CF3CH3 --> HF + CF2CH2: a non-RRKM reaction?

The experimental shock tube data recently reported by Kiefer et al. [J. Phys. Chem. A 2004, 108, 2443-2450] for the title reaction at temperatures between 1600 and 2400 K have been compared to master equation simulations using three models: (a) standard RRKM theory, (b) RRKM theory modified by local random matrix theory, which introduces dynamical corrections arising from slow intramolecular vibrational energy randomization, and (c) an ad hoc empirical non-RRKM model. Only the third model provides a good fit of the Kiefer et al. unimolecular reaction rate data. In separate simulations, all three models accurately reproduce the experimental 300 K chemical activation data of Marcoux and Setser [J. Phys. Chem. 1978, 82, 97-108] when the energy transfer parameters are freely varied to fit the data. When experimental energy transfer parameters for a geometrical isomer (1,1,2-trifluoroethane) are used, the standard RRKM model fits the chemical activation data better than the other models, but if energy transfer in the 1,1,1-trifluoroethane is significantly reduced in comparison to the 1,1,2 isomer, then the empirical ad hoc non-RRKM model also gives a good fit. While the ad hoc empirical non-RRKM model can be made to fit the data, it is not based on theory, and we argue that it is physically unrealistic. We also show that the master equation simulations can mimic the Kiefer et al. vibrational relaxation data, which was the first shock tube observation of double-exponential relaxation. We conclude that, until more data on the trifluoroethanes become available, the current evidence is insufficient to decide with confidence whether non-RRKM effects are important in this reaction, or whether the Kiefer et al. data can be explained in some other way.     

Quantifying the non-RRKM effect in the H + O2 ⇄ OH + O reaction

In the present investigation the non-RRKM behavior in the title reaction is quantified in two different ways: (1) Quasiclassical trajectory calculations of the thermal rate coefficient are compared with results from a microcanonical variational transition-state theory/RRKM model. Results on both the Varandas DMBE IV and Melius-Blint potentials indicate that the non-RRKM behavior acts to reduce the thermal rate coefficient by about a factor of two, independent of temperature from 250 K to 5500 K. The QCT thermal rate coefficients on the two potentials are in remarkably good agreement with experiment and with each other over the entire temperature range. (2) The non-RRKM behavior as a classical phenomenon is demonstrated and quantified on both potentials by a direct test of the fundamental assumption. Complex-forming classical trajectories, started as either O + OH or H + O₂, are shown preferentially to return to the region of configuration space from which they were started. This test is discussed in detail in the text. The transition of the non-RRKM behavior from classical to quantum mechanics is also discussed. © 1997 John Wiley & Sons, Inc. Int J Chem Kinet 29: 275–287, 1997.     

A shock tube and theoretical study on the pyrolysis of 1,4-dioxane

The dissociation of 1, 2 and 4% 1,4-dioxane dilute in krypton was studied in a shock tube using laser schlieren densitometry, LS, for 1550-2100 K with 56 ± 4 and 123 ± 3 Torr. Products were identified by time-of-flight mass spectrometry, TOF-MS. 1,4-dioxane was found to initially dissociate via C-O bond fission followed by nearly equal contributions from pathways involving 2,6 H-atom transfers to either the O or C atom at the scission site. The 'linear' species thus formed (ethylene glycol vinyl ether and 2-ethoxyacetaldehyde) then dissociate by central fission at rates too fast to resolve. The radicals produced in this fission break down further to generate H, CH(3) and OH, driving a chain decomposition and subsequent exothermic recombination. High-level ab initio calculations were used to develop a potential energy surface for the dissociation. These results were incorporated into an 83 reaction mechanism used to simulate the LS profiles with excellent agreement. Simulations of the TOF-MS experiments were also performed with good agreement for consumption of 1,4-dioxane. Rate coefficients for the overall initial dissociation yielded k(123Torr) = (1.58 ± 0.50) × 10(59) × T(-13.63) × exp(-43970/T) s(-1) and k(58Torr) = (3.16 ± 1.10) × 10(79) × T(-19.13) × exp(-51326/T) s(-1) for 1600 < T < 2100 K.     

