Theoretical study on the reaction of the methylidyne radical, CH(X(2)Π), with formaldehyde, CH2O.

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Theoretical Study on the Reaction of the Methylidyne Radical, CH(X#), with Formaldehyde, CHO 2

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Hue Minh Thi Nguyen, Nguyen Huu Tho, Trong-Nghia Nguyen, Hoang Van Hung, and Luc Vereecken J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/jp506175k • Publication Date (Web): 02 Sep 2014 Downloaded from http://pubs.acs.org on September 6, 2014

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The Journal of Physical Chemistry

Theoretical Study on the Reaction of the Methylidyne Radical, CH(X2Π), with Formaldehyde, CH2O Hue Minh Thi Nguyen,1* Nguyen Huu Tho,2 Trong-Nghia Nguyen,3 Hung Van Hoang 1 and Luc Vereecken 4* 1

Faculty of Chemistry and Center for Computational Science, Hanoi National University of Education, Hanoi, Vietnam

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College of Education-Gia Lai, 126 Le Thanh Ton, Pleiku, Gia Lai, Vietnam School of Chemical Engineering - Hanoi University of Science and Technology, Hanoi, Vietnam 4 Theoretical Atmospheric Chemistry, Max Planck Institute for Chemistry, Mainz, Germany 3

Abstract A theoretical study of the mechanism and kinetics of the CH(X2Π) + H2C=O reaction was carried out by ab initio molecular orbital theory based on the CCSD(T)/aug-ccpVTZ//BHandHLYP/aug-cc-pVDZ method in conjunction with statistical theoretical kinetic VTST and RRKM Master Equation calculations. The potential energy surface for the cis/transHCOH + CH reactions was also examined. Calculated results show that the association reaction of CH and CH2O occurs by addition of the CH radical onto the oxygen atom, cycloaddition onto the C=O bond, and for a small fraction insertion of CH into a C-H bond, forming CH2C-O-CH, cyclic H2COCH, and CH2CHO, respectively. These channels are all barrierless, leading to a rate coefficient near the collision limit with a slight negative temperature dependence, in excellent agreement with experimental data. The intermediates can undergo extensive isomerization across seven C2H3O isomers, many with multiple conformers, prior to fragmentation. Eight fragmentation product sets were characterized, where H2CCO + H and CH3 + CO are found to be 1

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the major products at lower temperatures, while 3CH2 + HCO starts to contribute at higher temperatures. CCHO + H2, C2H + H2O, HCCOH + H, C2H2+OH and HCCO + H2 have negligible contributions for temperatures below 3000K and pressures up to 100 atm. Collisional stabilisation of the C2H3O isomers is negligible except at the highest of pressures and low temperatures. Keywords: combustion ; interstellar space ; oxygenates ; carbonyl fuel additive

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1. Introduction Methylidyne (CH, also called carbyne) in its X2Π ground state is known to be one of the most reactive of all radicals, owing to a molecular structure containing both an unpaired radical electron, and a carbene functionality with a lone pair and vacant orbital combination:

This exceptional orbital arrangement allows for all traditional radical reactions, including recombination and abstraction reactions, as well as typical carbene reactions such as (cyclo-)additions to π-bonds and insertion reactions in σ-bonds, without energetic barriers.1–3 CH(X2Π) is an important species which plays a role in combustion, the interstellar medium, and extraterrestrial atmospheric chemistry. The CH radical has been detected unambiguously in diffuse clouds in the interstellar medium4–6 as well as in Titan's atmosphere7–11 where the reaction between C(1D) atom and H2 molecule was suggested as a source of methylidyne radicals, as well solar photodissociation of methane. In hydrocarbon combustion, the CH radical is known to be involved in many important aspects of the oxidation, such as the NOx cycle through prompt-NO chemistry,12–21 the formation of soot precursors,1,2,22 and the 430 nm blue chemiluminescence23 of the first excited state, CH(2∆) → CH(2Π) + hν. The formation of ground state CH(X2Π) in flames occurs primarily from aliphatic compounds with low carbon number such as CH4 and C2H2.24 In a laboratory setting, CH radicals have been generated by various techniques3,15–17,22,25–27 either in combustion systems or atomic flames, or directly through alkali 3



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reactions or photolysis of tri-halogenated methane such as CHBr3 and CHClBr2. Due to its importance, the reactions of CH radicals with numerous species have been investigated both by theoretical and experimental means;1–3,14–18,20–22,26–36 co-reactants include alkanes, alkenes, alkynes, N2, O2, NH3, H2S, CH, etc. The rate coefficients of these reactions are typically close to the collision limit, with a negative temperature dependence, indicating that these reactions are highly exothermic and show no potential energy barrier. With unsaturated hydrocarbons, three entrance channels are generally considered:1,22 insertion into a C−H bond, addition onto a single carbon atom of the π-system, and cycloaddition across the π-bond. Formaldehyde, H2C=O, was the first polyatomic organic compound to have been observed in the interstellar medium and in dark nebulae,5,37–39 and is predicted to be present in the atmosphere of Titan.11,40 It is also among the most abundant aldehyde molecules41,42 in the terrestrial lower atmosphere, where it is emitted, among other sources, from the combustion of fossil fuels and from biomass burning.43,44 In combustion systems, H2CO lies on the primary oxidation pathway of natural gas and other alkane-based hydrocarbon fuels,24 and motor vehicle emissions of H2CO have been shown to increase with the use of oxygenated fuels, including methanol, ethanol, and methyl tertiary butyl ether (MTBE) blended fuels.41,44 The reaction between formaldehyde and CH(2Π) can thus play a role in a wide range of reaction conditions ranging from the cold, low-pressure interstellar medium to high-temperature and -pressure combustion systems. The current drive towards addition of oxygenates including carbonyl/ester compounds in biofuels, and the increased formation and emission of formaldehyde in blended fuels using other oxygenates, make a detailed understanding of the 4


