Rapid Approximate Calculation of Numbers of Quantum States W(E,J) in the Phase Space Theory of Unimolecular Bond Fission Reactions

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...

Cyclotrimerization of Acetylene under Thermal Conditions: Gas-Phase Kinetics of V+ and Fe+ + C2H2

The kinetics of successive reactions of acetylene (C₂H₂) initiated on either vanadium or iron atomic cations have been investigated under thermal conditions using the variable-ion source and temperature-adjustable selected-ion flow tube apparatus. Consistent with the literature results, the reaction of Fe⁺ + C₂H₂ primarily yields Fe⁺(m/z = (C₂H₂)₃); however, analysis via quantum chemical calculations and statistical modeling shows that the mechanism does not form benzene upon the third acetylene addition. The kinetics are more consistent with successive addition of three acetylene molecules, yielding Fe⁺(C₂H₂)₃, followed by an addition of a fourth acetylene molecule, initiating cyclotrimerization, yielding either Fe⁺(C₂H₂) + neutral benzene or Fe⁺(Bz) + acetylene, where Bz is a benzene ligand. In contrast, the reaction of V⁺ + C₂H₂ yields products via successive associations V⁺(m/z = (C₂H₂)_n) either with or without a bimolecular step involving loss of one H₂ and V⁺C₂(m/z = (C₂H₂)_m), where n and m extend at least up to 11 under conditions of 0.32 Torr at 300 K. Stabilized V⁺(Bz) is not a significant intermediate in the association mechanism. We propose a plausible mechanism for the generation of neutral benzene in this reaction and compare with the Fe⁺ results. The reaction steps that produce benzene result in turnover of the single-atom catalyst, and the large hydrocarbons produced that remain associated to the catalyst are proposed to be polycyclic aromatic hydrocarbons.

Barrierless methane-to-methanol conversion: the unique mechanism of AlO. Phys Chem Chem Phys 2020;22:14544-14550. [PMID: 32589175 DOI: 10.1039/d0cp02316g]

The kinetics of AlO+ + CH4 are studied from 300-500 K using a selected-ion flow tube. At all temperatures the reaction proceeds near the Langevin-Gioumousis-Stevenson collision rate with two product channels: hydrogen atom abstraction (AlOH+ + CH3, 86 ± 5%) and methanol formation (Al+ + CH3OH, 14 ± 5%). Density functional calculations show the key Al-CH3OH+ intermediate is formed barrierlessly via a mechanism unique to aluminum, avoiding the rate-limiting step common to other MO+. The reaction of Al2O3+ + CH4 follows a similar mechanism to that for AlO+ through to the key intermediate; however, the conversion to methanol occurs only for AlO+ due to favorable energetics attributed to a weaker Al+-CH3OH bond. Importantly, that bond strength may be tuned independent of competing product channels by altering the acidity of the Al with electron-withdrawing or donating groups, indicating a key design criteria to develop a real world Al-atom catalyst.

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.

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.

Temperature and Pressure Dependences of the Reactions of Fe+ with Methyl Halides CH3X (X = Cl, Br, I): Experiments and Kinetic Modeling Results

The pressure and temperature dependences of the reactions of Fe⁺ with methyl halides CH₃X (X = Cl, Br, I) in He were measured in a selected ion flow tube over the ranges 0.4 to 1.2 Torr and 300-600 K. FeX⁺ was observed for all three halides and FeCH₃⁺ was observed for the CH₃I reaction. FeCH₃X⁺ adducts (for all X) were detected in all reactions. The results were interpreted assuming two-state reactivity with spin-inversions between sextet and quartet potentials. Kinetic modeling allowed for a quantitative representation of the experiments and for extrapolation to conditions outside the experimentally accessible range. The modeling required quantum-chemical calculations of molecular parameters and detailed accounting of angular momentum effects. The results show that the FeX⁺ products come via an insertion mechanism, while the FeCH₃⁺ can be produced from either insertion or S_N2 mechanisms, but the latter we conclude is unlikely at thermal energies. A statistical modeling cannot reproduce the competition between the bimolecular pathways in the CH₃I reaction, indicating that some more direct process must be important.

