Pressure dependence and branching ratios in the decomposition of 1-pentyl radicals: shock tube experiments and master equation modeling

The decomposition and intramolecular H-transfer isomerization reactions of the 1-pentyl radical have been studied at temperatures of 880 to 1055 K and pressures of 80 to 680 kPa using the single pulse shock tube technique and additionally investigated with quantum chemical methods. The 1-pentyl radical was generated by shock heating dilute mixtures of 1-iodopentane and the stable products of its decomposition have been observed by postshock gas chromatographic analysis. Ethene and propene are the main olefin products and account for >97% of the carbon balance from 1-pentyl. Also produced are very small amounts of (E)-2-pentene, (Z)-2-pentene, and 1-butene. The ethene/propene product ratio is pressure dependent and varies from about 3 to 5 over the range of temperatures and pressures studied. Formation of ethene and propene can be related to the concentrations of 1-pentyl and 2-pentyl radicals in the system and the relative rates of five-center intramolecular H-transfer reactions and β C-C bond scissions. The 3-pentyl radical, formed via a four-center intramolecular H transfer, leads to 1-butene and plays only a very minor role in the system. The observed (E/Z)-2-pentenes can arise from a small amount of beta C-H bond scission in the 2-pentyl radical. The current experimental and computational results are considered in conjunction with relevant literature data from lower temperatures to develop a consistent kinetics model that reproduces the observed branching ratios and pressure effects. The present experimental results provide the first available data on the pressure dependence of the olefin product branching ratio for alkyl radical decomposition at high temperatures and require a value of <ΔE(down)(1000 K)> = (675 ± 100) cm(-1) for the average energy transferred in deactivating collisions in an argon bath gas when an exponential-down model is employed. High pressure rate expressions for the relevant H-transfer reactions and β bond scissions are derived and a Rice Ramsberger Kassel Marcus/Master Equation (RRKM/ME) analysis has been performed and used to extrapolate the data to temperatures between 700 and 1900 K and pressures of 10 to 1 × 10(5) kPa.     

A model study of intramolecular energy transfer in polyatomic molecular reactions

Summary This paper reports a model study of intramolecular energy transfer in unimolecular isomerization reaction of cyclobutanone. The calculations of intramolecular energy flow were carried out using the theory of Gray and Rice as extended by Zhao and Rice. The results of the calculations are compared to those of local Lyapunov function analysis, and the agreement is found to be uniformly good.     

Ab initio molecular orbital and RRKM calculations of the thermal decomposition of CH2BrO radical

A theoretical study of the thermal decomposition and isomerization channels of bromomethoxy radical is carried out using ab initio molecular orbital methods and RRKM theory. Three kinds of reaction pathways are examined, bond scission, intramolecular three-center HBr elimination and isomerization. Energy-specific rate coefficients k(E) and thermal rate constants k(T,P) are evaluated using the ab initio data and RRKM theory. Relevance to existing experimental evidence is discussed.     

Influence of vibrational energy flow on isomerization of flexible molecules: incorporating non-Rice-Ramsperger-Kassel-Marcus kinetics in the simulation of dipeptide isomerization

The conformational isomerization of a dipeptide, N-acetyl-tryptophan methyl amide (NATMA), is studied computationally by including important dynamical corrections to Rice-Ramsperger-Kassel-Marcus (RRKM) theory for the transition rate between pairs of isomers. The dynamical corrections arise from incomplete or sluggish vibrational energy flow in the dipeptide, a property suggested by the mode-selective chemistry that has been observed by Dian et al. [J. Chem. Phys. 120, 133 (2004)]. We compute the extent and rate of vibrational energy flow in NATMA quantum mechanically using local random matrix theory, which we then use to correct the RRKM theory rates. The latter rates are then introduced into a master equation to study the population dynamics of the dipeptide. Incomplete or slow vibrational energy flow is found to enhance the conformational selectivity of NATMA over RRKM estimates.     

Competition between reaction and intramolecular energy redistribution in solution: observation and nature of nonstatistical dynamics in the ozonolysis of vinyl ethers

Experimental product ratios in ozonolyses of alkyl vinyl ethers in solution do not fit with expectations based on statistical rate theories. The selectivity among cleavage pathways increases with the size of the alkyl group but to an extent that is far less than RRKM theory would predict. Trajectory studies account for the observed selectivities and support a mechanism involving a competition between cleavage of the primary ozonide and intramolecular vibrational energy redistribution. A statistical model is presented that assumes that RRKM theory holds for a molecular subset of the primary ozonides, allowing the rates of energy loss from the ozonides to be estimated from the observed product ratios.     