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carbonyl chemistry ever more important. Despite the potential impact of the CH2O + CH reaction, very little data is available. The reaction was studied experimentally from 297 to 670 K in 100 Torr of argon using the two-laser photolysis/LIF probe technique by Zabarnick et al27 The reaction rate was found to be independent of total pressure between 20 and 300 Torr at room temperature, and the rate constant is near the collision limit, with values of k(T) = (1.57±0.14)×10−10 exp[(260±30)/T] cm3 molecule-1 s−1 for the temperature range 297 to 670 K. Recent work by Goulay et al.45,46 studied the reaction of CH radicals with two other carbonyl compounds, acetaldehyde and acetone, observing acetyl radicals, acrolein, ketene, methylketene, methyleneoxirane, dimethylketene, and methacrolein as dominant products. Ab initio calculations47,48 on the unimolecular rearrangement of formaldehyde showed that formaldehyde can isomerise, forming trans- and cis-HCOH, though the isomerisation barrier of appr. 330 kJ mol-1, and a reaction endoergicity of nearly 200 kJ mol-1 makes formation of these isomers less likely. The major objective of this work is to elucidate the mechanism for the reaction of formaldehyde with methylidyne in the gas-phase. The rate constants for the low-lying energy channels are predicted and compared with the available experimental data. Furthermore, the temperature- and pressure dependence of the product distribution is analysed extensively. The PES for CH + trans- and cis- (HCOH) reactions is also calculated.

2. Methodology 2. A. Quantum chemical calculations 5



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The geometric parameters of the reactants, transition states and products on the potential energy surfaces of the system were fully optimized using density functional theory (DFT)49 with the hybrid BHandHLYP functional50 and the Dunning’s correlation consistent basis sets of double-ζ quality (aug-cc-pVDZ).48–50 All the stationary points were confirmed to be local minima or transition states by harmonic vibrational analysis in which the reactants, intermediates, and products possess all real frequencies, whereas transition states have one and only one imaginary frequency. Intrinsic reaction coordinate (IRC) analyses were performed to confirm the connection between transition state and the reactants, intermediates, or products. For more accurate evaluation of energies, higher level single-point energy calculations of the stationary points were performed at the CCSD(T)/aug-cc-pVTZ level54–56 based on the optimized geometries at the BHandHLYP/aug-cc-pVDZ level. The relative energies presented in the potential energy surface (PES) are corrected for unscaled zero-point vibrational energies (ZPVE). The three barrierless entrance channels were characterized by a large set of constrained optimizations along the reaction coordinate at the M06-2X/aug-cc-pVTZ level of theory,57 using a pruned (99,590) DFT integration grid (ultrafine) and very tight convergence criteria. The M06-2X vibrational wavenumbers were scaled by 0.975,58,59 while the energy profile was improved by CCSD(T)/aug-cc-pVTZ single point calculations. For some of the geometries along the reaction coordinate, the lowest real wavenumber was adjusted manually to ensure a smooth transition from reactants to adduct following the trends in the other transitional modes; the lowest real mode is most susceptible to numerical inaccuracies due to mixing with the reaction coordinate and modes for molecular translation and rotation. The formation of 3CH2 + HCO from 6


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I7, a barrierless exit channel, has only a small contribution and is represented by a single intermediate geometry obtained by constrained optimization; this approximation leads to an upper limit on the channel contribution, which is sufficient for the case at hand. All calculations were carried out using the Gaussian 0360 and Gaussian 0961 packages. 2. B. Theoretical kinetic calculations Based on the rovibrational characteristics and relative energies obtained by the quantum chemical calculations, the rate and product distribution of the title reaction was calculated across a wide range of temperature and pressures. The absolute rate coefficients for the initial cycloaddition, chain addition and insertion in the CH(2Π)+H2CO reaction were calculated using E,J-microcanonical variational transition state theory (VTST),62,63 where the number of accessible quantum states of the transition states are minimized for each energy grain of size 0.012 kJ mol-1 (1 cm-1) and each rotational quantum J. Tunneling corrections on the rate coefficient were found to be negligible, as expected given that the entrance channels show no barrier and the reaction path has a high reduced mass. The impact of redissociation of adducts to the reactants remains below ~10% even at 3000K; this is well within the expected accuracy of about a factor of 3 for our implementation and quality of the input data in the calculation of k(T), and was thus not corrected for. The partition function for CH(X2Π) is based on the M06-2X rovibrational data but uses the experimental spin-orbit splitting of 27.95 cm-1.64,65 Prediction of the product formation from this reaction requires Master Equation analysis of the chemically activated intermediates on the multi-well PES, incorporating the competition