Modeling unimolecular reactions in photoelectron photoion coincidence experiments

A computer program has been developed to model and analyze the data from photoelectron photoion coincidence (PEPICO) spectroscopy experiments. This code has been used during the past 12 years to extract thermochemical and kinetics information for almost a hundred systems, and the results have been published in over forty papers. It models the dissociative photoionization process in the threshold PEPICO experiment by calculating the thermal energy distribution of the neutral molecule, the energy distribution of the molecular ion as a function of the photon energy, and the resolution of the experiment. Parallel or consecutive dissociation paths of the molecular ion and also of the resulting fragment ions are modeled to reproduce the experimental breakdown curves and time-of-flight distributions. The latter are used to extract the experimental dissociation rates. For slow dissociations, either the quasi-exponential fragment peak shapes or, when the mass resolution is insufficient to model the peak shapes explicitly, the center of mass of the peaks can be used to obtain the rate constants. The internal energy distribution of the fragment ions is calculated from the densities of states using the microcanonical formalism to describe consecutive dissociations. Dissociation rates can be calculated by the RRKM, SSACM or VTST rate theories, and can include tunneling effects, as well. Isomerization of the dissociating ions can also be considered using analytical formulae for the dissociation rates either from the original or the isomer ions. The program can optimize the various input parameters to find a good fit to the experimental data, using the downhill simplex algorithm.

SACM/CT Study of Product Energy Distributions in the Dissociation of n-Propylbenzene Cations

The distribution of translational, rotational, and vibrational energies in the fragments (benzylium ions and ethyl radicals) of the dissociation of n-propylbenzene cations has been determined by statistical adiabatic channel model/classical trajectory (SACM/CT) calculations. The reaction was treated by CT calculations of capture processes for transitional modes, starting with specified fragment energies. A short-range valence/long-range ion-induced dipole potential model for the transitional modes was employed. The derived distributions approach the results from phase space theory (PST) at small energies and angular momenta. At larger energies and angular momenta, the shapes of the distribution functions remain similar to those from PST; however, the average translational, rotational, and vibrational energies of the fragments increasingly differ from PST predictions. The present results are consistent with separate SACM/CT calculations on the same potential of specific rate constants k(E,J) and thermally averaged rate constants k ∞(T) of the dissociation/recombination reaction.

Classical Trajectory and Statistical Adiabatic Channel Study of the Dynamics of Capture and Unimolecular Bond Fission. VII. Thermal Capture and Specific Rate Constants k(E,J) for the Dissociation of Molecular Ions

Specific rate constants, k(E,J), and thermal capture rate constants, k cap(T), are determined by statistical adiabatic channel model/classical trajectory (SACM/CT) calculations for unimolecular dissociation and the reverse association reactions of representative polyatomic molecular ions. Simple short-range valence/long-range ion-induced dipole model potentials without reverse barriers have been employed, using the reactions C8H10 + ⇔ C7H7 + + CH3 and C9H12 + ⇔ C7H7 + + C2H5 as illustrative examples. Simplified representations of k(E) and k cap(T) from rigid activated complex Rice–Ramsperger–Kassel–Marcus (RRKM) theory are compared with the SACM/CT treatment and with experimental results. The Massey parameters of the transitional mode dynamics, for the systems considered, are smaller than unity such that their dynamics is nonadiabatic while the dynamics of the conserved modes is adiabatic. Because of the long-range/short-range switching character of the potential, simple rigid activated complex RRKM theory cannot be used without modifications. The effects of a shifting of the effective bottle-neck of the dynamics with increasing energy towards smaller interfragment distances in the present cases are amplified by a shift into a range of increasing anisotropy of the potential. As a consequence, the thermal capture rate constants markedly decrease with increasing temperature.

Monitoring the dissolution process of metals in the gas phase: reactions of nanoscale Al and Ga metal atom clusters and their relationship to similar metalloid clusters

Formation and dissolution of metals are two of the oldest technical chemical processes. On the atomic scale, these processes are based on the formation and cleavage of metal-metal bonds. During the past 15 years we have studied intensively the intermediates during the formation process of metals, i.e. the formation of compounds containing many metal-metal bonds between naked metal atoms in the center and ligand-bearing metal atoms at the surface. We have called the clusters metalloid or, more generally, elementoid clusters. Via a retrosynthetic route, the many different Al and Ga metalloid clusters which have been structurally characterized allow us to understand also the dissolution process; i.e. the cleavage of metal-metal (M-M) bonds. However, this process can be detected much more directly by the reaction of single metal atom clusters in the gas phase under high vacuum conditions. A suitable tool to monitor the dissolution process of a metal cluster in the gas phase is FT-ICR (Fourier transform ion cyclotron resonance) mass spectrometry. Snapshots during these cleavage processes are possible because only every 1-10 s is there a contact between a cluster molecule and an oxidizing molecule (e.g. Cl2). This period is long, i.e. the formation of the primary product (a smaller metal atom cluster) is finished before the next collision happens. We have studied three different types of reaction:(1) Step-by-step fragmentation of a structurally known metalloid cluster allows us to understand the bonding principle of these clusters because in every step only the weakest bond is broken.(2) There are three oxidation reactions of an Al13(-) cluster molecule with Cl2, HCl and O2 central to this review. These three reactions represent three different reaction types, (a) an exothermic reaction (Cl2), (b) an endothermic reaction (HCl), and (c) a kinetically limited reaction based on spin conservation rules (O2).(3) Finally, we present the reaction of a metalloid cluster with Cl2 in order to show that in this cluster only the central naked metal atoms are oxidized, and a smaller metalloid cluster results containing the entire protecting shell as the primary cluster. All the experimental results, supported by quantum chemical calculations, give a rough idea about the complex reaction cascades which occur during the dissolution and formation of metals. Furthermore, these results cast a critical light on many simplifying and generalizing rules in order to understand the bonding and structure of metal clusters. Finally, the experiments and some recent results provided by physical measurements on a crystalline Ga(84) compound build a bridge to nanoscience; i.e. they may be a challenge for chemistry in the next decades, since it has been shown that only with a perfect orientation of nanoscale metal clusters, e.g. in a crystal, can novel, unexpected properties (e.g. superconducting nanoscale materials) be obtained.

