Theoretical Study of Reaction of Ketene with Water in the Gas Phase ...

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Theoretical Study of Reaction of Ketene with Water in the Gas Phase: Formation of Acetic Acid? Thanh Lam Nguyen,† Bert C. Xue,† G. Barney Ellison,‡ and John F. Stanton*,† †

Department of Chemistry & Biochemistry, The University of Texas at Austin, Austin, Texas 78712-0165, United States Department of Chemistry and Biochemistry, University of Colorado at Boulder, 215 UCB, Boulder, Colorado 80309, United States

‡

S Supporting Information *

ABSTRACT: Production of acetic acid via gas-phase hydration of ketene by water (uncatalyzed and in the presence of an additional water molecule) was theoretically characterized using high-level coupled-cluster methods, followed by a two-dimensional master equation analysis to compute thermal reaction rate constants. The results show that the formation of acetic acid quite likely occurs in high-temperature combustion of biomass, but that the rate of formation should be negligible under ambient atmospheric conditions.

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INTRODUCTION A large amount of organic acids have been released to the atmosphere from burning biomass and fossil fuels, as well from other industrial emissions.1,2 Additionally, these compounds are also produced by photo-oxidation of volatile organic compounds.3−5 However, current kinetic models significantly underestimate the atmospheric concentration of organic acids.6 This underestimation is likely due to the fact that reaction mechanisms for formation of organic acids are not understood well. Because of their solubility properties, organic acids in the atmosphere are involved in aerosol and cloud formation.3 A major fraction of atmospheric organic acids are washed out by physical processes, such as wet and dry deposition of aerosols.1 The remaining organic acids are thought to mainly react with hydroxyl radicals to form various products.7−9 Therefore, an understanding of the mechanisms of organic acids is needed to better understand roles and effects of organic acids in the environment. Acetic acid, a very familiar and ubiquitous organic acid, has been observed in the atmosphere,10−13 where its concentration varies from 0.1 to a few parts per billion by volume (ppbv), depending on season and location. Near emission sources such as biomass combustion, acetic acid concentration can be 2 to 3 orders of magnitude higher than far away from the fire.10−13 Therefore, biomass burning (e.g., wood burning, forest fire, and agricultural burning) represents a potential and important anthropogenic source of acetic acid to the atmosphere.14 Previous studies show that pyrolysis of celluloses or lignins, principal components of plants, produces various reactive organic compounds.15 Three common products of this thermal cracking process are found to be 5-hydroxymethylfurfural, furfural, and furan.15 Pyrolysis studies of these initial organic © 2013 American Chemical Society

products have consistently observed ketene as a significant product.15−18 Consequently, one might speculate that ketene could be a precursor of acetic acid via its reaction with water vapor (which is a major end product of all combustion processes) in the gas phase. In aqueous solutions, the solvation of ketene (or substituted ketenes) has been extensively studied both experimentally and theoretically.19−24 These reactions have been reviewed by Tidwell19,20 as well as by Nguyen.21 It is now believed that H2O addition to ketenes takes place at the carbonyl group (>CO) rather than the alkene group (>CC2 clusters in the gas-phase is negligibly small under these conditions. In this work, we have used coupled-cluster theory in conjunction with various large basis sets to characterize key stationary points on potential energy surface of the title reaction, followed by computing thermal reaction rate constants using a two-dimensional master-equation technique under the low- and high-pressure limits. The theoretical results are then used to elucidate the mechanism and chemical kinetics of the title reaction. In the conclusions, we address the degree to which acetic acid might be formed in the gas phase from the uncatalyzed gas-phase hydration of ketene.

∞ ∞ ECBS = E HF + ΔECCSD( T ) + ΔE ZPE

(1)

E∞ HF

where is the extrapolated HF-SCF energy (using the three HF-SCF energies above and eq 2);34 and ΔE∞ CCSD(T) is the extrapolated CCSD(T) correlation energy (via two-point extrapolation of the aug-cc-pVTZ and aug-cc-pVQZ correlation energies and eq 3.35

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X ∞ E HF = E HF + a exp( −bX )

THEORETICAL METHODOLOGY Electronic Structure Calculations. Various stationary points on the potential energy surface (PES) governing reactions of ketene with one and two waters occurring in the gas phase were located with the CCSD(T)28 method (in the frozen core approximation) in combination with the atomic natural orbital basis set ANO of Almlof and Taylor.29,30 A truncated ANO basis set, here referred to as ANO1, with the truncation of 4s2p1d for H atom and 4s3p2d1f for C and O atoms, was used.31 The same level of theory, CCSD(T)/ ANO1, was then utilized to compute harmonic force fields as well as to characterize stationary points located, i.e., all real frequencies for a minimum and one imaginary frequency for a

X ∞ ΔECCSD( T ) = ΔECCSD(T ) +

(2)

a X3

(3)