Post-transition state dynamics for propene ozonolysis: Intramolecular and unimolecular dynamics of molozonide

A direct chemical dynamics simulation, at the B3LYP6-31G(d) level of theory, was used to study the post-transition state intramolecular and unimolecular dynamics for the O3 + propene reaction. Comparisons of B3LYP6-31G(d) with CCSD(T)/cc-pVTZ and other levels of theory show that the former gives accurate structures and energies for the reaction's stationary points. The direct dynamics simulations are initiated at the anti and syn O3 + propene transition states (TSs) and the TS symmetries are preserved in forming the molozonide intermediates. Anti<-->syn molozonide isomerization has a very low barrier of 2-3 kcalmol and its Rice-Ramsperger-Kassel-Marcus (RRKM) lifetime is 0.3 ps. However, the trajectory isomerization is slower and it is unclear whether this anti<-->syn equilibration is complete when the trajectories are terminated at 1.6 ps. The syn (anti) molozonides dissociate to CH3CHO + H2COO and H2CO + syn (anti) CH3CHOO. The kinetics for the latter reactions are in overall good agreement with RRKM theory, but there is a symmetry preserving non-RRKM dynamical constraint for the former. Dissociation of anti molozonide to CH3CHO + H2COO is enhanced and suppressed, respectively, for the trajectory ensembles initiated at the anti and syn O3 + propene TSs. The dissociation of syn molozonide to CH3CHO + H2COO may also be enhanced for trajectories initiated at the syn O3 + propene TS. At the time the trajectories are terminated at 1.6 ps, the ratio of the trajectory and RRKM values of the CH3CHO + H2COO product yield is 1.6 if the symmetries of the initiation and dissociation TSs are the same and 0.6 if their symmetries are different. There are coherences in the intramolecular energy flow, which depend on molozonide's symmetry (i.e., anti or syn). This symmetry related dynamics is not completely understood, but it is clearly related to the non-RRKM dynamics for anti<-->syn isomerization and anti molozonide dissociation to CH3CHO + H2COO. Correlations are found between the stretching motions of molozonide, indicative of nonchaotic and non-RRKM dynamics. The non-RRKM dynamics of molozonide dissociation partitions vibration energy to H2COO that is larger than statistical partitioning. Though the direct dynamics simulations are classical, better agreement is obtained using quantum instead of classical harmonic RRKM theory. This may result from the neglect of anharmonicity in the RRKM calculations, the non-RRKM dynamics of the classical trajectories, or a combination of these two effects. The trajectories suggest that the equilibrium syn/anti molozonide ratio is approximately 1.1-1.2 times larger than that predicted by the harmonic densities of state, indicating an anharmonic correction.     

An experimental and theoretical high temperature kinetic study of the thermal unimolecular dissociation of fluoroethane

The thermal dissociation of fluoroethane has been studied using shock tube (ST)/time-of-flight mass spectrometry (TOF-MS) at 500 and 1200 Torr over the temperature range 1200-1550 K. The ST/TOF-MS experiments confirm that elimination of HF is the only reaction channel and rate coefficients for this reaction were extracted from concentration/time profiles derived from the mass spectra. Results from a novel diaphragmless shock tube coupled to the TOF-MS are also presented and demonstrate the unique ability of this apparatus to generate sufficiently reproducible shock waves that signal averaging can be performed over multiple experiments; something that is not possible with a conventional shock tube. The dissociation is also studied with ab initio transition state theory based master equation simulations. A modest increase in the calculated barrier height (i.e., by 1 kcal mol(-1)) yields predicted high pressure rate coefficients that are in good agreement with the existing literature data. The present pressure dependent observations are accurately reproduced for a downwards energy transfer for neon at 1200 to 1500 K of approximately 270 cm(-1), which is somewhat smaller than that found in previous studies on fluorinated ethanes with the same bath gases.     