Falloff Curves for the Recombination Reaction Cl + FC(O)O + M → FC(O)OCl + M

The pressure dependence of the recombination reaction Cl + FC(O)O + M --> FC(O)OCl + M has been investigated at 296 K. FC(O)O radicals and Cl atoms were generated by laser flash photodissociation of FC(O)OO(O)CF at 193 nm in mixtures with Cl2 and He or SF6 over the total pressure range 8-645 Torr. The measured FC(O)O radical and F atom yields in the photolysis are 0.33 +/- 0.06 and 0.67 +/- 0.06. The reaction lies in the falloff range approaching the high-pressure limit. The extrapolations toward the limiting low- and high-pressure ranges were carried out using a reduced falloff curves formalism, which includes a recent implementation for the strong-collision broadening factors. The resulting values for the low-pressure rate coefficients are (2.2 +/- 0.4) x 10(-28)[He], (4.9 +/- 0.9) x 10(-28)[SF6], (1.9 +/- 0.3) x 10(-28)[Cl2] and (5.9 +/- 1.1) x 10(-28)[FC(O)OO(O)CF] cm3 molecule(-1) s(-1). The derived high-pressure rate coefficient is (4.4 +/- 0.8) x 10(-11) cm3 molecule(-1) s(-1). For the reaction Cl + FC(O)OCl --> Cl2 + FC(O)O a rate coefficient of (1.6 +/- 0.3) x 10(-11) cm3 molecule(-1) s(-1) was determined. The high-pressure rate coefficient was theoretically interpreted using SACM/CT calculations on an ab initio electronic potential computed at the G3S level of theory. Standard heat of formation values of -99.9 and -102.5 kcal mol(-1) were computed at the G3//B3LYP/6-311++G(3df,3pd) level of theory for cis-FC(O)OCl and trans-FC(O)OCl, respectively. The computed electronic barrier for the conversion between the trans and cis conformers is 8.9 kcal mol(-1). On the basis of the present results, the above reactions are expected to have a negligible impact on stratospheric ozone levels.

A Simple Method Relating Specific Rate Constants k(E,J) and Thermally Averaged Rate Constants k∞(T) of Unimolecular Bond Fission and the Reverse Barrierless Association Reactions

This work describes a simple method linking specific rate constants k(E,J) of bond fission reactions AB --> A + B with thermally averaged capture rate constants k(cap)(T) of the reverse barrierless combination reactions A + B --> AB (or the corresponding high-pressure dissociation or recombination rate constants k(infinity)(T)). Practical applications are given for ionic and neutral reaction systems. The method, in the first stage, requires a phase-space theoretical treatment with the most realistic minimum energy path potential available, either from reduced dimensionality ab initio or from model calculations of the potential, providing the centrifugal barriers E(0)(J). The effects of the anisotropy of the potential afterward are expressed in terms of specific and thermal rigidity factors f(rigid)(E,J) and f(rigid)(T), respectively. Simple relationships provide a link between f(rigid)(E,J) and f(rigid)(T) where J is an average value of J related to J(max)(E), i.e., the maximum J value compatible with E > or = E0(J), and f(rigid)(E,J) applies to the transitional modes. Methods for constructing f(rigid)(E,J) from f(rigid)(E,J) are also described. The derived relationships are adaptable and can be used on that level of information which is available either from more detailed theoretical calculations or from limited experimental information on specific or thermally averaged rate constants. The examples used for illustration are the systems C6H6+ <==> C6H5+ + H, C8H10+ --> C7H7+ + CH3, n-C9H12+ <==> C7H7+ + C2H5, n-C10H14+ <==> C7H7+ + C3H7, HO2 <==> H + O2, HO2 <==> HO + O, and H2O2 <==> 2HO.

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.