(2)D(5)) radicals with CH(2)Cl radicals. The unimolecular rate constant for HCl elimination was 8.7 x 10(7) s(-1), and the kinetic isotope effect was 4.0. Unified transition-state models obtained from density-functional theory calculations, with treatment of torsions as hindered internal rotors for the molecules and the transition states, were employed in the calculation of the RRKM rate constants for CF(3)CH(2)CH(2)Cl and CH(3)CH(2)CH(2)Cl. Fitting the calculated rate constants from RRKM theory to the experimental values provided threshold energies, E(0), of 58 and 71 kcal mol(-1) for the elimination of HCl or HF, respectively, from CF(3)CH(2)CH(2)Cl and 54 kcal mol(-1) for HCl elimination from CH(3)CH(2)CH(2)Cl. Using the hindered-rotor model, threshold energies for HF elimination also were reassigned from previously published chemical activation data for CF(3)CH(2)CH(3,) CF(3)CH(2)CF(3), CH(3)CH(2)CH(2)F, CH(3)CHFCH(3), and CH(3)CF(2)CH(3). In an appendix, the method used to assign threshold energies was tested and verified using the combined thermal and chemical activation data for C(2)H(5)Cl, C(2)H(5)F, and CH(3)CF(3).

A theoretical study for the reaction of vinyl cyanide C2H3CN(XA′1) with the ground state carbon atom C(P3) in cold molecular clouds

The reaction of the ground state atomic carbon, C(3P), with simple unsaturated nitrile, C2H3CN(X1A' (vinyl cyanide), is investigated theoretically to explore the probable routes for the formation of carbon-nitrogen-bearing species in extraterrestrial environments particularly of ultralow temperature. Five collision complexes without entrance barrier as a result of the carbon atom addition to the pi systems of C2H3CN are characterized. The B3YLP/6-311G(d,p) level of theory is utilized in obtaining the optimized geometries, harmonic frequencies, and energies of the intermediates, transition states, and products along the isomerization and dissociation pathways of each collision complex. Subsequently, with the facilitation of computed RRKM rate constants at collision energy of 0-10 kcal/mol, the most probable paths for each collision complexes are determined, of which the CCSD(T)/6-311G(d,p) energies are calculated. The major products predicted are exclusively due to the hydrogen atom dissociations, while the products of H2, CN, and CH2 decompositions are found negligible. Among many possible H-elimination products, cyano propargyl (p4) and 3-cyano propargyl (p5) are the most probable, in which p5 can be formed via two intermediates, cyano allene (i8) and cyano vinylmethylene (i6), while p4 is yielded from i8. The study suggests this class of reaction is an important route to the synthesis of unsaturated nitriles at the temperature as low as 10 K, and the results are valuable for future chemical models of interstellar clouds.

A theoretical study of the O( 1D) + CH 4 reaction II

The titled reaction is assumed to proceed via an insertion mechanism. Statistical branching ratios for various product channels are predicted with RRKM rate constants that are obtained based on ab initio calculations. A modified collision-complex model is utilized in the estimation of absolute reaction cross-sections for primary channels. The product energy partitions for H and H 2 formation pathways are obtained. Subsequently, the RRKM rate constants for secondary reactions are calculated with correction for the translational and rotational energies of primary products. The results give insight to reaction mechanism and provide probable explanations to disputes among previous experimental findings.

Structure and vibrational dynamics of the halogen-substituted butynes HCCCH2CH2X (X = F,Cl,Br) from molecular-beam high-resolution microwave and infrared spectroscopyElectronic supplementary information (ESI) available: Microwave transition frequencies. See http://www.rsc.org/suppdata/cp/b2/b211597b/