Computational studies on the thermal decomposition and isomerization of CHBr2O radical

The unimolecular decomposition study of dibromomethoxy radical, CHBr₂O, and its isomeric hydroxy dibromomethyl radical, CBr₂OH, is carried out using ab initio electronic molecular structure methods. Three kinds of reaction pathways are examined, C–H and C–Br bond scissions, intramolecular three-center HBr elimination and isomerization. Based on the ab initio results, energy-specific rate coefficients k(E) and thermal rate constants k(T,P) are evaluated using RRKM theory and master equation numerical analysis. Relevance to existing experimental evidence is discussed.     

Semiclassical quantum unimolecular reaction rate theory revisited

We describe a semiclassical quantum unimolecular reaction rate theory derived from the corresponding classical theory developed by Davis, Gray, Rice and Zhao (DGRZ). The analysis retains the intuitively useful mechanistic distinctions between intramolecular energy transfer and reaction, with the consequence that the semiclassical quantum theory version neglects some interference effects in the reaction dynamics. In the limiting case that intramolecular energy transfer is very fast compared to the rate of reaction we show that the DGRZ representation of the rate constant can be transformed, using the Weyl correspondence between quantum operators and classical variables, to the quantum flux–flux correlation function representation of the rate constant. In the more general case that the rate of intramolecular energy transfer influences the reaction dynamics, the semiclassical representation of the Wigner function for a classical system with both quasiperiodic and chaotic motion is used to obtain the reaction rate constant. Our analysis identifies the quantum analogue of the classical bottleneck to intramolecular energy transfer with the scars of unstable periodic orbits; it leads to a flux–flux correlation function representation of the rate constant for intramolecular energy transfer.     

H2S2的构型及其异构化反应的密度泛函理论研究

B3LYP calculations of density functional theory with the 6-311 + G（3df,2p）basis set level are used to investigate the equilibrium structures and intramolecular rearrangement reaction between the linear HSSH and branched H2SS isomers. The predicted geometrical parameters and scaled harmonic vibrational frequencies for HSSH are in good agreement with the available values experimentally. The predicted S-S and S-H bond lengths in the thiosulfoxide structure H2SS are 0.1986 and 0.1366 nm respectively and the values of 5SSH and 5HSH bond angles are 108. 3o and 89. 5o respectively. The transition-state for the unimolecular isomerization is suitably characterized by diagonalizing the matrix of energy second derivatives to determine the unique imaginary vibrational frequency and confirmed by the IRC calculation. The calculated results show that the linear structure is stable with respect to the branched form（lower 109.8 kJ/mol corrected with zero point vibrational energy）energetically. The calculated energy barrier for the direct intramolecular hydrogen atom transfer isomerization process is 190.3 kJ/mol. The kinetic results demonstrate that the isomerization is a unimolecular process,but the reaction rate is pretty slow. This agrees with the thermodynamical results. So the isomerization process should proceed via the other likely processes.     

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.     

Electron transfer to protonated beta-alanine N-methylamide in the gas phase: an experimental and computational study of dissociation energetics and mechanisms

Ammonium radicals derived from protonated beta-alanine N-methyl amide (BANMA) were generated by femtosecond collisional electron transfer to gas-phase cations prepared by chemical ionization and electrospray. Regardless of the mode of precursor ion preparation, the radicals underwent complete dissociation on the time scale of 5.15 micros. Deuterium isotope labeling and product analysis pointed out several competitive and convergent dissociation pathways that were not completely resolved by experiment. Ab initio calculations, which were extrapolated up to the CCSD(T)/6-311++G(3df,2p) level of theory, provided the proton affinity and gas-phase basicity of BANMA as PA = 971 kJ mol-1 and GB = 932 kJ mol-1 to form the most stable ion structure 1c+ in which the protonated ammonium group was internally solvated by hydrogen bonding to the amide carbonyl. Ion 1c+ was calculated to have an adiabatic recombination energy of 3.33 eV to form ammonium radical 1c*. The potential energy surface for competitive and consecutive isomerizations and dissociations of 1c* was investigated at correlated levels of theory and used for Rice-Ramsperger-Kassel-Marcus (RRKM) calculations. RRKM unimolecular rate constants suggested that dissociations starting from the ground electronic state of radical 1c* were dominated by loss of an ammonium hydrogen atom. In contrast, dissociations starting from the B excited state were predicted to proceed by reversible isomerization to an aminoketyl radical (1f*). The latter can in part dissociate by N-Calpha bond cleavage leading to the loss of the amide methyl group. This indicates that apparently competitive dissociations observed for larger amide and peptide radicals, such as backbone cleavages and losses of side-chain groups, may originate from different electronic states and proceed on different potential energy surfaces.     

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.     