The total energy computed by the procedure above is an approximation to the HEAT protocol36−38 that we have used in our previous kinetic studies, but makes several shortcuts (effects such as relativity, core-correlation, Born−Oppenheimer breakdown, and spin−orbit corrections are not included here), which significantly lessen the accuracy relative to the usual standards of the HEAT approach. Hence, rather than accuracy at the sub kJ/mol level, error bars appropriate to the present calculations are 1−2 kcal/mol. As will be seen, this is sufficient 10998

dx.doi.org/10.1021/jp408337y | J. Phys. Chem. A 2013, 117, 10997−11005

The Journal of Physical Chemistry A

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Figure 2. Schematic reaction profile for addition reaction of one-water molecule (A) and two-water molecule (B) on the CO bond of ketene (Path B).

dimensional master eq (1DME) problem (i.e., energy-dependent only). To obtain high-accuracy results for thermal reaction rates, however, the effect of angular momentum sometimes needs to be included. This leads to the two-dimensional master equation, which explicitly depends on both internal energy (E) and angular momentum (J).42 However, solutions of the twodimensional master equation problem are currently challenging43,44 because an energy transfer probability function that

to provide support to the principal conclusions of this study. The CFOUR quantum chemistry program is used for all calculations.39 Chemical Kinetics Calculations. To obtain thermal reaction rate coefficients as a function of both temperature and pressure (i.e., falloff curve), one must solve a master equation numerically. There are a number of freely available chemical kinetics software packages40,41 to solve the one10999



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depends on both energy and total angular momentum is unknown for most reaction systems including, of course, the title reaction.45,46 Fortunately, in some cases where the thermal reaction rate is pressure-independent or depends only weakly on pressure, one does not have to solve a master equation numerically, and analytical solutions can be obtained. This is the case for the title reaction. Under the two extreme conditions of low- and high-pressure limits, thermal rate constants of the title reaction derived from analytical solutions of the two-dimensional master equation (2DME)47−50 can be given by eqs 4a, 4b, and 5 for the one TS model path A (see next section and Figure 1) and by eqs 6 and 7 for two-TS model Path B (see Figure 2).

SCTST includes fully coupled vibrations and multidimensional tunneling. Rotational energy levels of a rigid symmetric top molecule are used for various species, given by Erot = B̅ J(J + 1) + (A − B̅ )K2 with B̅ = (B × C)1/2 and −J ≤ K ≤ J. Both the density of states of ketene (or H2O) and CRP of TS are computed using a modified version of Wang−Landau algorithm52 with an energy bin of 10 cm−1 and a ceiling energy of 5 × 104 cm−1 relative to the initial reactants. The latter is chosen to be sufficiently high to ensure that all reaction rates computed in the temperature range from 200 to 2500 K are converged. The rotational density of states is obtained by explicit state counting, using an energy bin of 10 cm−1 and a maximum J of 200. Equations 4a−7 are computed by simple summation, using step sizes of 10 cm−1 and 1 for E and J, respectively. Our results clearly show that the calculated thermal rate coefficients for the formation of acetic acid are almost pressure independent (see Tables S1−S2). For the reaction mechanism Path A (i.e., for H2O addition to the alkene group, see Figure 1), the thermal reaction rate is obviously pressure-independent. For Path B (H2O addition to the carbonyl group, see Figure 2A and B), the calculated thermal reaction rates depend slightly on pressure because of the presence of the reactive enediol intermediate. Differences between k(T,P = 0) and k(T,P = ∞) are found to be small, less than 20% in the wide temperature range considered, from 200 to 2500 K. So, unless otherwise noted, thermal reaction rates obtained at the low-pressure limit will be used as a basis for the discussions below, and should provide an appropriate representation of the nature of the reactions at pressures relevant to both the atmosphere and combustion processes.

A ⎛ ΔE A ⎞ QTS1 kBT ⎜− 0 ⎟ × × exp n h Q ketene × Q H2O ⎝ RT ⎠

k(T , n)PA=∞ =

(4a)

or A Q elec,trans 1 × n h Q ketene × Q H2O

k(T , n)PA=∞ =

∫E

∞

∑ (2J + 1) J=0

G A(E , J )exp( −E /RT )dE

PRC

A Q elec,trans 1 × n h Q ketene × Q H2O

k(T , n)PA= 0 =

J =∞

(4b)

J =∞

∑ (2J + 1) J=0

∞

∫E=0 G A(E , J)exp(−E/RT )dE k1B(T , n) × k 2B(T , n) k −1B(T , n) + k 2B(T , n)

k(T , n)PB=∞ =

k(T ,

n)PB= 0

B Q elec,trans 1 = × n h Q ketene × Q H2O ∞

1B

(5)

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RESULTS AND DISCUSSION Reaction Mechanism. Relative energies of various stationary points for the title reaction calculated with the level of theory used in this work (which we shall hereafter designate as CCSD(T)/CBS) are documented in Table 1. Literature data are also included for the purpose of comparison. To the best of our knowledge, the quantum-chemical methodology used in this work is the most accurate applied to this reaction system so far. As can be seen in Table 1, our calculated reaction enthalpy of −32.2 kcal/mol is in (fortuitously) perfect agreement with the experimental result.53 The values obtained with the G2 method by Cannizzaro and Houk25 are in close agreement with ours, within 1−2 kcal/mol, as is consistent with the high level theoretical treatment provided by the G2 treatment. The QCISD(T)/6-31G(d,p) values of Nguyen and Raspoet21 are also in close agreement with the CCSD(T)/CBS for the reaction of ketene with a single water molecule, but differences here become more significant for the two water reaction. Both water54 and ketene55 are polar molecules; μD(H2O) = 1.85 D and μD(CH2CO) = 1.41 D. Consequently, we anticipate that they will weakly bind to each other with a clustering energy of a few kcal/mol. As reported previously,21 water can add either on the CC bond (denoted hereafter as reaction Path A) of ketene or to the CO bond (denoted hereafter as reaction Path B). The hydration mechanism of ketene was described in detail in ref 21, so only a brief discussion will be given below. Reaction Path A. Reaction of ketene and water through pathway A provides a means for direct formation of acetic acid (a concerted addition mechanism, see Figure 1). In the onewater reaction, the HO−H bond of water adds across the C