The pure rotational and high-resolution acetylenic C–H stretch rovibrational spectra of a series of substituted butynes, HCCCH2CH2X (X = F,Cl,Br), are reported. For each of the molecules the pure rotational spectrum of two conformational isomers (trans and gauche) has been assigned. For the Cl and Br substituted compounds the pure rotational spectrum of two isotopic species has been assigned (35Cl, 37Cl and 79Br, 81Br) for each conformer. An analysis of the nuclear quadrupole hyperfine structure in the pure rotational spectrum shows good agreement with structural parameters obtained through electronic structure calculations. The rotational transitions are used to obtain full rotational assignment of the acetylenic C–H stretch vibrational band of the more stable trans conformers through infrared-microwave double-resonance spectroscopy. The rotational band contours are predominantly a-type for all three halobutynes. The rotational structure of the band displays separations characteristic of the trans conformer. This result reflects the fact that the bright state for the vibrational spectrum retains the ground state conformation. From the eigenstate-resolved spectra we determine the timescale for intramolecular vibrational energy redistribution (IVR). The IVR rate obtained from the high-resolution spectrum provides an upper limit to the isomerization rate following coherent vibrational excitation. The IVR lifetimes of the acetylenic C–H stretch have been determined to be 1.5 ns for trans-4-fluorobut-1-yne, 3.5 ns for trans-4-chlorobut-1-yne, and 2.0 ns for trans-4-bromobut-1-yne. In all cases, the upper limit isomerization rate inferred from the vibrational spectrum is three orders-of-magnitude slower than the RRKM rate calculated using the ab initio barrier heights. Although direct dynamical information about the isomerization rate cannot be obtained from the spectrum, evidence is found for conformational isomerization occurring through the J-dependent growth of the measured rovibrational state density.

Relationship between Mode Specific and Thermal Unimolecular Rate Constants for HOCl → OH + Cl Dissociation

Recent quantum dynamical calculations [Hauschildt, J.; et al. Chem. Phys. Lett. 1999, 300, 569] have shown that HOCl → OH + Cl dissociation on the ground-state potential energy surface, and for J = 0, occurs predominantly via isolated compound-state resonances, whose rates are highly mode-specific. In this work, these resonance rates are averaged to calculate the HOCl → OH + Cl unimolecular rate constant as a function of temperature and pressure. The result is compared with the standard pressure and temperature dependent RRKM unimolecular rate constant. It is found that the state-specificity makes the pressure-dependent rates significantly lower than the RRKM rates in the intermediate pressure regime.

Kinetics and mechanism for the H‐for‐X exchange process in the H + C6H5X reactions: A computational study

AbstractThe addition of H atoms to benzene and toluene and subsequent transformations were investigated using high level ab initio and density functional theory methods. Molecular structures and vibrational frequencies calculated at the B3LYP/6‐311++G(d,p) level of theory were used in combination with adjusted G2M energetic parameters for RRKM rate constant calculations. Standard heats of formation for cyclohexadienyl and cyclohexadienyl, 6‐methyl radicals calculated through isodesmic reactions amounted to 49.5 ± 2 and 42.9 ± 3 kcal/mol, respectively. Rate constants for various elementary reactions involved in the H‐for‐X exchange (X = D, CH3) were calculated and closely correlated with the available experimental kinetic data. © 2001 John Wiley & Sons, Inc. Int J Chem Kinet 33: 633–653, 2001

Reaction Coordinate and Rate Constants for Nitrous Acid cis−trans Isomerization

Nitrous acid is one of the simplest molecules that undergoes geometric isomerization. The reaction path properties and rate constants of isomerization have been determined at the MP2 and DFT levels of theory. Good agreement is obtained with experimental data. The calculated isomerization threshold energy is 10.8−12.0 kcal/mol, and the experimental value is 11.6 ± 0.2 kcal/mol. The microcanonical RRKM rate constants, which include the effects of the variational transition state and the J rotational quantum number, are calculated. High-pressure rate constants are determined for the 223−323 K temperature range.