Unimolecular dissociation of aniline molecular ion: A theoretical study

The potential energy surface (PES) for dissociation of aniline ion was determined using density functional theory molecular orbital calculations at the B3LYP/6-311+G(3df,2p)//B3LYP/6-31G(d) level. On the basis of the PES obtained, kinetic analysis was performed by Rice–Ramsperger–Kassel–Marcus (RRKM) calculations. The RRKM dissociation rate constants agreed well with previous experimental data. The most favorable channel was formation of the cyclopentadiene ion by loss of HNC, occurring through consecutive ring opening and re-closure to a five-membered ring. Loss of H could compete with the HNC loss at high energy, which occurred by direct cleavage of an N–H bond or through ring expansion.     

硝基胍H迁移异构化反应动力学的从头计算研究

Theoretical studies on the α- and β-forms nitroguanidine were carried out using ab initio theoretical methods, at the MP2/6-31G(d,p) level. The predicted geometrical parameters were in good agreement with the available theoretical values, which calculated by other author. The three C-N bond lengths in α-form nitroguanidine were different, the longest bond length was 1.430 A, the shortest was 1.283 A. But they were almost similar in β-form, the longest was 1.375 A, the shortest was 1.322 A. Therefore there were conjugative effects in β-form but not in α-form. The calculated results also show that the β-form is stable with respect to the α-form from energetically, lower 28.16 kJ/mol corrected with zero point vibrational energy. The transition-state for the unimolecular isomerization was conformed by the IRC calculation. The calculated energy barrier for the direct intramolecular hydrogen atom transfer isomerization process was 132.95 kJ/mol. The isomerization reaction, exothermal reaction, is a typical intramolecular hydrogen atom synfacial transfer reaction. Rate constants of the isomerization reaction were evaluated within the temperature range of 200-1773 K by the classical transition state theory. The rate constant was 1.99×10-11 s-1 and the equilibrium constant was 1.00×105 at 298 K. With the temperature increasing, the equilibrium value decayed and the reaction process was more difficult.     

Vibrational energy relaxation of the ND-stretching vibration of NH(2)D in liquid NH(3)

The vibrational energy relaxation from the first excited ND-stretching mode of NH(2)D dissolved in liquid NH(3) is studied using molecular dynamics simulations. The rate constants for inter- and intramolecular energy transfer are calculated in the framework of the quantum-classical Landau-Teller theory. At 273 K and an ammonia density of 0.642 g cm(-3) the calculated ND-stretch lifetime of τ = 9.1 ps is in good agreement with the experimental value of 8.6 ps. The main relaxation channel accounting for 52% of the energy transfer involves an intramolecular transition to the first excited state of the umbrella mode. The energy difference between both states is taken up by the near-resonant bending vibrations of the solvent. Less important for the ND-stretch lifetime are both the direct transition to the ground state and intramolecular relaxation via the NH(2)D bending modes contributing 23% each. Our calculations imply that the experimentally observed weak density dependence of τ is caused by detuning the resonance between the ND-stretch-umbrella energy gap and the solvent accepting modes which counteracts the expected linear increase of the relaxation rate with density.     

Experimental and theoretical studies of charge transfer and deuterium ion transfer between D2O+ and C2H4

The charge transfer and deuterium ion transfer reactions between D(2)O(+) and C(2)H(4) have been studied using the crossed beam technique at relative collision energies below one electron volt and by density functional theory (DFT) calculations. Both direct and rearrangement charge transfer processes are observed, forming C(2)H(4) (+) and C(2)H(3)D(+), respectively. Independent of collision energy, deuterium ion transfer accounts for approximately 20% of the reactive collisions. Between 22 and 36 % of charge transfer collisions occur with rearrangement. In both charge transfer processes, comparison of the internal energy distributions of products with the photoelectron spectrum of C(2)H(4) shows that Franck-Condon factors determine energy disposal in these channels. DFT calculations provide evidence for transient intermediates that undergo H/D migration with rearrangement, but with minimal modification of the product energy distributions determined by long range electron transfer. The cross section for charge transfer with rearrangement is approximately 10(3) larger than predicted from the Rice-Ramsperger-Kassel-Marcus isomerization rate in transient complexes, suggesting a nonstatistical mechanism for H/D exchange. DFT calculations suggest that reactive trajectories for deuterium ion transfer follow a pathway in which a deuterium atom from D(2)O(+) approaches the pi-cloud of ethylene along the perpendicular bisector of the C-C bond. The product kinetic energy distributions exhibit structure consistent with vibrational motion of the D-atom in the bridged C(2)H(4)D(+) product perpendicular to the C-C bond. The reaction quantitatively transforms the reaction exothermicity into internal excitation of the products, consistent with mixed energy release in which the deuterium ion is transferred in a configuration in which both the breaking and the forming bonds are extended.     