(6)

J =∞

∑ (2J + 1) J=0

2B

∫E=0 GG1B((EE ,, JJ)) +× GG2B((EE ,, JJ)) exp( −E /RT )dE

(7)

Here, n is the number of water molecules reacting with ketene. In this work, n = 1 or 2. h is Planck’s constant and kB is Boltzmann’s constant. Qketene and QH2O are total partition functions of ketene and water, respectively. QAtrans,elec is a product of translational and electronic partition functions corresponding to the transition structure, TS1A. GA(E,J) is the rovibrational cumulative reaction probability (CRP) at each pair of (E,J) for TS1A. In this work, rotations are treated as active modes (i.e., assuming that rotational energy can exchange with vibrational energy freely). In addition, vibration and rotation are assumed to be separable, so ρ(E,J) and G(E,J) can be computed by convolution and are expressed as ρ (E , J ) =

∫0

G (E , J ) =

∫0

E

ρvib (E − Erot)ρrot (Erot)dErot

(8)

Gvib(E − Erot)ρrot (Erot)dErot

(9)

E

Here, the vibrational density of states for ketene (or H2O) and vibrational CRP for TS are calculated using ADENSUM51 and SCTST52 codes, respectively, as implemented in Multiwell.40 11000



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(TS1B), to form a 1,1-enediol. This step faces a barrier height of 38.6 kcal/mol, which is 4.1 kcal/mol lower than the H2O addition step to the CC bond (but still very high). When the enediol is produced, it can either lose H2O to regenerate ketene or carry out a 1,3 H-migration via TS2B to form acetic acid. Because these two reaction steps have similar barrier heights, roughly half of the enediol should convert to acetic acid. For the two-water reaction (see Figure 2B), the reaction mechanism is similar to Path A above. The first step is formation of the complex Com1B that has a binding energy of 7.2 kcal/mol, followed by addition to the CO bond leading Com2B, which quickly dissociates to enediol and water. The two-water addition on the carbonyl group faces a barrier of 16.1 kcal/mol relative to the initial reactants and is 4.6 kcal/mol lower than the two-water addition of Path A. Therefore, Path B is found to be more energetically favorable than Path A, in agreement with other studies.21,22 The nascent enediol can react catalytically with a single water molecule to either regenerate ketene or to form acetic acid. The formation of acetic acid has a lower barrier by 7.4 kcal/mol, and thus should be the dominant channel. As a result, when the enediol is formed, it will rapidly isomerize to acetic acid in the presence of water. Chemical Kinetics Results. As discussed above, reactions of ketene with two water molecules proceeds through a prereactive complex (PRC), followed by H2O addition leading to products. Given that the termolecular reaction probability (i.e., one ketene and two free water molecules come together to collide at the same time) is very small under realistic conditions, either a hydrogen-bonded water−ketene complex or a water dimer is expected to form first, followed by attack of the third molecule to this nascent complex. In the atmosphere as well as in combustion, the concentration of water vapor is much higher than that of ketene, so involvement of water dimer is clearly the operative scenario. Because the H-abstraction step has a high barrier (it is the rate-determining step, see Figures 1 and 2), the microcanonical equilibrium between ketene and two water molecules with the PRC is rapidly set up before the subsequent H2O-addition step can occur (see eq 10).

Table 1. Calculated Relative Energies (kcal/mol) for Various Species in the Reactions of Ketene with One and Two Water Molecules in the Gas Phase Species Ketene + H2O Acetic acid Enediol TS1A TS1B TS2B Ketene +2H2O PRC PPC Com1B Com2B Com3B Com4B TS1A_H2O TS1B_H2O TS2B_H2O

This worka

Nguyen & Raspoetb

Cannizzaro & Houkc

Exptl.d

0.0

0.0

0.0

0.00

−32.2 −5.9 42.7 38.6 39.3 0.0

−38.5 −6.5 40.6 38.5 39.0 0.0

−34.4 −6.6 42.0 38.2 38.7

−32.19

−6.3 −34.2 −7.2 −10.7 −10.5 −36.1 20.7 16.1 8.7

−10.3 −43.0 −11.2 −15.3 N/A −49.9 15.8 12.7 4.1

a

Calculated at CCSD(T)/CBS(aVTZ,aVQZ) level of theory; see text. Obtained at QCISD(T)/6-31G(d,p)//MP2/6-31G(d,p) level of theory, ref 21. cObtained with G2//MCSCF/6-31G(d) level of theory, ref 25. dThe experimental value is derived from heats of formation at 0 K for water, ketene, and acetic acid to be −57.10, −10.64, and −99.93 kcal/mol, respectively, taken from http://cccbdb. nist.gov.53 b