Unimolecular isomerization/decomposition of cyclopentadienyl and related bimolecular reverse process:ab initio MO/statistical theory study

The cyclopentadienyl radical decomposition has been studied in detail by high-level correlation MO methods combined with multichannel RRKM rate constant calculations. The product channels of the reaction were examined by calculating their pressure-dependent branching rate constants. The overall reaction rate has been shown to be controlled by the first transition state corresponding to 1,2-hydrogen atom migration. Also, the reverse bimolecular reactions (C3H3 + C2H2 → products) have been included in the study. We provide a summary of pressure dependent rate constant expressions for the 1000–3000 K temperature range that may be useful for kinetic modeling of relevant combustion systems. © 2000 John Wiley & Sons, Inc. J Comput Chem 21: 415–425, 2000

Ultrafast photodissociation studies of acetyl cyanide and acetic acid and unimolecular decomposition rates of the acetyl radical products

Unimolecular decomposition rates for acetyl radical following the photodissociation of acetyl cyanide and acetic acid near 193 nm have been studied using ultrafast mass-resolved photoionization spectroscopy. In both cases, the parent decays with an instrumentally limited lifetime, while the acetyl radical behaves in a manner consistent with an RRKM mechanism, in contrast to our previous results on acetone. It is necessary to convolute the population distribution with the microcanonical RRKM rates in order to achieve this agreement. We have also undertaken an ab initio study of the excited states of acetyl cyanide to clarify the assignments of these states. The state excited at 193 nm arises from a π→π* transition with a calculated transition velocity dipole moment oriented at an angle of 57° with respect to the C–C≡N bond, resulting in an anisotropy parameter of −0.22. This is in reasonable agreement with the previous data of North et al. [J. Phys. Chem. A 101, 9224 (1997)]. The apparent RRKM behavior of the acetyl radical formed by the photodissociation of acetic acid and acetyl cyanide indicates that acetyl radical produced by the photodissociation of acetone at 193 nm may exhibit “extrinsic non-RRKM” effects, i.e., dynamic bottlenecks or mode specific effects.

Modeling Internal Energy Distributions in Ion Clusters: Comparison between Experiment and Simulations

The internal energy distribution of Na+(CH3OH)1-8 cluster ions has been evaluated by comparing experimental unimolecular rate constants measured in a triple quadrupole spectrometer to an RRKM rate analysis developed within the evaporative ensemble formalism. The significant ion−solvent binding energies give rise to broad distributions, particularly for the smallest cluster ions. The role of internal energy on the number and type of cluster ion structures was then assessed by using Monte Carlo simulation methods. Predicted onsets of hydrogen bond formation and the number of hydrogen-bonded O−H stretching bands in Na+(CH3OH)1-7 were found to agree with previous vibrational spectroscopy experiments. The methodology introduced here can be used to estimate the internal energy content of any cluster that undergoes unimolecular dissociation utilizing experimental or theoretical values for properties such as binding energies and vibrational frequencies.

Accurate computation of quantum densities of states and RRKM rate constants for large polyatomic molecules: The STAIR method

A new method is given for the computation of quantum mechanical microcanonical densities of states of large molecules. The method is based on the observation that for large molecules with many vibrational degrees of freedom, the complex time partition function dephases rapidly allowing for a good short-time approximation. The short-time approximation up to third order gives an Airy function expression for the thermal density of states at a given temperature T. The microcanonical density of states is then deduced from the thermal density. The input needed for the method is the first three moments of the Hamiltonian at a series of temperatures, which adequately cover the energy range of interest. These may be computed using quantum Monte Carlo methods. The method is tested for a harmonic model of trans-stilbene, a separable anharmonic model of cyclopropane, and a separable anharmonic model of a system with 50 degrees of freedom. The short-time Airy method is found to give accurate estimates for the density of states, the integrated density of states, and RRKM microcanonical rate constants.

Unimolecular Reactions of Proton-Bound Cluster Ions: Competition between Dissociation and Isomerization in the Methanol−Acetonitrile Dimer

The metastable proton-bound dimer of acetonitrile and methanol, (CH3CN)(CH3OH)H+, exhibits two unimolecular reactions on the microsecond time scale, a simple bond cleavage reaction to form CH3CNH+ and CH3OH, and the loss of water to form CH3CNCH3+. The latter process is preceded by the isomerization of the proton-bound dimer to a second isomer, (CH3CNCH3)(H2O)+. Collision-induced dissociation mass spectrometry was used to identify the two sets of reaction products, and the results of isotopic labeling experiments suggest that there is a rate-limiting isomerization step going from the proton-bound dimer to the second complex. The competition between the two channels was modeled with ab initio calculations and RRKM rate theory to obtain relative energies for the reaction surface. The transition structure for the rate-determining isomerization could not be located with ab initio calculations, and so its relative energy was estimated using RRKM theory. The 0 K binding energy of the (CH3CN)(CH3OH)H+ complex was calculated to be 121 kJ mol-1 at the G2 level of theory (relative to the dissociation products CH3CNH+ and CH3OH).