Non-RRKM dynamics in the CH3O2 + NO reaction system

Quasi-classical trajectory (QCT) calculations on a model potential energy surface (PES) show strong deviations from statistical Rice-Ramsperger-Kassel-Marcus (RRKM) rate theory for the decomposition reaction (1) CH3OONO* --> CH3O + NO2, where the highly excited CH3OONO* was formed by (2) CH3O2 + NO --> CH3OONO*. The model PES accurately describes the vibrational frequencies, structures, and thermochemistry of the cis- and trans-CH3OONO isomers; it includes cis-trans isomerization in addition to reactions 1 and 2 but does not include nitrate formation, which is too slow to affect the decay rate of CH3OONO*. The QCT results give a strongly time-dependent rate constant for decomposition and damped oscillations in the decomposition rate, not predicted by statistical rate theory. Anharmonicity is shown to play an important role in reducing the rate constant by a factor of 10 smaller than predicted using classical harmonic RRKM theory (microcanonical variational transition state theory). Master equation simulations of organic nitrate yields published previously by two groups assumed that RRKM theory is accurate for reactions 1 and 2 but required surprising parametrizations to fit experimental nitrate yield data. In the present work, it is hypothesized that the non-RRKM rate of reaction (1) and vibrational anharmonicity are at least partly responsible for the surprising parameters.     

On modeling the pressure-dependent photoisomerization of trans-stilbene by including slow intramolecular vibrational energy redistribution

Experimental data for the photoisomerization of trans-stilbene (S(1)) in thermal bath gases at pressures up to 20 bar obtained previously by Meyer, Schroeder, and Troe (J. Phys. Chem. A 1999, 103, 10528-10539) are modeled by using a full collisional-reaction master equation that includes non-RRKM (Rice-Ramsperger-Kassel-Marcus) effects due to slow intramolecular vibrational energy redistribution (IVR). The slow IVR effects are modeled by incorporating the theoretical results obtained recently by Leitner et al. (J. Phys. Chem. A 2003, 107, 10706-10716), who used the local random matrix theory. The present results show that the experimental rate constants of Meyer et al. are described to within about a factor of 2 over much of the experimental pressure range. However, a number of assumptions and areas of disagreement will require further investigation. These include a discrepancy between the calculated and experimental thermal rate constants near zero pressure, a leveling off of the experimental rate constants that is not predicted by theory and which depends on the identity of the collider gas, the need to use rate constants for collision-induced IVR that are larger than the estimated total collision rate constants, and the choice of barrier-crossing frequency. Despite these unsettled issues, the theory of Leitner et al. shows great promise for accounting for possible non-RRKM effects in an important class of reactions.     

Relaxation, incubation, and dissociation in CO2

The dissociation and relaxation of CO2 has been reexamined in the incident shock wave with the laser-schlieren technique. These new experiments covered 1377-6478 K, and 42-750 Torr, and improvements partly described herein have permitted accurate determination of both rate and incubation time. In general the steady rate measurements are in agreement with other recent determinations. The one anomaly is that the new rates are not fully second order; they vary about 50% over 70-600 Torr. This unexpected feature is actually quite consistent with the recent literature, which shows a similar trend. However, attempts to produce this result with RRKM calculations were unsuccessful. Relaxation times are in agreement with available literature, and incubation time to relaxation time ratios lie between 1.5 and 3 over 4000-6600 K, consistent with findings for other molecules. These ratios are much smaller than those recently derived from reflected-shock experiments by Oehlschlaeger et al. (Z. Phys. Chem. 2005, 219, 555). A simple argument suggests such large values are indeed anomalous, although why they are too large is not clear.     