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between energy-specific unimolecular reactions, and energy loss through collisions with the bath gas explicitly. The energy-specific rate coefficients k(E) of the unimolecular reactions are calculated using RRKM theory66–69 based on the available quantum chemical data, in a rigidrotor harmonic-oscillator approximation for most intermediates. For the intermediates and TS that have multiple conformers interconnected by low-lying barriers, i.e. degrees of freedom for internal rotation (e.g. I8) or pseudo-rotation (e.g. I10/I11), two different approximations were applied to calculate the state density factor in the prediction of k(E). The first is a multiconformer analysis (MC-RRKM) where the energy well is modeled as a set of joint minima, each described in a rigid-rotor harmonic-oscillator approximation; this MC-RRKM approach emphasizes the specific rovibrational properties and relative energies of the different conformers, and is appropriate mostly at low energies. The second approach is the description of the energy well using degrees of freedom for hindered internal rotation (HR-RRKM), where the degree of freedom for internal rotation is calculated as a harmonic oscillator at low energies and a free 1D rotor at high energies. This approach emphasizes the different state density properties of internal rotations; as it is the most appropriate method at higher internal energies, we will refer to this methodology unless indicated otherwise. The difference between the two approaches will be used as a metric in the error analysis. The state density of the separable degrees of freedom was convoluted using the Beyer-Swinehart-Stein-Rabinovitch algorithm.70–72 Tunneling was found to have a negligible influence on the predictions as all unimolecular reactions involve chemically activated intermediates with internal energies well above the transition states, and was not implemented in the final results.

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The collision rate between the intermediates and the bath gas was predicted using the Lennard-Jones collision number, using air as a bath gas, and estimating a well-depth of ε = 260 K, and a collision diameter of σ = 4.5 Å for all H3C2O intermediates. Energy transfer on collision is modeled using the simple Troe bi-exponential model,73 with an estimated average energy transfer parameter ∆E = -3.59 kJ mol-1 (300 cm-1). The temperature- and pressure dependence of the product distribution is then obtained by Master Equation analysis, incorporating the temperature-specific formation distribution, the energy-specific unimolecular reaction rates, and the T,P-specific collisional energy transfer. Fragmentation into separated products was modeled as an irreversible reaction. The Master Equation was solved using the fast CSSPI methodology,74 using an energy grain size of 1 kJ mol-1, and an energy ceiling ≥ 320 kJ mol-1 above the free reactants. The temperature range considered was 300 to 3000K, and the pressure range was 103 to 107 Pascal (~0.01 atm to ~100 atm); this allows modeling of most practical applications incorporating the title reaction. 2.C. Sensitivity analysis To assess the uncertainty on the predicted product distribution using a brute force approach, Master Equation analyses were performed where groups of parameters were changed twice, once to each extreme of their confidence interval, and examining the impact on the product predictions. A first parameter changed is the relative energy of the reactants, CH + CH2O, by ±20 kJ mol-1. A second variation changed the relative contribution of the dominant chain- versus cyloaddition initiation reactions by 15 %. Thirdly, the isomerisation transition states were varied by ±13 kJ mol-1, while a fourth set of variations changed the dissociation 9



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transition states by ±13 kJ mol-1; in these variations, transition states 7/8 and 7/P3 were kept constant, and 5/6 was treated as a dissociation TS. The fifth set involved changing the relative energy of the two most critical transition states 7/8 and 7/P3 by ±13 kJ mol-1. A sixth set of calculations altered the average transferred energy per collision ∆E by ±40 %. A seventh set of variations treated the internal degrees of freedom for internal rotation in a harmonic oscillator versus hindered internal rotor model, as described higher.

3. Description of the PES The [C2H3O] potential energy surface is shown in Figure 1 and depicted as a reaction scheme in Figure S1, while the geometries of critical points are shown in Figure 2, Figure 3, and Figure 4. The reactants connect to 10 intermediate states labeled I3 through I12, two complexes C1 and C2, and 8 product sets P1 through P8. The 27 transition states are labeled as x/y in which x and y are the corresponding complexes, intermediates or products. Thus, 4/5 is the transition state connecting I4 and I5, and 8/P2 describes fragmentation of I8 to product set P2. For those occasions where we refer to all conformers of a specific isomer as a set, we denote all conformer numbers in the set in subscript, e.g. I3,4 comprises all CH2OCH conformers I3 and I4; this emphasizes the fast interconversion by internal rotation as appropriate at the high internal energies found in this system. 3. A. Reaction initiation

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Similar to the reactions of 2CH radicals with unsaturated hydrocarbons, CH + CH2O shows three barrierless entrance channels involving insertion of CH radical into a C−H bond, chain addition of CH onto the oxygen atom, and cycloaddition across the C=O π-system, forming intermediate states I7 (CH2CHO: -449.6 kJ mol-1), I4 (CH2C-O-CH: -151.5 kJ mol-1), and I5 (cyclic H2COCH: -300.7 kJ mol-1), respectively. Chain addition to the H2CO carbon atom was not found as a separate route, merging instead with the insertion or cycloaddition channel depending on the angle of attack. The reaction of HCOH, the high-energy conformer of CH2O, proceeds by the formation of pre-reactive complexes both for the cis- and trans conformers of HCOH. These complexes, C1 and C2, have a stability of ∼20 kJ mol-1, and lead to the formation of CH2COCH adducts through transition states 1/3 and 2/4 40-50 kJ mol-1 above the separated CH + HCOH reactants. 3. B. Isomerisation The nascent adducts readily interconvert through channels well below the entrance channels and the fragmentation channels. Two stable conformers were found for CH2O−CH, I3 and I4 separated by 15 kJ mol-1, corresponding to internal rotation around the CH2O−CH bond. Cyclization of these adducts through TS 3/5 and 4/5 (-84.8 and -93.69 kJ mol-1 respectively) yields the cyclic I5 intermediate, which in turn can open the three-membered ring to form I7 (5/7, -235.7 kJ mol-1). A 1,2-H-migration in I7 forming I8, the most stable C2H3O isomer (CH3CO, -477.9 kJ mol-1), has a fairly high barrier of 170 kJ mol-1 (7/8, -579.7 kJ mol-1), which is comparable to the fragmentation channels but remains easily accessible considering the excess energy of the nascent C2H3O radicals. The remaining isomers are only accessible through higher 11