Fitting classical microcanonical unimolecular rate constants to a modified RRK expression: Anharmonic and variational effects

Classical RRKM (i.e., microcanonical) rate constants are often calculated for analytic potential energy surfaces (PESs) developed to represent unimolecular decomposition reactions. The values for these rate constants reflect the complete anharmonicities of the PESs. A common procedure is to fit these rate constants with the expression of RRK theory, which is the harmonic limit of classical RRKM theory. These RRK fits often give values for s significantly less than 3n−6(5), which are not meaningful, since anharmonic rate constants are represented with a harmonic model. In this work different schemes are proposed for introducing anharmonic and also variational transition state effects into the RRK expression. These modified RRK schemes allow one to fit classical anharmonic RRKM rate constants with s=3n−6(5). The fits give information about the importance of anharmonicity in the unimolecular reactant’s density of states and the transition state’s sum of states.

RRKM Theory beyond the Separable Harmonic Approximation: The HCO2 → H + CO2 Unimolecular Decomposition

We report variational calculations of a large number of vibrational states of HCO2 and the H···CO2 transition state for J = 0 using the code MULTIMODE and a realistic six degree-of-freedom potential energy surface. State-dependent rotational constants for both species are calculated for the same sets of vibrational states from exact rotation/vibration calculations for J = 1. The results of these variational calculations are used to obtain RRKM rate constants for the decomposition of HCO2 to form H + CO2. Comparison is made between these nonseparable RRKM results and those obtained from a standard, separable harmonic oscillator/rigid rotor evaluation of the RRKM rate constant expression. Significant differences between the nonseparable and separable results are found.

The rotational spectra of single molecular eigenstates of 2-fluoroethanol: Measurement of the conformational isomerization rate at 2980 cm−1

The rotational spectroscopy of single molecular eigenstates has been used to measure the conformational isomerization rate in 2-fluoroethanol. Eigenstates in the asymmetric –CH2(F) stretch spectrum of the Gg′ conformer near 2980 cm−1 are prepared with an infrared laser. These eigenstates are approximately 2000 cm−1 above the barrier to Gg′−Tt conformational isomerization. The rotational spectrum is measured using an infrared-microwave double-resonance technique based on the Autler–Townes splitting of states in a strong microwave field. This technique does not require saturation of the infrared preparation step. Two types of rotational transitions are observed. These are assigned to rotational transitions from vibrational states with Tt conformation (near 15.8 GHz) and to “isomerization states” (near 17.1 GHz) where the torsional wave functions are above the isomerization barrier. The isomerization kinetics are obtained from the linewidth of the ensemble eigenstate rotational spectrum. The lifetime for the Tt conformer is 2.7 ns. The isomerization states relax at approximately twice the rate of the Tt states (1.5 ns lifetime). This result is consistent with a kinetics model where the isomerization proceeds by “over-the-barrier” pathways. Both lifetimes are longer than the bright-state IVR lifetime (275 ps) indicating that the intramolecular dynamics occur on two distinct time scales. The isomerization rate for the Tt states is three orders-of-magnitude slower than predicted by a simple RRKM rate expression.

Vacuum ultraviolet photoionization and photodissociation of ferrocene

Photoionization and photodissociation of ferrocene [Fe(C 5H 5) 2] is examined by using vacuum ultraviolet (VUV) photons from a synchrotron radiation source and a time-of-flight (TOF) photoionization mass spectrometer. VUV absorption by ferrocene results in Fe(C 5H 5) 2 ·+, FeC 5H 5 +, FeC 3H 3 +, Fe ·+ and C 10H x ·+ (x = 8 − 10). The dependency of the product distribution on photon energy indicates sequential elimination of C 5H 5· ligands as a major dissociation channel, but concerted elimination of two C 5H 5· ligands also takes place to a lesser degree. Through analysis of TOF peak shape, it is found that Fe(C 5H 5) 2 ·+ molecular ion dissociates into FeC 5H 5 + and C 5H 5· via two channels. One is nonstatistical dissociation with a fast rate, and the other is slow unimolecular decay that becomes more discernible at low photon energy. The rate of unimolecular decay, exemplified by a value of k = 2.4 ± 1.0 × 10 6 s −1 at photon energy of 14.76 eV, is well in accord with the RRKM rate.