Can a single oxidant with two spin states masquerade as two different oxidants? A study of the sulfoxidation mechanism by cytochrome p450

Density functional calculations were performed on the sulfoxidation reaction by a model compound I (Cpd I) of cytochrome P450. By contrast to previous alkane hydroxylation studies, which exhibit a dominant low-spin (LS) pathway, the sulfoxidation follows a dominant high-spin (HS) reaction. Thus, competing hydroxylation and sulfoxidation processes as observed for instance by Jones et al. (Volz, T. J.; Rock, D. A.; Jones, J. P. J. Am. Chem. Soc. 2002, 124, 9724) are the result of a two-state reactivity scenario, whereby the hydroxylation originates from the LS pathway and the sulfoxidation from the HS pathway. In this manner, two spin states of a single oxidant (Cpd I) can be disguised as two different oxidants. The calculations rule out the possibility that a second oxidant (the ferric peroxide, Cpd 0 species) interferes in the observed results of Jones et al.     

A crossed beam and ab initio study of the reaction of atomic boron with ethylene

The reaction of atomic boron, B(2P), with the simplest alkene, C2H4, has been investigated under single collision conditions in crossed beam experiments with mass spectrometric detection. Our experimental data clearly showed that the atomic boron versus hydrogen exchange reaction led to molecule(s) of gross formula C2H3B via bound intermediate(s). According to the experimentally derived fraction of the available energy released as product translational energy, we propose that an important reaction pathways is the one leading to the borirene plus atomic hydrogen and/or the one leading to ethynylborane plus atomic hydrogen. The experimental results are accompanied by electronic structure calculations of the relevant potential energy surface and RRKM estimates of the product branching ratio. According to RRKM calculations, within the limit of complete energy randomization, the three isomers borirene, BH=C=CH2 and BH2-CCH, are all formed, with BH2-CCH being the dominant one. The discrepancies between the trend of the product translational energy distributions and the picture emerging from RRKM estimates are a symptom that a statistical treatment is not warranted for this system.     

Thermal dissociation of ethylene glycol vinyl ether

The pyrolysis of ethylene glycol vinyl ether (EGVE), an initial product of 1,4-dioxane dissociation, was examined in a diaphragmless shock tube (DFST) using laser schlieren densitometry (LS) at 57 ± 2 and 122 ± 3 Torr over 1200-1800 K. DFST/time-of-flight mass spectrometry experiments were also performed to identify reaction products. EGVE was found to dissociate via two channels: (1) a molecular H atom transfer/C-O scission to produce C(2)H(3)OH and CH(3)CHO, and (2) a radical channel involving C-O bond fission generating ˙CH(2)CH(2)OH and ˙CH(2)CHO radicals, with the second channel being strongly dominant over the entire experimental range. A reaction mechanism was constructed for the pyrolysis of EGVE which simulates the LS profiles very well over the full experimental range. The decomposition of EGVE is clearly well into the falloff region for these conditions, and a Gorin model RRKM fit was obtained for the dominant radical channel. The results are in good agreement with the experimental data and suggest the following rate coefficient expressions: k(2,∞) = (6.71 ± 2.6) × 10(27) × T(-3.21)exp(-35512/T) s(-1); k(2)(120 Torr) = (1.23 ± 0.5) × 10(92) × T(-22.87)exp(-48?248/T) s(-1); k(2)(60 Torr) = (2.59 ± 1.0) × 10(88) × T(-21.96)exp(-46283/T) s(-1).     

Exploring the dynamics of reaction N((2)D)+C2H4 with crossed molecular-beam experiments and quantum-chemical calculations