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energy isomerisation TS. I6 (CH3OC, -247.1 kJ mol-1) is accessible only through 5/6 (-90.9 kJ mol-1); furthermore, I6 was found to be unstable, decomposing to P2 (CH3+CO, -442.8 kJ mol-1) without barrier through 6/P2. The H2C=COH radical, I9 (-349.3 kJ mol-1) can be formed from I7 and I8 through two fairly high energy barriers 7/9 (-271.8 kJ mol-1) and 8/9 (-141.8 kJ mol-1). Both I7 and I9 provides access to the CH=CHOH intermediate, of which 4 conformers were located (I10, I11, I12 and I13 with energies ranging from -333.3 to -321.1 kJ mol-1) which readily interconvert over low-lying internal rotation or pseudo-rotation TS. Again, the energy barriers to be surmounted to form CH=CHOH are high, where 7/11, 9/10, 9/11, and 9/12 have energies ranging from -189.7 to -133.6 kJ mol-1. From this, we expect that the main isomers active in the 2

CH + H2CO reaction are I3,4, I5, I7 and I8. 3. C. Fragmentation The four main C2H3O isomers allow access to a set of fragmentation channels with highly

different product energies. The energetically most favorable products are CH3+CO (P2, -442.8 kJ mol-1), accessible through the low-lying TS 8/P2 (-413.1 kJ mol-1), or by spontaneous dissociation of I6. Product set P3 (H2CCO + H, -301.5 kJ mol-1) is the second lowest fragmentation channel, accessible through 8/P3 and 7/P3, at -286.4 and -279.7 kJ mol-1, respectively. Despite the significantly higher energy of these TS compared to 8/P2, P3 is still expected to be a major exit channel, as P2 is only accessible after clearing 7/8 or higher isomerisation TS, directly comparable to 7/P3 in energy. Furthermore, 7/P3 represent a loose dissociation TS, while 7/8 is a much more rigid 1,2-H-migration, making formation of P3 entropically more favorable. Two other product sets are accessible from the 4 main C2H3O isomers, but these are significantly higher in energy and not expected to play a significant role. 12


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The first is H2-elimination from I7 forming P4 (H2+CCHO) through 7/P4 (-37.5 kJ mol-1). Both I3,4 and I7 allow formation of 3CH2 + HCO (P1, -53.2 kJ mol-1) through 4/P1 (-27.3) and 7/P1 (barrierless) respectively. This latter TS is not treated as a barrierless reaction in the current work, but is instead incorporated in the calculations as a localized bottleneck at a position randomly chosen along the reaction coordinate. This provides an upper limit to the rate coefficients of the (micro)variationally optimized barrierless TS, which still prove small compared to those of the much more facile channels 5/7, 7/8 and especially 7/P3. Four additional product sets can be formed from the isomers I9 and I10,11,12,13. The lowestlying set of these, P8 (H2 + HCCO, -295.9 kJ mol-1) is only accessible through a high-lying H2elimination TS 12/P8 at +9.4 kJ mol-1, making ketenyl formation from the title reaction negligible. Formation of C2H2 + OH (P7, -214.2 kJ mol-1) is more accessible through 10/P7 (-200.7 kJ mol-1), as is formation of P6 (HCCOH + H) through 9/P6, 12/P6 and 11/P6, with energies ranging from -145.7 to -137.7 kJ mol-1. Finally, formation of C2H + H2O (P5, -145.0 kJ mol-1) is hampered by the high TS barrier, with 9/P5 at -46.0 kJ mol-1. From the above, we expect the main product formation channels to be I7 → P3, and I7 → I8 → P2, where the competition between the transition states 7/8 an 7/P3 will determine the P3/P2 ratio. At higher temperatures, formation of P1 could gain in importance, i.e. CH + H2CO → I4 → P1, as it derives from the chain adduct I4 where the competing unimolecular reactions have rigid cyclization isomerisation TS at fairly high energy. Likewise, H2 + CCHO (P4) might become accessible from I7 at high temperatures. The energetically most favorable channels to the other product sets are I7 → I9 → P5; I7 → I10,11,12,13 → P6; I7 → I10,11,12,13 → P7; and I7 → I10,11,12,13 →

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P8. C2H2+OH (P7) and HCCOH+H (P6) are much more accessible than P5 and P8, and might have a minor contribution in the final product distribution.