Combined CASSCF and MR-CI study on photoinduced dissociation and isomerization of acryloyl chloride

The potential energy surfaces of isomerization and dissociation reactions for CH2CHCOCl in the S0, T1, T2, and S1 states have been mapped with DFT, CASSCF, MP2, and MR-CI calculations. Rate constants for adiabatic and nonadiabatic processes have been calculated with the RRKM rate theory, in conjugation with the vibronic interaction method. Mechanistic photochemistry of CH2CHCOCl at 230-310 nm has been characterized through the computed potential energy surfaces and rate constants. Upon photoexcitation of CH2CHCOCl at 310 nm, the S1-->T1 intersystem crossing is the dominant primary process, which is followed by the 1,3-Cl migration along the T1 pathway. Meanwhile, the S1-->S0 internal conversion occurs with considerable probability and the subsequent trans-cis isomerization proceeds in the ground state. The C-Cl bond cleavage is an exclusive primary channel upon photoexcitation of gaseous CH2CHCOCl at 230 nm. The direct C-Cl bond cleavage is partially blocked by effects of the matrix, and the internal conversion from S1 to S0 becomes an important process for the excited molecule to deactivate in the condensed phase. The present calculations not only provide a reasonable explanation of the experimental findings, but also give new insight into the mechanistic photochemistry of CH2CHCOCl.     

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.     

Isomerization and decomposition reactions in the pyrolysis of branched hydrocarbons: 4-methyl-1-pentyl radical

The kinetics of the decomposition of 4-methyl-1-pentyl radicals have been studied from 927-1068 K at pressures of 1.78-2.44 bar using a single pulse shock tube with product analysis. The reactant radicals were formed from the thermal C-I bond fission of 1-iodo-4-methylpentane, and a radical inhibitor was used to prevent interference from bimolecular reactions. 4-Methyl-1-pentyl radicals undergo competing decomposition and isomerization reactions via beta-bond scission and 1, x-hydrogen migrations (x = 4, 5), respectively, to form short-chain radicals and alkenes. Major alkene products, in decreasing order of concentration, were propene, ethene, isobutene, and 1-pentene. The observed products are used to validate a RRKM/master equation (ME) chemical kinetics model of the pyrolysis. The presence of the branched methyl moiety has a significant impact on the observed reaction rates relative to analogous reaction rates in straight-chain radical systems. Systems that result in the formation of substituted radical or alkene products are found to be faster than reactions that form primary radical and alkene species. Pressure-dependent reaction rate constants from the RRKM/ME analysis are provided for all four H-transfer isomers at 500-1900 K and 0.1-1000 bar pressure for all of the decomposition and isomerization reactions in this system.     

Anharmonic Effect of N‐Propyl Peroxy Dissociation

The anharmonic and harmonic dissociation rate constants of alkylperoxy (RO₂) in different pathways, as well as those for the reactions of the n‐propyl peroxy radical, were calculated using the Rice–Ramsperger–Kassel–Marcus (RRKM) theory. When the temperature/total energy increased, the rate constants of the different pathways varied independently, causing changes in the dominating/leading products. Anharmonic rate constants were larger than harmonic rate constants, and their difference increased with increasing temperature/energy. Therefore, the anharmonic effect cannot be neglected. The rate‐determining steps of CH₃CH₂CH₂OO dissociation are discussed. Then the anharmonic effect was found clearly for CH₃CH₂CH₂OO dissociation, especially for the hydroperoxyalkyl radical (QOOH) dissociation. At low temperature, the rate constants were similar to those found from experiment, which indicated the RRKM theory was suitable for calculating the dissociation rates of RO₂ species.     

Large Nonstatistical Branching Ratio in the Dissociation of Pentane-2,4-dione Radical Cation: An Ab Initio Direct Classical Trajectory Study

The dissociation of pentane-2,4-dione radical cation has been studied by ab initio direct classical trajectory calculations at the MP2/6-31G(d) level of theory. A bond additivity correction has been used to improve the MP2 potential energy surface (BAC-MP2). A microcanonical ensemble was constructed using quasiclassical normal-mode sampling by distributing 10 kcal/mol of excess energy above ZPE for the transition state for the tautomerization of the enol with a terminal double bond, 4-hydroxypent-4-en-2-one radical cation, to the diketo form. A total of 244 trajectories were run starting from this transition state, yielding pentane-2,4-dione radical cation and depositing energy in the terminal CC bond. As a result, the branching ratio for dissociation of the terminal CC bond versus the interior CC bonds is significantly larger than expected from RRKM theory. The branching ratio for the dissociation of the two interior CC bonds is ～20:1, with the one closest to the activated methyl breaking more often. Since the two interior bonds are equivalent and should dissociate with equal probability, this branching ratio represents a very large deviation from statistical behavior. A simple kinetic scheme has been constructed to model the dissociation rates. The nonstatistical behavior is seen because the rate of energy flow within the molecule is comparable to or less than the rates of dissociation for the activated system. In addition to the expected dissociation products, some of the trajectories also lead to the formation of an ester-like product, prop-1-en-2-yl acetate radical cation.