C double bond of ketene, such that the hydroxyl group adds to the carbonyl carbon to form the carboxylic acid while the hydrogen adds to the CH2 group to form a methyl group. The transition state, TS1A, of this addition step has a fourmembered ring structure and is 42.7 kcal/mol above the initial reactants. For the two-water reaction, a prereactive complex (PRC) with a binding energy of 6.3 kcal/mol is formed. Next, a similar addition of a hydrogen atom and a hydroxyl group across the CC bond occurs. This path is catalyzed by the presence of additional water. In this process, the transition state (TS1A_H2O) is a six-membered ring with considerably less strain than that in TS1A. Consequently, the two-water reaction significantly lowers the barrier height by 22.0 kcal/mol, from 42.7 to 20.7 kcal/mol. It has been reported in the literature21,22 that addition of yet more water molecules further decreases the barrier height, but such reactions are not likely to occur in the gas phase. Therefore, they will not be further considered in this work. Reaction Path B. Reaction of ketene and water through reaction pathway B provides an indirect route to acetic acid, proceeding through an enediol intermediate (a stepwise addition mechanism, see Scheme 1 and Figure 2). For the one-water reaction, a concerted H2O addition on the carbonyl group proceeds, again via a four-membered ring

fast

fast

slow

H 2CCO + 2H 2O ⇐ ⇒ H 2CCO + (H 2O)2 ⇐ ⇒ PRC ⎯⎯⎯→ TS → Products

(10)

This results in reaction rate constants for producing acetic acid that are nearly pressure-independent. Consequently, the prereactive complex plays a very minor role in the chemical kinetics of the title reaction. In other words, formation of the PRC does not affect the calculated thermal reaction rate constants. For readers who are interested in chemical kinetics treatments for a reaction that passes through a prereactive complex, more details can be found in ref 56. Thermal rate constants for the reactions of ketene with one and two water molecules via both Path A and Path B calculated as a function of temperature are presented in Figures 3−5. Figure 3 displays thermal rate constants for a bimolecular reaction of ketene with a single water molecule calculated at combustion conditions of T = 700−2500 K. Because of the high barriers, these simple bimolecular reactions with high barriers and four-membered-ring transition states are negligible at lower temperatures. Inspection of Figure 3 shows that reaction rate curves for both Path A and Path B cross at around 1000 K. Below 1000 K, the reaction rate via Path B is faster than that of Path A because the former has a lower barrier

Scheme 1. Reaction Scheme of Ketene with a Single Water Molecule to Produce Acetic Acid via an Enediol

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Figure 3. Thermal rate constants for bimolecular reactions of ketene with a single water molecule.

Figure 4. Thermal reaction constants for termolecular reactions of ketene with two water molecules.

height (see Figures 1 and 2). In contrast, above 1000 K, Path A becomes dominant because TS1A is looser than TS1B. This is due to the fact that entropy plays a more important role at higher temperatures. It is of interest to know whether or not acetic acid can be produced from the bimolecular reaction of ketene with a single water molecule at high temperatures in combustion. For this purpose, we calculated the pseudo firstorder rate constants of ketene decay at 1500 K using a concentration [H2O] ≈ 7.5 × 1016 molecules/cm3 (equivalent to a partial pressure of 12 Torr, ca. 50% relative humidity at room temperature). We obtained the decay rates of ketene producing acetic acid to be 2.4 × 10−3 and 7.5 × 10−4 s−1 via Path A and Path B, respectively. Thus, the total reaction rate of ketene decay under these conditions is about 3.2 × 10−3 s−1. This leads to a ketene lifetime of ca. 5 min, with a plausible factor of 2 in error. So, we conclude that ketene can convert to acetic acid under the combustion conditions such as in biomass burnings. It should be noted here that the reaction of ketene with two water molecules cannot compete with the one-water reaction under these conditions (see below). It should be noted

in passing that, since ketene reacts very slowly with water vapor, we did not see the formation of acetic acid in our heated microtubular reactor,27 which was built for the study of fast reactions on time scales of ca. 100 μs. Thermal reaction rate constants calculated at lower temperatures (200−500 K) for reactions of ketene with two water molecules are plotted in Figure 4. The reason to choose this low temperature range is because the two-water addition reaction becomes dominant as compared to the one-water reaction (see Figure 5). As can be seen in Figure 4, the thermal rates of Path B are about 2 to 3 orders of magnitude faster than that of Path A, although the magnitude of the difference becomes smaller as the temperature increases. This is easy to understand because TS1B_H2O for the rate-determining step in Path B lies 4.6 kcal/mol below TS1A_H2O in Path A (see Figures 1 and 2), and the fact that barrier heights largely control the reaction rate at low temperatures. Therefore, the two-water addition process onto the carbonyl group of ketene is both energetically and kinetically favored relative to addition to the alkene group in this temperature range. Nguyen et al. 11002



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Figure 5. Thermal rate constants for the pseudo first-order reactions of ketene with one and two water molecules in the gas phase.