4. Rate coefficient of CH + H2CO Figure 5 shows the predictions of the E,J-microcanonical VTST calculations over the three barrierless entrance channels for the CH(X2Π) + CH2O reaction; the energy profiles (Figure S3) and vibrational wavenumbers (Figures S3, S4 and S5) used in these calculations are shown in the supporting information. For the temperature range from 298 to 670 K, the predicted absolute rate coefficient is within 40% of the experimental results by Zabarnick et al.,27 though our predictions show a slightly more negative temperature dependence. The predicted total rate coefficient is well-reproduced, within 2 % over the 300-3000 K interval, by the following modified Arrhenius expression:  386 K  k (T ) = 7.62 × 10 −10 ⋅ T −0.32 ⋅ exp   T 

and within 20% by the linear Arrhenius expression k(T)=5.82×10-11 exp(655K/T). Rate expressions for the individual entrance channels are given in Table 1. The cycloaddition and chain addition channels are the two main pathways, with roughly equal contribution at lower temperatures, and higher contribution of the entropically more favorable chain addition at higher T. Both channels show a monotonous negative T-dependence, as is typical for barrierless reaction; the T-dependence is more pronounced for the cycloaddition.

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Insertion of CH into the C−H bond has a minor contribution. However, it is interesting to look at this reaction channel more closely, as its temperature dependence shifts from negative at low T to positive at higher temperatures. Most barrierless dissociation/association reactions have their most rigid structures at the adduct side, and the least rigid structures towards large fragment separations, owing to the conversion of molecular vibrations of the adduct to degrees of freedom for relative rotation and translation of the fragments, which have much smaller quanta and concomitantly higher state densities. Combined with the energy profile, this induces a negative temperature dependence of the rate coefficient when minimizing the state density of the TS at each energy. The insertion reaction likewise has several transitional degrees of freedom, but also has the unique feature that a C−H vibration of the adduct gets absorbed in the reaction coordinate mode along the dissociation path and then re-appears as a different, non-transitional C−H vibration in the fragments. Hence, this mode becomes more rigid towards either side of the energy profile, yet allows for a more loose TS at intermediate distances around 2 Å separation where the actual H-translation process takes place. A few other modes that are affected by this phenomenon likewise rigidify (to a much smaller extent) towards the fragments. At the lowest internal energies, the TS is located towards the separated fragments as this represents the lowest state density. At increasing internal energies, the TS then shifts towards the more rigid structures closer to the adduct, with a negative T-dependence of k(T), but for the CH+H2CO insertion reaction this continued shift towards the adduct is then blocked by the more loose region along the reaction coordinate. Hence, at higher energies, the kinetic bottleneck is no longer variational, and remains virtually localized at the same fragment separation. This localization of the energyspecific TS then leads to a traditional positive temperature dependence as also found for regular 15



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reaction with an energy barrier. The effect is enhanced by the energy profile of this reaction, which remains very flat at the separations considered. We are not aware of any other reactions showing this fortuitous combination of mode characteristics and energy profile; we should consider that it might be an artifact of the quantum chemical input data for the VTST calculations, or shortcomings in the description of the state density of the degrees of freedom. The small contribution of insertion combined with the fast interconvertion of all adducts make further investigation of this phenomenon nugatory.

5. Product distribution Figure 6 shows the dominant products from the CH + CH2O reaction, as a function of temperature and pressure. In all reaction conditions, formation of ketene, (P3, H2CCO + H) is the dominant product, with yields up to 81.5% at low temperatures and pressures (Figure 6a), and decreasing to 57.2% at 3000K. At low temperatures, it is complemented mostly with CH3+CO (P2) with yields of 16.1% to 10.5% (Figure 6b), while at high temperatures formation of P1 (3CH2 + HCO) becomes important with yields up to 30 % (Figure 6c). In all cases, the ratio of P3:P2 remains virtually constant at about 5:1, indicating that this ratio is determined by the rates of reaction across transition states 7/P3 and 7/8. The combined yield of P3 + P2 is anti-correlated with the emergence of P1 as a significant product at higher temperatures. The increase in the yield of this latter product depends on the formation of the chain adduct I3,4 as the dominant entrance channel, combined with a looser formation path 4/P1 that is able to compete effectively with the rigid cyclisation TS 4/5 and 3/5 at high internal energies. For the other nascent adducts, 16


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I5 and I7, the energy difference between the isomerisation TS and the high-lying product channels is significantly larger, such that other products remain negligible. Likewise, isomerisation towards I9 and I10,11,12,13 remains uncompetitive, making product formation from these intermediates negligible, with a maximum yield of 1.3 % for P6 (HCCO + H2), 0.8% for P4 (H2+CCHO), 0.7 % for P7 (C2H2 + OH), and negligible yields for the other product sets. At pressures above 10 atm. and temperatures below 700 K, some stabilization of I3,4 is predicted with a maximum yield of 24.3% at 300K and 100 atm. (Figure 6d), again a direct result of the smaller nascent energy content of this adduct combined with comparatively rigid isomerisation TS. None of the other C2H3O isomers have an appreciable yield of stabilization across the reaction conditions examined. Despite the complexity of the underlying potential energy surface with a high number of isomerisation and exit channels, only a small subset of the reaction channels carry a significant flux, and the main products comprise only four products. We can thus simplify the reaction scheme as shown schematically in Figure 7. The energetically most stable set of products, CH3 + CO, is not the dominant exit channel despite that it originates from the most stable intermediate I8, and its formation TS 8/P2 is the lowest TS on the PES. This behavior is for a large part related to the very high exothermicity of the reaction, where the nascent H3C2O compounds contain as much as 500 kJ mol-1 of internal energy, hundreds of kJ mol-1 above the lowest accessible transition states. At these energies, the unimolecular isomerisation and dissociation reactions of the small intermediates are very fast, nearing the vibrational periods of the internal degrees of freedom. Even at 100 atm., the collision frequency is barely competitive against these unimolecular rates, as tens to hundreds of collisions are needed for the intermediates to lose 17



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sufficient energy to be stabilized into the energy wells below the lowest TS. As such, collisional energy loss is not competitive across all reaction conditions examined, except for the least stable isomer I3,4. C2H3O intermediates are small and have a low molar heat capacity, such that the nascent energy content is comparatively narrow and does not change drastically with differing temperatures compared to the reaction exoergicity. The relative flux through the lowest TS thus remains mostly independent of temperature, with only a few of the higher TS significantly gaining mass flux at increasing temperatures.

