Approximate determination of rovibrational densities of states ρ(E,J) and numbers of states W(E,J)

Kinetics of O3 with Ca+ and Its Higher Oxides CaOn+ (n = 1-3) and Updates to a Model of Meteoric Calcium in the Mesosphere and Lower Thermosphere

The room-temperature rate constants and product branching fractions of CaO_n⁺ (n = 0-3) + O₃ are measured using a selected ion flow tube apparatus. Ca⁺ + O₃ produces CaO⁺ + O₂ with k = 9 ± 4 × 10^-10 cm³ s^-1, within uncertainty equal to the Langevin capture rate constant. This value is significantly larger than several literature values. Most likely, those values were underestimated due to the reformation of Ca⁺ from the sequential chemistry of higher calcium oxide cations with O₃, as explored here. A rate constant of 8 ± 3 × 10^-10 cm³ s^-1 is recommended. Both CaO⁺ and CaO₂⁺ react near the capture rate constant with ozone. The CaO⁺ reaction yields both CaO₂⁺ + O₂ (0.80 ± 0.15 branching) and Ca⁺ + 2O₂. Similarly, the CaO₂⁺ reaction yields both CaO₃⁺ + O₂ (0.85 ± 0.15 branching) and CaO⁺ + 2O₂. CaO₃⁺ + O₃ yield CaO₂⁺ + 2O₂ at 2 ± 1 × 10^-11 cm³ s^-1, about 2% of the capture rate constant. The results are supported using density functional calculations and statistical modeling. In general, CaO_n⁺ + O₃ yield CaO_n+1⁺ + O₂, the expected oxidation. Some fraction of CaO_n+1⁺ is produced with sufficient internal energy to further dissociate to CaO_n-1⁺ + O₂, yielding the same products as the oxidation of O₃ by CaO_n⁺. Mesospheric Ca and Ca⁺ concentrations are modeled as functions of day, latitude, and altitude using the Whole Atmosphere Community Climate Model (WACCM); incorporating the updated rate constants improves agreement with concentrations derived from lidar measurements.

Activation of Methane by Zr+: A Deep-Dive into the Potential Surface via Pressure- and Temperature-Dependent Kinetics with Statistical Modeling

The kinetics of Zr⁺ + CH₄ are measured using a selected-ion flow tube apparatus over the temperature range 300-600 K and the pressure range 0.25-0.60 Torr. Measured rate constants are small, never exceeding 5% of the Langevin capture value. Both collisionally stabilized ZrCH₄⁺ and bimolecular ZrCH₂⁺ products are observed. A stochastic statistical modeling of the calculated reaction coordinate is used to fit the experimental results. The modeling indicates that an intersystem crossing from the entrance well, necessary for the bimolecular product to be formed, occurs faster than competing isomerization and dissociation processes. That sets an upper limit on the lifetime of the entrance complex to crossing of 10^-11 s. The endothermicity of the bimolecular reaction is derived to be 0.09 ± 0.05 eV, in agreement with a literature value. The observed ZrCH₄⁺ association product is determined to be primarily HZrCH₃⁺ not Zr⁺(CH₄), indicating that bond activation has occurred at thermal energies. The energy of HZrCH₃⁺ relative to separated reactants is determined to be -0.80 ± 0.25 eV. Inspection of the statistical modeling results under best-fit conditions reveals reaction dependences on impact parameter, translation energy, internal energy, and angular momentum. Reaction outcomes are heavily affected by angular momentum conservation. Additionally, product energy distributions are predicted.