arrived at the same conclusion earlier.21 Now, it is of interest to address the question whether acetic acid can be produced from the gas-phase hydration of ketene at ambitious temperatures in the atmosphere: as mentioned in the Introduction a previous paper27 reported that acetic acid was observed within 1 to 2 h when mixing ketene with water vapor (with a partial pressure of 10 Torr) at room temperature in the gas phase. Using the same reaction conditions applied in the experiment (i.e., T = 300 K and [H2O] = 3.2 × 1016 molecules/cm3 at 10 Torr), we calculated pseudo first-order reaction rate constants for the decay of ketene and obtained values of 1.5 × 10−19 and 1.5 × 10−16 s−1 for Path A and Path B, respectively (also see Figure 5). This result suggests that the water addition to ketene in the gas phase to form acetic acid is many orders of magnitude too slow to be observable at room temperature. Therefore, the observed room-temperature formation of acetic acid cannot have come from either of the mechanisms documented in this work. Hence, either another mechanism exists that we have completely missed, or perhaps surface reactions similar to that observed previously26 are responsible. Pseudo first-order reaction rate constants for both Paths A and B with one and two waters have been calculated and are shown pictorially in Figure 5. This shows that the two water (catalyzed) mechanisms are overwhelmingly dominant at low temperatures, with a crossover point well below 1000 K above which the uncatalyzed reactions dominate. This reflects the energy−entropy trade-off mentioned earlier: the uncatalyzed reactions have fewer entropic constraints, but are forced to surmount significantly larger barriers. It is also clear from this analysis that all reactions involving additional catalytic water are entirely negligible at high temperatures. Finally, it is appropriate to make some remarks about the atmospheric implications of our results. As noted in the Introduction, ketene is a demonstrated product of the thermolysis of molecules such as furan and furfural,57,58 which are readily produced by combustion of biomass. Our calculations suggest that, in and near the fire, the production of acetic acid from ketene does indeed represent a plausible means to generate acetic acid in the atmosphere. However, there are two other factors that should be considered. First, it has been conjectured that such hydration of ketene by environmental

water would produce samples of CH3COOH high in the troposphere. Acetic, and other, carboxylic acids would then be excellent nucleation sites for aerosols and, consequently, be important in the formation of clouds. However, given that this homogeneous reaction would appear to proceed at a rate much too slow to be consistent with this picture, it must either be rejected or amended to involve only the acetic acid generated by industry or forest fires. Second, it is useful to consider the difference between ketene and the substituted ketenes that are generated by pyrolysis of substances such as 2,5-dimethyl furan (DMF).59 Experiments have demonstrated that the methyl ketene molecules generated by pyrolysis of DMF do not survive, but quickly fragment to ethylene and CO. This behavior can be rationalized by considering that the parent molecule H2CCO is ”special”, as it can fragment to methylene and CO, while substituted ketenes would produce correspondingly substituted methylenes. For CH2, the ground state is a triplet, and the thermal dissociation of ketene to ground state products is therefore a spin-forbidden process; only the CH2 (1A1) channel (which is about 9 kcal/mol higher) is allowed: +

CH 2CO → CH 2(X̃ 3B1) + CO(X1 ∑ ) DH 298 = 78.4 ± 0.5kcal/mol

(11a) +

CH 2CO → CH 2(a1̃ A1) + CO(X1 ∑ ) DH 298 = 87.4 ± 0.5kcal/mol

(11b)

However, for most substituted methylenes RCH, the singlet− triplet gap is either negative or much smaller, and the thermal dissociation to RCH and CO becomes more accessible, and the RCH carbenes will rapidly isomerize to the corresponding olefins. Accordingly, ketene might be a special case where the unimolecular decomposition is slowed down sufficiently that hydration can take place at high temperatures, while the same is not true for substituted ketenes. 11003



