Theory of Multichannel Thermal Unimolecular Reactions. 2. Application to the Thermal Dissociation of Formaldehyde

Thermal Decomposition of 2-Methyltetrahydrofuran behind Reflected Shock Waves over the Temperature Range of 1179-1361 K

The thermal unimolecular decomposition of 2-methyltetrahydrofuran (2-MTHF) was studied behind reflected shock waves in a single-pulse shock tube over the temperature range of 1179-1361 K and pressure range of 9-17 atm. Methane, ethylene, ethane, 1,3-butadiene, propylene, acetaldehyde, and acetylene were identified as products in the decomposition of 2-MTHF. A reaction scheme was proposed to explain the mechanism for the observed products. The experimentally determined rate coefficients were best fit to an Arrhenius expression for the overall decomposition and is represented as k_total^exp(1179-1361 K) = (3.23 ± 0.59) × 10¹¹ s^-1 exp(-51.3 ± 1.4 kcal mol^-1/RT). Quantum chemistry methods were used to calculate the energetics and kinetics of various possible unimolecular dissociation pathways involved in the thermal decomposition of 2-MTHF. The initial decomposition of 2-MTHF occurs predominantly via ring-methyl (C-CH₃) single bond fission, leading to the formation of tetrahydrofuran (C₄H₇O) radical, and methyl radical was found to be the major reaction compared to all the possible initial bond fission, ring opening, and molecular elimination channels. The temperature-dependent rate coefficients for the unimolecular dissociation of 2-MTHF were calculated using the RRKM (Rice-Ramsperger-Kassel-Marcus) theory in combination with the CCSD(T)/cc-pVTZ//B3LYP/cc-pVTZ level of electronic structure calculations over the temperature range of 800-1500 K. The computed high-pressure limiting rate coefficients for the initial decomposition of 2-MTHF through C-CH₃ single bond fission channel were found to be ∼2 times higher in the temperatures between 800 and 900 K, and above this temperature, they agree well with the values reported in the literature.

Two-Dimensional Master Equation Modeling of Some Multichannel Unimolecular Reactions

Multichannel thermal decomposition reactions of n-propyl radicals, 1-pentyl radicals, and toluene are investigated by solving a two-dimensional master equation formulated as a function of total energy (E) and angular momentum (J). The primary aim of this study is to elucidate the role of angular momentum in the kinetics of multichannel unimolecular reactions. The collisional transition processes of the reactants colliding with argon are characterized based on the classical trajectory calculations and implemented in the master equation. The rate constants calculated by using the two-dimensional master equation are compared with those of one-dimensional master equations. The consequence of the explicit treatment of angular momentum depends on the J dependence of the microscopic rate constants and is particularly emphasized in the thermal decomposition of toluene, for which the C-H and C-C bond fission channels are considered. The centrifugal effect is insignificant in the energetically favored C-H bond fission but is substantial in the energetically higher C-C bond fission, which causes rotational channel switching of the microscopic rate constants. The proper treatment of the J-dependent channel coupling effect, weak collisional transfer of J, and initial-J-dependent collisional energy transfer are found to be essential for predicting the branching fractions at low pressures.

Simplified Representation of Multichannel Thermal Unimolecular Reactions. II. Refined Parametrization of Formaldehyde Dissociation

Simplified representations of branching fractions for thermal unimolecular two-channel reactions are discussed. The dissociation of formaldehyde serves as an illustrative example. Quantum-corrected classical trajectory calculations on an ab initio potential energy surface are combined with master equation calculations for collisional energy transfer. The treatment accounts for roaming atom dynamics. The dependence of the channel branching fractions on the bath gas pressure and temperature, on the collision efficiencies, and on the difference of channel threshold energies, are explored. It is discussed to what extent the derived simplified representations of channel branching fractions can be generalized.

Modeling Collisional Transitions in Thermal Unimolecular Reactions: Successive Trajectories and Two-Dimensional Master Equation for Trifluoromethane Decomposition in an Argon Bath

Collisional transition processes in thermal unimolecular reactions are modeled by collision frequency, Z, and probability distribution function, P(E, J; E', J'), which describes the probabilities of collisional transitions from the initial state specified by the total energy and angular momentum, (E', J'), to the final states, (E, J). The validity of the collisional transition model, consisting of Z and P(E, J; E', J'), is assessed here for the title reaction. The present model and its parameters are derived from the moments of transition probabilities calculated by classical trajectory simulations. The model explicitly accounts for coupling between the energy and angular momentum transfer and the dependence of transition probability on the initial state. The performance of the model is evaluated by comparing the rate constants calculated by solving the two-dimensional master equation with those obtained from the classical trajectory calculations of the sequence of successive collisions. The rate constants are also compared with available experimental data. The present collisional transition model is found to perform fairly well for predicting the pressure-dependent rate constants. The uncertainty in the prediction and sensitivities of the rate constants to the model parameters are discussed. A simplified version of the model is proposed, which performs as well as the full model. The simplifications and robust procedures for calculating the model parameters are described.