6. Sensitivity analysis The relative rigidity and energy of the two key transition states, 7/P3 and 7/8, are found to be the key parameters in our kinetic model determining the yields of the two main products, P2 and P3. The critical entropic difference is that 7/8 is a rigid TS that looses 1 degree of freedom for internal rotation, while 7/P3 is a loose decomposition pathway where the internal rotor become less hindered compared to I7, and where 3 transitional degrees of freedom for relative translation of the H-atom emerge. Similar to our reference hindered-rotor (HR) approach, the multi-conformer (MC) results still favor P3 (H2CCO + H) as the main product yields between 62 and 81%, and we also find a 5:1 ratio for P3:P2 across all reaction conditions with P2 yields between 12.9 and 16.8%. The formation of P1 (3CH2+HCO) is slightly decreased in the MC treatment to a maximum of 20.3% as the isomerisation TS 3/4 and 3/5 suffer less from the loss of 2 internal rotors; this remains compatible with the HR model. It should be noted that this robustness against the rotor model depends on the internal energy considered, as the harmonic 18


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oscillator approach has a linear quantum state spacing, while the hindered rotor model has a higher state density at lower energies but a quadratically increasing quantum state spacing at higher energies. At the nascent H3C2O energies, these trends cancel out, leading to near-identical ratios of the energy-specific unimolecular rates k(E). At about half the nascent energy, however, the ratio of ki(E) changes by up to a factor of 2, which would induce a much stronger dependence on the internal rotor model. We estimate an uncertainty on the predicted product distribution using the HR-RRKM methodology of a few % absolute for products P1, P2, P3 and P4, due to this cancellation at the critical energies. Changing the relative energy of 7/P3 and 7/8 has a more direct impact on the ratio of P3 versus P2, with the ratio shifting between 4:1 to 7:1 upon the ±13 kJ mol-1 relative energy variations in our error analysis; the other applied variations in parameters do not affect the P3:P2 ratio to a significant extent. The yield of P1 relative to P2+P3 is determined mostly by the energy of the dissociation TS, in particular 4/P1; the error analysis variations change the predicted P1 yield by up to 8 %. The largest uncertainty in the model concerns the yield of stabilized I3,4, which occurs under low-temperature, high-pressure conditions. The two rotor models show large differences, where the MC model shows virtually no stabilisation of I3,4, with a maximum yield of 0.2%, a stark difference with the 24% predicted in the HR model. The internal rotors in I3,4 are both nearly free, leading to a much higher state density for this intermediate compared to a simple harmonic oscillator model. In contrast, the cyclisation TS 3/5 and 4/5 that are the main exit channels from the I3,4 energy well do not have internal rotors and are appropriately described by a harmonic oscillator model. Hence, the absolute rate constants for I3,4 are significantly lower in the HR model compared to the MC model, allowing collisional energy loss to compete more 19



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effectively in the HR model. Other factors that affect the stabilization yield are the relative energy of the reactants CH + CH2O, changing the highest predicted yield of I3,4 at 100 atm. and 300 K by ±13% absolute, while the energy transferred per collision ∆E (±10 %), and the energy of the isomerisation TS (±22%) have likewise a large sensitivity. The combined T,P-dependent errors from all these variations indicate that the onset of the fall-off regime as shown in Figure 6d could be shifted by up to an order of magnitude in pressure, with a concomitant gain or reduction of the other products in that T,P-region. Even for the model variations that favor collisional stabilization most, however, we only observe thermalization of I3,4 and none for the other intermediates. For the low-pressure regime, i.e. lower pressures or higher temperatures, the product yield predictions are comparatively insensitive to the aforementioned variations in the kinetic model, with changes of a few percent only. These reaction conditions cover most practical applications in combustion, experimental setups, and extraterrestrial systems.

7. Conclusions The reaction of CH(X2Π) with formaldehyde was studied by quantum chemical and theoretical kinetic methodologies. The reaction was found to proceed through three barrierless entrance channels, corresponding to chain addition, cycloaddition, and insertion in a C−H bond. The rate coefficient was calculated using E,J-microcanonical VTST, and was predicted to be close to the collision limit, showing a negative temperature dependence. The initial reaction was thus found to be similar to other reaction of the CH radical with unsaturated compounds. Master Equation analysis of the product distribution predicts the formation of ketene, H2CCO, as the 20