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(5) Calvert, J. G.; Atkinson, R.; Kerr, J. A.; Madronich, S.; Moorgat, G. K.; Wallington, T. J.; Yarwood, G. The Mechanisms of Atmospheric Oxidation of Alkenes; Oxford University Press: New York, Oxford, 2000. (6) Poisson, N.; Kanakidou, M.; Crutzen, P. J. Impact of NonMethane Hydrocarbons on Tropospheric Chemistry and the Oxidizing Power of the Global Troposphere: 3-Dimensional Modelling Results. J. Atmos. Chem. 2000, 36, 157−230. (7) Silva, G. D. Oxidation of Carboxylic Acids Regenerates Hydroxyl Radicals in the Unpolluted and Nighttime Troposphere. J. Phys. Chem. A 2010, 114, 6861−6869. (8) De Smedt, F.; Bui, X. V.; Nguyen, T. L.; Peeters, J.; Vereecken, L. Theoretical and Experimental Study of the Product Branching in the Reaction of Acetic Acid with OH Radicals. J. Phys. Chem. A 2005, 109, 2401−2409. (9) Butkovskaya, N. I.; Kukui, A.; Pouvesie, N.; Le Bras, G. Rate Constant and Mechanism of the Reaction of OH Radicals with Acetic Acid in the Temperature Range of 229−300 K. J. Phys. Chem. A 2004, 108, 7021−7026. (10) Jacob, D. J.; Heikes, B. G.; Fan, S. M.; Logan, J. A.; Mauzerall, D. L.; Bradshaw, J. D.; Singh, H. B.; Gregory, G. L.; Talbot, R. W.; Blake, D. R.; et al. Origin of Ozone and NOx in the Tropical Troposphere: A Photochemical Analysis of Aircraft Observations Over the South Atlantic Basin. J. Geophys. Res. Atmos. 1996, 101, 24235−24250. (11) Talbot, R. W.; Beecher, K. M.; Harris, R. C.; Cofer, W. R. Atmospheric Geochemistry of Formic and Acetic-Acids at MidLatitude Temperature Site. J. Geophys. Res. Atmos. 1988, 93, 1638− 1652. (12) Goldman, A.; Murcray, F. H.; Murcray, D. G.; Rinsland, C. P. A Search for Formic Acid in the Upper Troposphere − a Tentative Identification of the 1105-CM(−1) Nu-6 Band-Q Branch in HighResolution Ballon-Borne Solar Absorption-Spectra. Geophys. Res. Lett. 1984, 11, 307−310. (13) Klemm, O.; Talbot, R. W.; Fitzgerald, D. R.; Klemm, K. I.; Lefer, B. L. Low to Middle Tropospheric Profiles and Biosphere/Troposphere Fluxes of Acidic Gases in the Summertime Canada Taiga. J. Geophys. Res. Atmos. 1994, 99, 1687−1698. (14) Bui, V. X. PhD Thesis. Kinetic and Product Distribution Study of the Tropospheric Reaction of OH Radicals with Acetic Acid over an Extended Temperature Range; Katholieke Universiteit Leuven, 2008. (15) Vasiliou, A.; Nimlos, M. R.; Daily, J. W.; Ellison, G. B. Thermal Decomposition of Furan Generates Propargyl Radicals. J. Phys. Chem. A 2009, 113, 8540−8547 and references therein.. (16) Sendt, K.; Bacskay, G. B.; Mackie, J. C. Pyrolysis of Furan: Ab Initio Quantum Chemical and Kinetic Modeling Studies. J. Phys. Chem. A 2000, 104, 1861−1875. (17) Tian, Z.; Yuan, T.; Fournet, R.; Glaude, P. A.; Sirjean, B.; BattinLeclerc, F.; Zhang, K.; Qi, F. Combust. Flame 2011, 158, 756−773. (18) Wei, L.; Tang, C.; Man, X.; Jiang, X.; Huang, Z. HighTemperature Ignition Delay Times and Kinetic Study of Furan. Energy Fuels 2012, 26, 2075−2081. (19) Tidwell, T. T. Ketenes; Wiley-InterScience, 2006. (20) Tidwell, T. T. Ketene Chemistry after 100 Years: Ready for a New Century. Eur. J. Org. Chem. 2006, 563−576. (21) Nguyen, M. T.; Raspoet, G. The Hydration Mechanism of Ketene: 15 Years Later. Can. J. Chem. 1999, 77, 817−829 and references therein.. (22) Wu, X. P.; Wei, X. G.; Sun, X. M.; Ren, Y.; Wong, N. B.; Li, W. K. Theoretical Study on the Role of Cooperative Solvent Molecules in the Neutral Hydrolysis of Ketene. Theor. Chem. Acc. 2010, 127, 493− 506. (23) Allen, B. M.; Hegarty, A. F.; O’Neill, P.; Nguyen, M. T. Hydration of Bis(pentamethylphenyl)- and Bismesityl-Ketenes Leading to Ene-1,1-diols (Enols of Carboxylic Acids). J. Chem. Soc., Perkin Trans. 2 1992, 927−934. (24) Bothe, E.; Dessouki, A. M. Schulte-Frohlinde D. Rate and Mechanism of the Ketene Hydrolysis in Aqueous Solution. J. Phys. Chem. 1980, 84, 3270−3272.

SUMMARY Addition reaction mechanisms of ketene involving one and two water molecules in the gas phase were theoretically characterized using the CCSD(T) method in combination with Dunning’s correlation consistent basis sets and extrapolation techniques. The calculated relative energies of stationary points on the lowest-lying singlet PES are predicted to be accurate within 2.0 kcal/mol. Two-water addition reaction was found to lower the barrier height significantly by ca. 22 kcal/mol as compared to one-water addition. So, the additional water molecule plays an important autocatalytic role. The H2O addition onto the carbonyl group of ketene is found to be more energetically favorable than onto the alkene group, in agreement with previously theoretical studies. Thermal reaction rate constants were then computed using the SCTST/2D-ME approach under the low- and high-pressure limits. The calculated rate constants are found to be nearly pressureindependent. The single water addition to form acetic acid (within a few minutes) is dominant at high temperatures in biomass burnings, whereas the two-water addition becomes the major channel at lower temperatures. Under atmospheric conditions, the formation of acetic acid from the gas-phase hydration of ketene is predicted to be negligibly slow.