Simplified Analysis and Representation of Multichannel Thermal Unimolecular Reactions

Two-channel and multichannel thermal unimolecular reactions are analyzed by simple models, starting with the calculation of separated-channel rate constants and accounting for intrinsic channel coupling afterward. Reactions with rigid- and with loose-activated complex channels are distinguished. Weak-collision, energy-transfer, effects are suggested to govern the competition between rigid-activated complex channels, while angular-momentum, "rotational channel switching", effects dominate the competition between rigid- and loose-activated complex channels. The models are tested against master equation treatments of the dissociations of formaldehyde and of glyoxal from the literature. Besides giving insight into the influence of various molecular input parameters, the present approach leads to compact representations of rate constants suitable for inclusion in databases.

Experimental and modelling study of the multichannel thermal dissociations of CH3F and CH2F

The thermal unimolecular dissociation of CH₃F was studied in shock waves by monitoring the UV absorption of a dissociation product identified as CH₂F.

Dissociation channels, collisional energy transfer, and multichannel coupling effects in the thermal decomposition of CH3F

The multichannel character of the thermal decomposition of CH₃F and its dependency on the collisional energy transfer model are elucidated.

Primary Formation Path of Formaldehyde in Hydrothermal Vents

Formaldehyde is abundant in the universe and one of the fundamental molecules for life. Hydrothermal vents produce a substantial amount of hydrogen molecules by serpentinization and promote reductive reactions of single carbon compounds. The abundance of formaldehyde is expected to be low due to the high Gibbs free energy in hydrothermal vents. We consider two competing formation pathways of formaldehyde: (1) the reduction of CO by H₂ and (2) the reduction of HCOOH by H₂ to form a methanediol, followed by the dehydration of the methanediol. We performed a number of quantum chemical simulations to examine the formation of formaldehyde in the gas phase as well as in aqueous solution. The energy barrier is significantly reduced by the catalytic effect of water molecules in aqueous solution and becomes lowest when a water cluster consisted of 5 water molecules catalyzes the reduction. The energy barrier to form a methanediol by the reduction of HCOOH is lower by 17.5 kcal/mol than that to form a formaldehyde by the reduction of CO. Considering the low energy barrier to dehydrate methanediol, the primary pathway to form formaldehyde in hydrothermal vents is concluded to be the reduction of HCOOH by H₂, followed by the dehydration of methanediol.

Simplified Representation of Partial and Total Rate Constants of Complex-Forming Bimolecular Reactions

The temperature and pressure dependence of partial and total rate constants of complex-forming bimolecular reactions are investigated with the goal to obtain simplified and compact rate constant expressions suitable for data compilations. The transition of the reactions from low pressure chemical activation to high pressure association character is analyzed. The two processes are modeled separately first by solving master equations, leading to "inverse" and "normal" falloff curves, respectively, and allowing for a compact representation of the separated rate constants. It is shown that broadening factors of the two falloff curves are different, and those of chemical activation often approaching unity. Coupling of the two separate processes then is modeled in a simplified manner. Finally, thermal redissociation of the adducts formed by association is accounted for.

Photodissociation dynamics of the reaction H2CO-->H+HCO via the singlet (S0) and triplet (T1) surfaces

We have explored the photodissociation dynamics of the reaction H(2)CO+hnu-->H+HCO in the range of 810-2600 cm(-1) above the reaction threshold. Supersonically cooled formaldehyde was excited into selected J(Ka,Kc) rotational states of six vibrational levels (1(1)4(1), 5(1), 2(2)6(1), 2(2)4(3), 2(3)4(1), and 2(4)4(1)) in the A((1)A2) state. The laser induced fluorescence spectra of the nascent HCO fragment provided detailed product state distributions. When formaldehyde was excited into the low-lying levels 1(1)4(1), 5(1), and 2(2)6(1), at E(avail)<1120 cm(-1), the product state distribution can be modeled qualitatively by phase space theory. These dynamics are interpreted as arising from a reaction path on the barrierless S0 surface. When the initial states 2(2)4(3) and 2(3)4(1) were excited (E(avail)=1120-1500 cm(-1)), a second type of product state distribution appeared. This second distribution peaked sharply at low N, Ka and was severely truncated in comparison with those obtained from the lower lying states. At the even higher energy of 2(4)4(1) (E(avail) approximately 2600 cm(-1)) the sharply peaked distribution appears to be dominant. We attribute this change in dynamics to the opening up of the triplet channel to produce HCO. The theoretical height of the barrier on the T1 surface lies between 1700 and 2100 cm(-1) and so we consider the triplet reaction to proceed via tunneling at the intermediate energies and proceed over the barrier at the higher energies. Considerable population was observed in the excited (0,0,1) state for all initial H(2)CO states that lie above the appearance energy. Rotational populations in the (0,0,1) state dropped more rapidly with (N,Ka) than did the equivalent populations in (0,0,0). This indicates that, although individual rotational states are highly populated in (0,0,1), the total v3=1 population might not be so large. Specific population was also measured in the almost isoenergetic Kc and J states. No consistent population preference was found for either asymmetry or spin-rotation component.