Ab Initio and Density Functional Investigation of Reactions of NO with XCO (X = H, F, Cl)

Ab initio as well as density functional methods are used to investigate various reaction paths for XCO + NO (X = H, F, Cl) with a special focus on the reaction path through the collisional complex CX(O)NO, which is experimentally proposed for X = H and F. It is revealed that the dissociation channels of CH(O)NO to HNO + CO and CF(O)NO to FNO + CO have a higher barrier, while the CCl(O)NO has a dissociation barrier lower than that of the redissociation to reactants. It is expected that this channel should be the major one for the disappearance of CCl(O)NO. To gauge the relative importance of various channels of CX(O)NO disappearance, high-pressure RRKM rate constants are obtained. These results suggest the necessity of reinvestigation of a model based on experiments for the HCO + NO reaction. For the reactions of FCO and ClCO with NO, the MP2 and B3LYP stationary point structures and relative energies are in reasonable agreement with each other, whereas for the HCO + NO reaction, the MP2 level PES is markedly different from the QCISD and B3LYP counterparts.

Direct Dynamics Quasiclassical Trajectory Study of the Thermal Stereomutations of Cyclopropane

Classical trajectories are computed for the stereomutations of cyclopropane-1,2-d2 at 695 K using direct dynamics on an AM1-SRP potential energy surface (AM1 with specific reaction parameters). The trajectories were initiated on a dividing surface, separating the cyclopropane reactants from the stereomutation products, with momenta and coordinates sampled from a 695 K Boltzmann distribution. The quasiclassical procedure was used, with two different sampling schemes, to ensure zero-point energy and vibrational quantization conditions for the energy levels on the dividing surface. From the product distribution, the ratio of rate constants for double and single methylene rotation, k12/k1, is 2.3 and 3.5 for the two sampling methods. These are between the values of 1.0 and 5−42 deduced from two separate experimental studies. A harmonic-oscillator/rigid-rotor transition-state theory calculation of k12/k1, assuming trimethylene as an intermediate, gives k12/k1 = 1.35 on the AM1-SRP potential energy surface. The lifetime distribution of reactive trajectories is nonexponential, in contrast to the nearly exponential decay computed from a Boltzmann average of RRKM rates. However, the initial 70% of the decay is single exponential, and the ratio of the time constants for decay of the single and double rotation rates is essentially the same as k12/k1 computed from the product ratios. Nearly all the trajectories cyclize on the first approach to a (90, 90) conformation. The data support a range of mechanistic descriptions. Most double rotations are conrotatory and occur via direct, short-lived trajectories. A quantity of 23% of trajectories have lifetimes >400 fs and include multiple independent rotations and both single and double rotation isomerizations.

Nonequilibrium unimolecular dissociation influenced by intramolecular vibrational energy redistribution

Unimolecular dissociation rates of energized molecules influenced by the slow intramolecular vibrational energy redistribution (IVR) are formulated for no-barrier potentials of the reaction coordinate R. The master equation as to states projected on the reactive mode is presented and is solved by reducing the equation to an equivalent diffusion equation. An approximate solution for the steady state condition gives the generalized dissociation rate constant kD which is expressed as kD−1=kdiff−1+kde−1+kRRKM−1, where kdiff, kde, and kRRKM represent the internal energy diffusion rate constant, equilibrium barrier crossing rate constant by bound-continuum transitions, and the fragmentation rate constant corresponding to the flux which crosses the critical configuration R=R‡, respectively. The former two rates, which are due to IVR, are expressed by the transition kernel between states of the reactive mode, and the latter gives the RRKM rate which is valid in the rapid IVR limit. The rate limiting steps for various reactions are discussed.