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ASSOCIATED CONTENT

S Supporting Information *

Optimized geometries, rovibrational parameters, anharmonic constants, and energies for various species in the reaction of ketene with water are given. This material is available free of charge via the Internet at http://pubs.acs.org.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS J.F.S. and T.L.N. are supported by the Robert A. Welch Foundation (Grant F-1283) and the Department of Energy, Office of Basic Energy Sciences (Contract Number DE-FG0207ER15884). G.B.E. and J.F.S. are also supported by the US National Science Foundation, under Grant CHE-1112466.

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REFERENCES

(1) Paulot, F.; Wunch, D.; Crounse, J. D.; Toon, G. C.; Millet, D. B.; DeCarlo, P. F.; Vigouroux, C.; Deutscher, N. M.; González Abad, G.; Notholt, J.; et al. Importance of Secondary Sources in the Atmospheric Budgets of Formic and Acetic Acids. Atmos. Chem. Phys. 2011, 11, 1989−2013. (2) Veres, P.; Reberts, J. M.; Burling, I. R.; Warneke, C.; de Gouw, J.; Yokelson, R. J. Measurements of Gas-Phase Inorganic and Organic Acids from Biomass Fires by Negative-Ion Proton-Transfer ChemicalIonization Mass Spectrometry. J. Geophys. Res. Atmos. 2010, 115, D23302. (3) Carlton, A. G.; Turpin, B. J.; Lim, H. J.; Altieri, K. E.; Seitzinger, S. Link between Isoprene and Secondary Organic Aerosol (SOA): Pyruvic Acid Oxidation Yields Low Volatility Organic Acids in Clouds. Geophys. Res. Lett. 2006, 33, L06822(1−4). (4) Andrews, D. U.; Heazlewood, B. R.; Maccarone, A. T.; Conroy, T.; Payne, R. J.; Jordan, M. J. T.; Kable, S. H. Photo-Tautomerization of Acetaldehyde to Vinyl Alcohol: A Potential Route to Tropospheric Acids. Science 2012, 337, 1203−1206. 11004



Article

(25) Cannizzaro, C. E.; Houk, K. N. Theoretical Study of the Stereoselective Additions of Chiral Alcohols to Ketene. J. Am. Chem. Soc. 2004, 126, 10992−11008. (26) Blake, P. G.; Davies, H. H. Reactions of Ketene. Part III. Kinetics of the Spontaneous and Acetic Acid-Catalysed Reactions of Ketene with Water. J. Chem. Soc. Perkin II 1972, 321−323. (27) Kahan, T. F.; Ormond, T. K.; Ellison, G. B.; Vaida, V. Acetic Acid Formation via the Hydration of Gas-Phase Ketene under Ambient Conditions. Chem. Phys. Lett. 2013, 565, 1−4. (28) Raghvachari, K.; Trucks, G. W.; Pople, J. A.; Head-Gorden, M. A Fifth-Order Perturbation Comparison of Electron Correlation Theories. Chem. Phys. Lett. 1989, 157, 479−483. (29) Almlof, J.; Taylor, P. R. General Constraction of Gaussian-Basis Sets. 1. Atomic Natural Orbitals for 1st-Row and 2nd-Row Atoms. J. Chem. Phys. 1987, 86, 4070−4077. (30) Almlof, J.; Taylor, P. R. General Constraction of Gaussian-Basis Sets. 2. Atomic Natural Orbitals and the Calculation of Atomic and Molecular-Properties. J. Chem. Phys. 1990, 92, 551−560. (31) McCaslin, L. M.; Stanton, J. F. Calculation of Fundamental Frequencies for Small Polyatomic Molecules: A Comparison of Correlation-Consistent and Atomic Natural Orbital Basis Sets. Mol. Phys. 2013, 111, 1492−1496. (32) Mills, I. M. Vibration−Rotation Structure in Asymmetric- and Symmetric-Top Molecules. In Molecular Spectroscopy: Modern Research; Rao, K. N., Mathews, C. W., Eds.; Academic Press: New York, 1972; Vol. 1, p 115. (33) Dunning, T. H., Jr. Gaussian Basis Sets for Use in Correlated Molecular Calculations. I. The Atoms Boron through Neon and Hydrogen. J. Chem. Phys. 1989, 90, 1007−1023. (34) Feller, D. Application of Systematic Sequences of WaveFunctions to the Water Dimer. J. Chem. Phys. 1992, 96, 6104−6114. (35) Helgaker, T.; Klopper, W.; Koch, H.; Noga, J. Basis-Set Convergence of Correlated Calculations on Water. J. Chem. Phys. 1997, 106, 9639−9646. (36) Tajti, A.; Szalay, P. G.; Csaszar, A. G.; Kallay, M.; Gauss, J.; Valeev, E. F.; Flowers, B. A.; Vazquez, J.; Stanton, J. F. HEAT: High Accuracy Extrapolated Ab Initio Thermochemistry. J. Chem. Phys. 2004, 121, 11599−11613. (37) Bomble, Y. J.; Vazquez, J.; Kallay, M.; Michauk, C.; Szalay, P. G.; Csaszar, A. G.; Gauss, J.; Stanton, J. F. High-Accuracy Extrapolated Ab Initio Thermochemistry. II. Minor Improvements to the Protocol and a Vital Simplification. J. Chem. Phys. 2006, 125, 064108−8. (38) Harding, M. E.; Vazquez, J.; Ruscic, B.; Wilson, A. K.; Gauss, J.; Stanton, J. F. High-Accuracy Extrapolated Ab Initio Thermochemistry. III. Additional Improvements and Overview. J. Chem. Phys. 2008, 128, 114111−15. (39) Stanton, J. F.; Gauss, J.; Harding, M. E.; Szalay, P. G.; Auer, w. c. f. A. A.; Bartlett, R. J.; Benedikt, U.; Berger, C.; Bernholdt, D. E.; Bomble, Y. J.; et al. CFOUR, Coupled-Cluster Techniques for Computational Chemistry, 2009. (40) Barker, J. R.; Ortiz, N. F.; Preses, J. M.; Lohr, L. L.; Maranzana, A.; Stimac, P. J.; Nguyen, T. L.; Kumar, T. J. D. Ann Arbor, Michigan, USA (http://aoss.engin.umich.edu/multiwell/), 2011. (41) Glowacki, D. R.; Liang, C. H.; Morley, C.; Pilling, M. J.; Robertson, S. H. MESMER: An Open-Source Master Equation Solver for Multi-Energy Well Reactions. J. Phys. Chem. A 2012, 116, 9545− 9560. (42) Smith, S. C.; Gilbert, R. G. Angular-Momentum Conservation in Unimolecular and Recombination Reactions. Int. J. Chem. Kinet. 1988, 20, 307−329. (43) Miller, J. A.; Klippenstein, S. J. Master Equation Methods in Gas Phase Chemical Kinetics. J. Phys. Chem. A 2006, 110, 10528−10544 and reference therein.. (44) Miller, J. A.; Klippenstein, S. J.; Raffy, C. Solution of Some One and Two-Dimensional Master Equation Models for Thermal Dissociation: The Dissociation of Methane in the Low-Pressure Limit. J. Phys. Chem. A 2002, 106, 4904−4913 and references therein. (45) Pilling, M. J. Reactions of Hydrocarbon Radicals and Biradicals. J. Phys. Chem. A 2013, 117, 3697−3717.