We conducted the title reaction using a crossed molecular-beam apparatus, quantum-chemical calculations, and RRKM calculations. Synchrotron radiation from an undulator served to ionize selectively reaction products by advantage of negligibly small dissociative ionization. We observed two products with gross formula C(2)H(3)N and C(2)H(2)N associated with loss of one and two hydrogen atoms, respectively. Measurements of kinetic-energy distributions, angular distributions, low-resolution photoionization spectra, and branching ratios of the two products were carried out. Furthermore, we evaluated total branching ratios of various exit channels using RRKM calculations based on the potential-energy surface of reaction N((2)D)+C(2)H(4) established with the method CCSD(T)/6-311+G(3df,2p)//B3LYP/6-311G(d,p)+ZPE[B3LYP/6-311G(d,p)]. The combination of experimental and computational results allows us to reveal the reaction dynamics. The N((2)D) atom adds to the C=C π-bond of ethene (C(2)H(4)) to form a cyclic complex c-CH(2)(N)CH(2) that directly ejects a hydrogen atom or rearranges to other intermediates followed by elimination of a hydrogen atom to produce C(2)H(3)N; c-CH(2)(N)CH+H is the dominant product channel. Subsequently, most C(2)H(3)N radicals, notably c-CH(2)(N)CH, further decompose to CH(2)CN+H. This work provides results and explanations different from the previous work of Balucani et al. [J. Phys. Chem. A, 2000, 104, 5655], indicating that selective photoionization with synchrotron radiation as an ionization source is a good choice in chemical dynamics research.     

Proton mobility in protonated peptides: a joint molecular orbital and RRKM study

The mobile proton model was critically evaluated by using purely theoretical models which include quantum mechanical calculations to determine stationary points on the potential energy surface (PES) of a model compound, and Rice-Ramsperger-Kassel-Marcus (RRKM) calculations to determine the rate constants of various processes (conformational changes, proton transfer reactions) which occur during mass analysis of protonated peptides. Extensive mapping of the PES of protonated N-formylglycinamide resulted in various minima which were stabilized by one or more of the following types of interaction: internal hydrogen bond, charge transfer interaction, charge delocalization, and ring formation. The relative energies of most of the investigated minima are less then 20 kcal mol(-1) compared with the most stable species. More importantly, the relative energies of the transition structures connecting these minima are fairly low, allowing facile transitions among the energetically low-lying species. It is demonstrated that a path can be found leading from the energetically most stable species, protonated on an amide oxygen, to the structure from which the energetically most favorable fragmentation occurs. It is also shown that the added proton can sample all protonation sites prior to fragmentation. The RRKM calculations applied the results of ab initio computations (structures, energetics, vibrational frequencies) to the reactions (internal rotations, proton transfers) occurring in protonated N-formylglycinamide, and clearly lend additional evidence to the mobile proton model. Based on the results of the PES search on protonated N-formylglycinamide, we also comment on the mechanism proposed by Arnot et al. (Arnot D, Kottmeier D, Yates N, Shabanowitz J, Hunt D F. 42(nd) ASMS Conference on Mass Spectrometry, 1994; 470) and Reid et al. (Reid G E, Simpson R J, O'Hair R A J. J. Am. Soc. Mass Spectrom. 1998; 9:945) for the formation of b(2)(+) ions. According to the high level ab initio results, the mechanism relying on amide oxygen protonated species seems to be less feasible than the one which involves N-protonated species.     

Thermal decomposition of methyl nitrite in shock waves studied by laser probing

The unimolecular decomposition of methyl nitrite in the temperature range 680–955 K and pressure range 0.64 to 2.0 atm has been studied in shock-tube experiments employing real-time absorption of CW CO laser radiation by the NO product. Computer kinetic modeling using a set of 23 reactions shows that NO product is relatively unreactive. Its initial rate of production can be used to yield directly the unimolecular rate constant, which in the fall-off region, can be represented by the second-order rate coefficient in the Arrhenius form: A RRKM model calculation, assuming a loose CH₃ONO^≠ complex with two degrees of free internal rotation, gives good agreement with the experimental rate constants.     