Effect of Intersystem Crossings on the Kinetics of Thermal Ion-Molecule Reactions: Ti+ + O2, CO2, and N2O

A selected-ion flow tube apparatus has been used to measure rate constants and product branching fractions of ²Ti⁺ reacting with O₂, CO₂, and N₂O over the range of 200-600 K. Ti⁺ + O₂ proceeds at near the Langevin capture rate constant of 6-7 × 10^-10 cm³ s^-1 at all temperatures to yield ⁴TiO⁺ + O. Reactions initiated on doublet or quartet surfaces are formally spin-allowed; however, the 50% of reactions initiated on sextet surfaces must undergo an intersystem crossing (ISC). Statistical theory is used to calculate the energy and angular momentum dependences of the specific rate constants for the competing isomerization and dissociation channels. This acts as an internal clock on the lifetime to ISC, setting an upper limit on the order of τ_ISC < 1e^-11 s. ²Ti⁺ + CO₂ produces ⁴TiO⁺ + CO less efficiently, with a rate constant fit as 5.5 ± 1.3 × 10^-11 (T/300)^{-1.1 ± 0.2} cm³ s^-1. The reaction is formally spin-prohibited, and statistical modeling shows that ISC, not a submerged transition state, is rate-limiting, occurring with a lifetime on the order of 10^-7 s. Ti⁺ + N₂O proceeds at near the capture rate constant. In this case, both Ti⁺ON₂ and Ti⁺N₂O entrance channel complexes are formed and can interconvert over a barrier. The main product is >90% TiO⁺ + N₂, and the remainder is TiN⁺ + NO. Both channels need to undergo ISC to form ground-state products but TiO⁺ can be formed in an excited state exothermically. Therefore, kinetic information is obtained only for the TiN⁺ channel, where ISC occurs with a lifetime on the order of 10^-9 s. Statistical modeling indicates that the dipole-preferred Ti⁺ON₂ complex is formed in ∼80% of collisions, and this value is reproduced using a capture model based on the generic ion-dipole + quadrupole long-range potential.

The unimolecular decomposition of dimethoxymethane: channel switching as a function of temperature and pressure

Branching ratios of competing unimolecular reactions often exhibit a complicated temperature and pressure dependence that makes modeling of complex reaction systems in the gas phase difficult. In particular, the competition...

Methane Adducts of Gold Dimer Cations: Thermochemistry and Structure from Collision-Induced Dissociation and Association Kinetics

The bond dissociation energies at 0 K (BDE) of Au₂⁺-CH₄ and Au₂CH₄⁺-CH₄ have been determined using two separate experimental methods. Analyses of collision-induced dissociation cross sections for Au₂CH₄⁺ + Xe and Au₂(CH₄)₂⁺ + Xe measured using a guided ion beam tandem mass spectrometer (GIBMS) yield BDEs of 0.71 ± 0.05 and 0.57 ± 0.07 eV, respectively. Statistical modeling of association kinetics of Au₂(CH₄)_0-2⁺ + CH₄ + He measured from 200 to 400 K and at 0.3-0.9 Torr using a selected-ion flow tube (SIFT) apparatus yields slightly higher values of 0.81 ± 0.21 and 0.75 ± 0.25 eV. The SIFT data also place a lower limit on the BDE of Au₂C₂H₈⁺-CH₄ of 0.35 eV, likely an activated isomer, not Au₂(CH₄)₂⁺-CH₄. Particular emphasis is placed on determining the uncertainty in the derivation from association kinetics measurements, including uncertainties in collisional energy transfer, calculated harmonic frequencies, and possible contribution of isomerization of the association complexes. This evaluation indicates that an uncertainty of ±0.2 eV should be expected and that an uncertainty of better than ±0.1 eV is unlikely to be reasonable.

Thermal activation of methane by MgO+: temperature dependent kinetics, reactive molecular dynamics simulations and statistical modeling

The kinetics methane activation (MgO⁺ + CH₄) was studied experimentally and computationally by running and analyzing reactive atomistic simulations.

Temperature- and pressure-dependent kinetics of the competing C–O bond fission reactions of dimethoxymethane

Under typical shock tube conditions, dimethoxymethane decomposes mainly to give CH₃ + OCH₂OCH₃.