Phase Space Analysis of Formaldehyde Dissociation Branching and Comparison with Quasiclassical Trajectory Calculations†

We investigate the dependence of the branching ratio of formaldehyde dissociation to molecular and radical products on the total energy and angular momentum and the HCO rotational state distributions by using a combination of transition state/Rice-Ramsperger-Kassel-Marcus theory and phase space theory. Comparisons are made with recent quasiclassical trajectory (QCT) calculations [Farnum, J. D.; Zhang, X.; Bowman, J. M. J. Chem. Phys. 2007, 126, 134305]. The combined phase-space analysis is in semiquantitative agreement with the QCT results for the rotational distributions of HCO but is only in qualitative agreement for the branching ratio. Nevertheless, that level of agreement serves to provide insight into the QCT results, which showed suppression of the radical channel with increasing total angular momentum for a fixed total energy.

Formaldehyde photodissociation: Dependence on total angular momentum and rotational alignment of the CO product

Quasiclassical trajectory calculations are reported to investigate the effects of rotational excitation of formaldehyde on the branching ratios of the fragmentation products, H2+CO and H+HCO. The results of tens of thousands of trajectories show that increased rotational excitation causes suppression of the radical channel and enhancement of the molecular channel. Decomposing the molecular channel into "direct" and "roaming" channels shows that increased rotation switches from suppressing to enhancing the roaming products across our chosen energy range. However, decomposition into these pathways is difficult because the difference between them does not appear to have a distinct boundary. A vector correlation investigation of the CO rotation shows different characteristics in the roaming versus direct channels and this difference is a potentially useful signature of the roaming mechanism, as first speculated by Kable and Houston in their experimental study of photodissociation of acetaldehyde [P. L. Houston and S. H. Kable, Proc. Nat. Acad. Sci. 103, 16079 (2006)].

Analysis of Quantum Yields for the Photolysis of Formaldehyde at λ > 310 nm

Experimental quantum yields of the photolysis of formaldehyde at lambda > 310 nm are combined with absolute and relative rate calculations for the molecular elimination H2CO --> H2 + CO (1), the bond fission H2CO --> H + HCO (2), and the intramolecular hydrogen abstraction H2CO --> H ... HCO --> H2 + CO (3) taking place in the electronic ground state. Temperature and pressure dependencies of the quantum yields are analyzed with the goal to achieve consistency between experiment and modeling. Two wavelength ranges with considerably different properties are considered: 340-360 nm, where channel 1 competes with collisional deactivation of excited molecules, and 310-340 nm, which is dominated by the competition between the formation of radical and molecular products. The close relation between photolysis and pyrolysis of formaldehyde, such as analyzed for the pyrolysis in the companion paper, is documented and an internally consistent treatment of the two reaction systems is provided. The quantum yields are modeled and represented in analytical form such that values outside the available experimental range can be predicted to some extent.

Refined Analysis of the Thermal Dissociation of Formaldehyde

New experimental results for the thermal dissociation of formaldehyde to radical and molecular products (Proc. Combust. Inst. 2007, 31, in press) form the basis of the present analysis of the respective low-pressure rate coefficients k(Rad,0) and k(Mol,0) of the reaction. The article supersedes an earlier analysis (J. Phys. Chem. A 2005, 109, 8320) which used less accurate and more preliminary input information. In addition, refined rotational factors F(rot) are determined and specific energy and angular momentum dependent branching ratios from a more detailed analysis of photolysis quantum yields (J. Phys. Chem. A 2007, 111, 3868) are employed as well. It is emphasized again that pyrolysis and photolysis are intimately related and should be analyzed in an internally consistent manner. The combination of the new with earlier experimental results for pyrolysis rates allows one to fit the height of the energy barrier for the molecular elimination channel with improved precision. A value of E0,1 = 81.7(+/-0.5) kcal mol(-1) is obtained. In addition, employing anharmonicity factors F(anh) from the earlier work, a total average energy transferred per collision of -DeltaE/hc = 100(+/-20) cm(-1) is fitted from the experiments in the bath gas Ar. This value is consistent with the value -DeltaE/hc = 80(+/-40) cm(-1) for the bath gas N(2) such as fitted from photolysis quenching experiments (using the same molecular parameters as for the pyrolysis). Rate coefficients for the temperature range 1200-3500 K are represented in the form k(Mol,0)/[Ar] = 7.3 x 10(14) T -6.1 exp(-47300 K/T) cm(3) molecule(-1) s(-1) and k(Rad,0)/[Ar] = 2.1 x 10(12) T -5.5 exp(-47300 K/T) cm(3) molecule(-1) s(-1) (accuracy +/-25%) and recommended for use in combustion chemistry.