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main product, with yields up to 82%. Other products include the formation of methyl radicals + CO, and at high temperatures the formation of 3CH2 + HCO. Only at temperatures below 700K and pressures above 30 atm. is collisional stabilization of the intermediates feasible, and then only for the CH2OCH isomer that has a particular combination of low nascent energy content and rigid exit transition states. The yield of stabilized CH2OCH depends on the model applied to the internal rotors and is sensitive to the energies of the TS surrounding CH2OCH; the yield could be as high as 25% at 300K and 100 atm., with almost an order of magnitude uncertainty on the pressure of the onset of the fall-off regime. Barring this contribution of stabilization, the yield of the remaining products is found to be essentially independent of pressure, i.e. the ratio of the dominant products remains constant for pressures from 10-2 to 102 atm. Combined uncertainties in this regime where deduced to be about 25% relative error on the yield predictions for 3CH2 + HCO, anti-correlated with the summed yield P2+P3, and where the ratio P3:P2, i.e. H2CCO+H to CH3+CO is 5±1.5:1. All other product formation channels carry a very minor to negligible flux. The results described above are in agreement with literature data on CH reactivity. In particular, the radical + carbene functionality of the 2CH radical allows for fast, barrierless reactions with many unsaturated species, and our rate predictions are in excellent agreement with the direct measurements of Zabernick et al.27 Our findings are also compatible with the recent experimental product study on the reaction of 2CH with acetaldehyde by Goulay et al.,45 who observed formation of (methyl)ketene, ethyl radicals and CO as dominant exit channels. Several of the products in that study were explained via the insertion of CH into CH3CHO bonds. For the current mechanism, we find that the insertion reaction has only a very small contribution, but the insertion product CH2CHO was found to be among the most stable C2H3O isomers, and is readily 21



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formed from the chain and cycloaddition adducts, CH2OCH and cyclic CH2CHO, by facile isomerisation reactions. These results shows that the reaction of CH radical with carbonyl compounds, in particular the H2CO molecule, can play an important role in combustion systems. Both CH and carbonyl compounds are known to be present in these systems in important concentrations, and the increased reliance on oxygenated fuel additives containing carbonyl groups makes the elucidation of these reactions even more important. As formaldehyde in the troposphere is for a large part emitted from combustion systems, both from anthropogenic sources as natural biomass burning, a correct analysis of the H2CO life cycle in combustion systems could have repercussion towards air quality. The impact of the CH + H2CO reaction in the interstellar medium and extraterrestrial atmosphere such as of Titan is less clear, as its relevance depends strongly on the relative concentration of the reactants. However, as the reaction proceeds without a barrier, it will remain competitive even at the lowest of temperatures, where the products consist mostly of ketene + H, and CH3+CO.

Supporting Information Available: The full reaction scheme for the CH + CH2O system, tables of Gibbs free energies (∆G) and entropies (∆S) at 298K, vibrational wavenumbers, Cartesian coordinates, potential energies and zero-point vibrational energies (ZPE) of all reactants, intermediates, TS and products, and

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graphs for the barrierless entrance channels. This material is available free of charge via the internet at http://pubs.acs.org. Author information Corresponding authors: * *

H.M.T. Nguyen: Email: [email protected], phone : +84-944566456 L. Vereecken: Email: [email protected], phone: +49-6131-3054075

Acknowledgements Hue M. T. Nguyen et al. thank the National Foundation for Science and Technology Development (Nafosted), Vietnam, which has sponsored this work under project number 104.03.2010.29. Luc Vereecken is supported by the Max Planck Graduate Center with the Johannes Gutenberg-Universität Mainz (MPGC), Germany. References (1) Vereecken, L.; Pierloot, K.; Peeters, J. B3LYP-DFT Characterization of the Potential Energy Surface of the CH(X 2Π)+C2H2 Reaction. J. Chem. Phys. 1998, 108, 1068. (2) Vereecken, L.; Peeters, J. Detailed Microvariational RRKM Master Equation Analysis of the Product Distribution of the C2H2 + CH(X2Π) Reaction over Extended Temperature and Pressure Ranges. J. Phys. Chem. A 1999, 103, 5523–5533. (3) Fleurat-Lessard, P.; Rayez, J. C.; Bergeat, A.; Loison, J. C. Reaction of Methylidyne CH(X2Π) Radical with CH4 and H2S: Overall Rate Constant and Absolute Atomic Hydrogen Production. Chem. Phys. 2002, 279, 87–99. (4) Swings, P.; Rosenfeld, L. Considerations Regarding Interstellar Molecules. Astrophys. J. 1937, 86, 483–486. (5) Mann, A.; Williams, D. List of Inter-Stellar Molecules. Nature 1980, 283, 721– 725. (6) Kaiser, R. I. Experimental Investigation on the Formation of Carbon-Bearing Molecules in the Interstellar Medium via Neutral-Neutral Reactions. Chem. Rev. 2002, 102, 1309–1358. 23



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Figure 1: Detailed potential energy surface (kJ mol-1) of the CH(X2Π) + H2CO and CH(X2Π) + HCOH reactions obtained at the ZPE-corrected CCSD(T)/aug-cc-pVTZ//BHandHLYP/aug-cc-pVDZ level of theory.

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CH ( C∞v )

H2CO (C2v)

C1 (Cs)

C2 (Cs)

I3 (C1)

I4 (Cs)

I5 (C1)

I6 (Cs)

I7 (Cs)

I8 (Cs)

I9 (C1)

I10 (Cs)

I11 (Cs)

I12 (Cs)

I13 (Cs)

Figure 2: Optimized geometries of reactants and intermediates obtained at the BHandHLYP/aug-cc-pVDZ level of theory. Bond lengths are shown in Å, angles in degrees.