On the Role of Hydrogen Atom Transfer (HAT) in Thermal Activation of Methane by MnO+: Entropy vs. Energy

The temperature dependent kinetics and product branching fractions of first-row transition metal oxide cation MnO+ with CH4 and CD4 at temperatures between 200 and 600 K are measured using a selected-ion flow tube apparatus. Likely reaction mechanisms are determined by comparison of temperature dependent kinetics to statistical modeling along calculated reaction coordinates. The data is well-modeled with the reaction proceeding over a rate limiting four-centered transition state leading to an insertion intermediate, similar to reactions of NiO+ and FeO+, and showing characteristics of proton-coupled electron transfer (PCET). However, a more direct pathway traversing a transition state of hydrogen atom transfer (HAT) character to a hydroxyl intermediate is found to possibly be competitive, especially with increasing temperature. While uncertainties in calculated energetics limit quantitative assessment of the role of HAT at thermal energies, it is clear that this mechanism becomes increasingly prevalent in higher energy regimes.

Thermal Decomposition of NCN: Shock-Tube Study, Quantum Chemical Calculations, and Master-Equation Modeling

The thermal decomposition of cyanonitrene, NCN, was studied behind reflected shock waves in the temperature range 1790-2960 K at pressures near 1 and 4 bar. Highly diluted mixtures of NCN3 in argon were shock-heated to produce NCN, and concentration-time profiles of C atoms as reaction product were monitored with atomic resonance absorption spectroscopy at 156.1 nm. Calibration was performed with methane pyrolysis experiments. Rate coefficients for the reaction (3)NCN + M → (3)C + N2 + M (R1) were determined from the initial slopes of the C atom concentration-time profiles. Reaction R1 was found to be in the low-pressure regime at the conditions of the experiments. The temperature dependence of the bimolecular rate coefficient can be expressed with the following Arrhenius equation: k1(bim) = (4.2 ± 2.1) × 10(14) exp[-242.3 kJ mol(-1)/(RT)] cm(3) mol(-1) s(-1). The rate coefficients were analyzed by using a master equation with specific rate coefficients from RRKM theory. The necessary molecular data and energies were calculated with quantum chemical methods up to the CCSD(T)/CBS//CCSD/cc-pVTZ level of theory. From the topography of the potential energy surface, it follows that reaction R1 proceeds via isomerization of NCN to CNN and subsequent C-N bond fission along a collinear reaction coordinate without a tight transition state. The calculations reproduce the magnitude and temperature dependence of the rate coefficient and confirm that reaction R1 is in the low-pressure regime under our experimental conditions.

On the Model Dependence of Kinetic Shifts in Unimolecular Reactions: The Dissociation of the Cations of Benzene and n-Butylbenzene

Statistical adiabatic channel model/classical trajectory (SACM/CT) calculations have been performed for transitional mode dynamics in the simple bond fission reactions of C(6)H(6)(+) --> C(6)H(5)(+) + H and n-C(6)H(5)C(4)H(9)(+) --> C(7)H(7)(+) + n-C(3)H(7). Reduced-dimensionality model potentials have been designed that take advantage of ab initio results as far as available. Average anisotropy amplitudes of the potentials were fitted by comparison of calculated specific rate constants k(E,J) with measured values. The kinetic shifts of the calculated k(E) curves and the corresponding bond energies E(0)(J=0), derived as 3.90 +/- 0.05 eV for C(6)H(6)(+) and 1.78 +/- 0.05 eV for n-C(6)H(5)C(4)H(9)(+), were in good agreement with literature values from thermochemical studies. Kinetic shifts from fixed tight activated complex Rice-Ramsperger-Kassel-Marcus (RRKM) theory, which also reproduces the measured k(E), were larger than the present SACM/CT results as well as earlier results from variational transition state theory (for C(6)H(6)(+)). The approach using RRKM theory was found to underestimate E(0)(J=0) by about 0.2-0.3 eV. A simplified SACM/CT-based method is also proposed which circumvents the trajectory calculations and allows derivation of E(0)(J=0) on the basis of measured k(E) and which provides similar accuracy as the full SACM/CT treatment.