(46) Barker, J. R.; Weston, R. E. Collisional Energy Transfer Probability Densities P(E,J;E′,J′) for Monatomics Colliding with Large Molecules. J. Phys. Chem. A 2010, 114, 10619−10633. (47) Miller, W. H. Unified Statistical-Model for Complex and Direct Reaction-Mechanisms. J. Chem. Phys. 1976, 65, 2216−2223. (48) Troe, J. The Polanyi Lecture-The Colorful World of ComplexForming Bimolecular Reactions. J. Chem. Soc., Faraday Trans. 1994, 90, 2303−2317. (49) Peeters, J.; Vereecken, L. International Gas Kinetics Conference; GK2006 Orleans; July 22−27, 2006. (50) Greenwald, E. E.; North, S. W.; Georgievskii, Y.; Klippenstein, S. J. A Two Transition State Model for Radical-Molecule Reactions: A case Study of the Addition of OH to C2H4. J. Phys. Chem. A 2005, 109, 6031−6044. (51) Nguyen, T. L.; Barker, J. R. Sums and Densities of Fully Coupled Anharmonic Vibrational States: A Comparison of Three Practical Methods. J. Phys. Chem. A 2010, 114, 3718−3730. (52) Nguyen, T. L.; Stanton, J. F.; Barker, J. R. A Practical Implementation of Semi-Classical Transition State Theory for Polyatomics. Chem. Phys. Lett. 2010, 499, 9−15. (53) NIST Computational Chemistry Comparison and Benchmark Database, NIST Standard Reference Database Number 101, Release 16a, August 2012, Editor: Russell D. Johnson III; http://cccbdb.nist.gov/. (54) Lovas, F. J. Microwave Spectral Tables II. Triatomic Molecules. J. Phys. Chem. Ref. Data 1978, 7, 1448−1750. (55) Johnson, H. R.; Strandberg, M. W. P. The Microwave Spectrum of Ketene. J. Chem. Phys. 1952, 20, 687−695. (56) Nguyen, T. L.; Stanton, J. F. Ab Initio Rate Calculations of HO + HO = O(3P) + H2O Reaction and Isotopologues. J. Phys. Chem. A 2013, 117, 2678−2686. (57) Mettler, M. S.; Mushrif, S. H.; Paulsen, A. D.; Javadekar, A. D.; Vlachos, D. G.; Dauenhauer, P. J. Revealing Pyrolysis Chemistry for Biofuels Production: Conversion of Cellulose to Furans and Small Oxygenates. Energy Env. Sci. 2012, 5, 5414−5424. (58) Urness, K. N.; Golan, A.; Daily, J. W.; Nimlos, M. R.; Stanton, J. F.; Ahmed, M.; Ellison, G. B. Pyrolysis of Furan in a Microreactor J. Chem. Phys. 2013, accepted. (59) Kim, J. H.; Ormond, T. K.; Urness, K. N.; Guan, Q.; Golan, A.; Daily, J. W.; Nimlos, M. R.; Stanton, J. F.; Ahmed, M.; Ellison, G. B. Pyrolysis of the Biofuel, 2, 5-dimethylfuran, in a Microreactor. J. Org. Chem. 2013.

11005