Energy dependence of the roaming atom pathway in formaldehyde decomposition

Recently, a new mechanism of formaldehyde decomposition leading to molecular products CO and H(2) has been discovered, termed the "roaming atom" mechanism. Formaldehyde decomposition from the ground state via the roaming atom mechanism leads to rotationally cold CO and vibrationally hot H(2), whereas formaldehyde decomposition through the conventional molecular channel leads to rotationally hot CO and vibrationally cold H(2). This discovery has shown that it is possible to have multiple pathways for a reaction leading to the same products with dramatically different product state distributions. Detailed investigations of the dynamics of these two pathways have been reported recently. This paper focuses on an investigation of the energy dependence of the roaming atom mechanism up to 1500 cm(-1) above the threshold of the radical channel, H(2)CO-->H+HCO. The influence of excitation energy on the roaming atom and molecular elimination pathways is reported, and the branching fraction between the roaming atom channel and molecular channel is obtained using high-resolution dc slice imaging and photofragment excitation spectroscopy. From the branching fractions and the reaction rates of the radical channel, the overall competition between all three dissociation channels is estimated. These results are compared with recent quasiclassical trajectory calculations on a global H(2)CO potential energy surface.

Classical Trajectory Study of the Reaction between H and HCO

The thermal reaction between H and HCO was studied by classical trajectory calculations on an ab initio potential. The formation of H2+CO, the exchange of hydrogen atoms, and nonreactive encounters, proceeding either via direct or via complex-forming pathways, were separated. The reaction H+HCO-->H2+CO, with direct and complex-forming components, was found to have a low-pressure rate coefficient of 2.0(+/-0.15)x10(-10) cm3 molecule(-1) s(-1), being nearly independent of temperature between 200 and 1000 K. This value is in agreement with the recent experimental value of 1.83(+/-0.4)x10(-10) cm3 molecule(-1) s(-1). Thermal lifetime distributions of H2CO* complexes formed in the reaction are only weakly temperature dependent due to a compensation of energy and angular momentum effects.

The roaming atom pathway in formaldehyde decomposition

We present a detailed experimental and theoretical investigation of formaldehyde photodissociation to H(2) and CO following excitation to the 2(1)4(1) and 2(1)4(3) transitions in S(1). The CO velocity distributions were obtained using dc slice imaging of single CO rotational states (v=0, j(CO)=5-45). These high-resolution measurements reveal the correlated internal state distribution in the H(2) cofragments. The results show that rotationally hot CO (j(CO) approximately 45) is produced in conjunction with vibrationally "cold" H(2) fragments (v=0-5): these products are formed through the well-known skewed transition state and described in detail in the accompanying paper. After excitation of formaldehyde above the threshold for the radical channel (H(2)CO-->H+HCO) we also find formation of rotationally cold CO (j(CO)=5-28) correlated to highly vibrationally excited H(2) (v=6-8). These products are formed through a novel mechanism that involves near dissociation followed by intramolecular H abstraction [D. Townsend et al., Science 306, 1158 (2004)], and that avoids the region of the transition state entirely. The dynamics of this "roaming" mechanism are the focus of this paper. The correlations between the vibrational states of H(2) and rotational states of CO formed following excitation on the 2(1)4(3) transition allow us to determine the relative contribution to molecular products from the roaming atom channel versus the conventional molecular channel.

Pathways and Rate Coefficients for the Decomposition of Vinoxy and Acetyl Radicals

The potential in the vicinity of the stationary points on the surface for the decomposition of ground-state vinoxy and acetyl radicals has been calculated using the RQCISD(T) method extrapolated to the infinite-basis set limit. Rate coefficients for the decomposition pathways of these two radicals were computed using the master equation and variational transition state theory. Agreement between our calculated rate coefficients for H + CH(2)CO <--> CH(3) + CO and experimental data is very good, without the need for empirical adjustments to the ab initio energy barriers. Multireference configuration-interaction calculations indicate two competitive channels for vinoxy decomposition, with the channel leading to H + CH(2)CO being preferred at photodissociation energies. However, at typical combustion conditions, vinoxy decomposes primarily to CO and methyl. In contrast, decomposition of acetyl shows only one decomposition channel, leading to CO and methyl. The implications of a low-lying exit channel for the calculation of theoretical rate coefficients are discussed briefly.