Comparisons of classical chemical dynamics simulations of the unimolecular decomposition of classical and quantum microcanonical ensembles

Previous studies have shown that classical trajectory simulations often give accurate results for short-time intramolecular and unimolecular dynamics, particularly for initial non-random energy distributions. To obtain such agreement between experiment and simulation, the appropriate distributions must be sampled to choose initial coordinates and momenta for the ensemble of trajectories. If a molecule's classical phase space is sampled randomly, its initial decomposition will give the classical anharmonic microcanonical (RRKM) unimolecular rate constant for its decomposition. For the work presented here, classical trajectory simulations of the unimolecular decomposition of quantum and classical microcanonical ensembles, at the same fixed total energy, are compared. In contrast to the classical microcanonical ensemble, the quantum microcanonical ensemble does not sample the phase space randomly. The simulations were performed for CH(4), C(2)H(5), and Cl(-)---CH(3)Br using both analytic potential energy surfaces and direct dynamics methods. Previous studies identified intrinsic RRKM dynamics for CH(4) and C(2)H(5), but intrinsic non-RRKM dynamics for Cl(-)---CH(3)Br. Rate constants calculated from trajectories obtained by the time propagation of the classical and quantum microcanonical ensembles are compared with the corresponding harmonic RRKM estimates to obtain anharmonic corrections to the RRKM rate constants. The relevance and accuracy of the classical trajectory simulation of the quantum microcanonical ensemble, for obtaining the quantum anharmonic RRKM rate constant, is discussed.     

Ab initio molecular dynamics-based assignment of the protonation state of pepstatin A/HIV-1 protease cleavage site

A recent 13C NMR experiment (Smith et al. Nature Struct. Biol. 1996, 3, 946-950) on the Asp 25-Asp25' dyad in pepstatin A/HIV-1 protease measured two separate resonance lines, which were interpreted as being a singly protonated dyad. We address this issue by performing ab initio molecular dynamics calculations on models for this site accompanied by calculations of 13C NMR chemical shifts and isotopic shifts. We find that already on the picosecond time-scale the model proposed by Smith et al. is not stable and evolves toward a different monoprotonated form whose NMR pattern differs from the experimental one. We suggest, instead, a different protonation state in which both aspartic groups are protonated. Despite the symmetric protonation state, the calculated 13C NMR properties are in good agreement with the experiment. We rationalize this result using a simple valence bond model, which explains the chemical inequality of the two C sites. The model calculations, together with our calculations on the complex, allow also the rationalization of 13C NMR properties on other HIV-1 PR/inhibitor complexes. Both putative binding of the substrate to the free enzyme, which has the dyad singly protonated (Piana, S.; Carloni, P. Proteins: Struct., Funct., Genet. 2000, 39, 26-36), and pepstatin A binding to the diprotonated form are consistent with the inverse solvent isotope effect on the onset of inhibition of pepsin by pepstatin and the kinetic iso-mechanism proposed for aspartic proteases (Cho, T.-K.; Rebholz, K.; Northrop, D.B. Biochemistry 1994, 33, 9637-9642).     

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.     

Experimental and theoretical differential cross sections for the N(2D) + H2 reaction

In this paper, we report a combined experimental and theoretical study on the dynamics of the N(2D) + H2 insertion reaction at a collision energy of 15.9 kJ mol(-1). Product angular and velocity distributions have been obtained in crossed beam experiments and simulated by using the results of quantum mechanical (QM) scattering calculations on the accurate ab initio potential energy surface (PES) of Pederson et al. (J. Chem. Phys. 1999, 110, 9091). Since the QM calculations indicate that there is a significant coupling between the product angular and translational energy distributions, such a coupling has been explicitly included in the simulation of the experimental results. The very good agreement between experiment and QM calculations sustains the accuracy of the NH2 ab initio ground state PES. We also take the opportunity to compare the accurate QM differential cross sections with those obtained by two approximate methods, namely, the widely used quasiclassical trajectory calculations and a rigorous statistical method based on the coupled-channel theory.     

The pressure and temperature dependence of methane decomposition

Single-channel hindered Gorin model RRKM calculations were performed on reaction (1). (1) Good agreement between theory and experiment was obtained for the temperature and pressure dependence of reaction (1). Isotopic data for the reverse association reaction, (?1), reported previously, are consistent with the model. Rate constants were cast in the form of an analytical expression and appropriate parameters were tabulated.