29



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Page 30 of 37

0/5 (Cs)

4/P1 (Cs)

8/P2 (Cs)

1/3 (C1)

7/P3 (C1)

9/10 (C1)

2/4 (C1)

6/P2 (Cs)

9/P3 (C1)

3/5 (C1)

4/5 (C1)

7/11 (Cs)

5/7 (C1)

7/9 (Cs)

9/11 (C1)

7/P4 (Cs)

7/8 (C1)

8/P3 (Cs)

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8/9 (C1)

9/P6 (C1)

10/P7 (Cs)

5/6 (C1)

11/P6 (C1)

9/12 (C1)

9/P5 (C1)

10/11 (Cs)

10/13 (C1)

12/P6 (Cs)

11/12 (C1)

13/12 (Cs)

12/P8 (Cs) Figure 3: Optimized geometries of transition states obtained at the BHandHLYP/aug-cc-pVDZ level of theory. Bond lengths are shown in Å, angles in degrees.

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CH2 (C2v)

HCO (Cs)

HCCO (Cs)

C2H2 ( D∞h )

C2H ( C∞v )

Page 32 of 37

OH ( C∞v )

CO ( C∞v )

CH3 (D3h)

HCCOH (Cs)

trans-HCOH (Cs)

H2 ( D∞h )

H2O (C2v)

H2CCO (C2v)

cis-HCOH (Cs)

Figure 4: Optimized geometries of reaction products obtained at the BHandHLYP/aug-cc-pVDZ level of theory. Bond lengths are shown in Å, angles in degrees

32


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Figure 5: Site-specific and total rate coefficients predicted by E,J-microcanonical VTST based on CCSD(T)/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ analysis along the reaction coordinate. Experimental data by Zabarnick et al.27

33



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Figure 6: Predicted yields of the dominant products in the CH+H2CO reaction as a function of temperature and pressure.

34


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chain addition I 3,4 CH2OCH 2

CH(X ) + CH2O cycloaddition

[M]

4/5 I5

H2C

CH

4/P1

CH2OCH thermalized 3CH

2

I3,4

+ HCO P1

O

5/7 I7

CH2CHO

7/P3

H + H2CCO

P3

CH3 + CO

P2

7/8 I8

CH3CO

8/P2

Figure 7: Simplified reaction scheme for the CH + CH2O reaction showing the principal reaction routes leading to the dominant products.

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Page 36 of 37

Table 1: Modified Arrhenius expressions k(T) = A⋅⋅Tn⋅exp(-Ea/T) for the site-specific and total rate coefficients for 2CH + H2CO, fitted to the E,J-microcanonical VTST predictions (Error indicates the largest deviation factor between k(T) and VTST between 300 and 3000K).

Channel

A / cm3 s-1

n

Ea / K

Fitting error

Cycloaddition

-10

1.62×10

-0.28

-605

1.17

Chain addition

2.06×10-9

-0.50

-137

1.07

Insertion

1.50×10-13

0.38

-434

1.62

Total

7.62×10-10

-0.32

-386

1.02

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Table of content graphic and byline The fast reaction of CH radicals with formaldehyde proceeds without barrier through three entrance channels, forming ketene, CO, methyl radicals, triplet CH2, and HCO radicals.

37


Theoretical study on reaction mechanism of ground-state cyano radical with 1,3-butadiene: prospect of pyridine formation.

Reaction of chlorine radical with tetrahydrofuran: a theoretical investigation on mechanism and reactivity in gas phase.

Theoretical Study on the Dynamics of the Reaction of HNO((1)A') with HO2((2)A″).

Kinetics and Thermodynamics of the Reaction between the (•)OH Radical and Adenine: A Theoretical Investigation.

Theoretical study on the reaction mechanism of carbaryl with OH radicals.

Reaction of formaldehyde with calf-thymus nucleohistone.

Theoretical Investigation on the Reaction between OH Radical and 4,4-Dimethyl-1-pentene in the Presence of O2.

Theoretical study of the reaction of hydroxyl radicals with uridine: the influence of ribose and solvent.

Theoretical study of the reaction formalhydrazone with singlet oxygen. Fragmentation of the C=N bond, ene reaction and other processes.

Fluctuational opening of the double helix as revealed by theoretical and experimental study of DNA interaction with formaldehyde.

Thermochemistry, reaction paths, and kinetics on the tert-isooctane radical reaction with O2.

Substrate dependent reaction channels of the Wolff-Kishner reduction reaction: A theoretical study.

Reaction mechanism and product branching ratios of the CH + C₃H₈ reaction: a theoretical study.

Formaldehyde as a probe of DNA structure. r. Mechanism of the initial reaction of Formaldehyde with DNA.

Theoretical study of mechanism and dynamics on reaction of (CH3)2NH with CH3.

Metabolism of dihalomethanes to formaldehyde and inorganic halide--II. Studies on the mechanism of the reaction.

Theoretical study of the ring expansion reaction mechanism of cyclopropenylidene with azetidine.

Theoretical study of the Wittig reaction of cyclic ketones with phosphorus ylide.

An experimental and theoretical study of the electronic spectrum of the HBCl free radical.

Theoretical study of the first electronic state of the FCO2 radical.

Reaction of formaldehyde with polynucleotides by master equation approach.

Theoretical study of salt effects on the Diels-Alder reaction of cyclopentadiene with methyl vinyl ketone using RISM-SCF theory.

Reaction of the nitroxyl radical TAN with glutathione.

Reaction of the carbonate radical anion with substituted phenols.