Organic Acids Tunably Catalyze Carbonic Acid Decomposition - The

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Organic Acids Tunably Catalyze Carbonic Acid Decomposition Manoj Kumar, Daryle H. Busch, Bala Subramaniam, and Ward Hugh Thompson J. Phys. Chem. A, Just Accepted Manuscript • Publication Date (Web): 16 Jun 2014 Downloaded from http://pubs.acs.org on June 17, 2014

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The Journal of Physical Chemistry

Organic Acids Tunably Catalyze Carbonic Acid Decomposition

Manoj Kumar, †, ‡ Daryle H. Busch, †, ‡ Bala Subramaniam, ‡,¤ and Ward H. Thompson†, ‡,*

†

Department of Chemistry, University of Kansas, Lawrence 66045

‡

Center for Environmentally Beneficial Catalysis, 1501 Wakarusa Drive, Lawrence, KS 66047

¤

Department of Chemical and Petroleum Engineering, University of Kansas, Lawrence, KS

66045.

AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]

ACS Paragon Plus Environment

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ABSTRACT. Density functional theory calculations predict that the gas-phase decomposition of carbonic acid, a high energy, 1,3-hydrogen atom transfer reaction, can be catalyzed by a monocarboxylic acid or a dicarboxylic acid, including carbonic acid itself. Carboxylic acids are found to be more effective catalysts than water. Among the carboxylic acids, the monocarboxylic acids outperform the dicarboxylic ones wherein the presence of an intramolecular hydrogen bond hampers the hydrogen transfer. Further, the calculations reveal a direct correlation between the catalytic activity of a monocarboxylic acid and its pKa, in contrast to prior assumptions about carboxylic acid-catalyzed hydrogen transfer reactions. The catalytic efficacy of a dicarboxylic acid, on the other hand, is significantly affected by the strength of an intramolecular hydrogen bond. Transition state theory estimates indicate that effective rate constants for the acidcatalyzed decomposition are four orders-of-magnitude larger than for the water-catalyzed reaction. These results offer new insights into the determinants of general acid catalysis with potentially broad implications.

KEYWORDS. Electronic Structure • Atmospheric Chemistry • Hydrogen Atom Transfer • Acid Catalysis • Reaction Mechanisms

1. INTRODUCTION


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Carbonic acid (H2CO3) is a molecule of wide importance.1-5 Despite the long-held notion that it is kinetically unstable, there is now growing experimental and theoretical evidence suggesting that H2CO3 is quite long-lived in the gas-phase.6-17 Pure H2CO3 has been synthesized, isolated, and characterized using various techniques6-11 and the half-life of an isolated gaseous H2CO3 molecule is estimated to be 0.18 million years at 300 K.12 However, the kinetic stability of H2CO3 is reduced in the presence of water (H2O) vapor, e.g., the half-life of H2O-bound H2CO3 is only 10 h at 300 K, reflecting an enhancement of ~108 in the decomposition rate constant (Scheme 1).12-13 In addition, it has recently been reported that H2CO3, which forms dimers in the gas-phase,7,18,19,20 can catalyze its own decomposition.17 Interestingly, recent FT-IR21 and matrix isolation11 experiments suggest that H2CO3 in the troposphere is stable even in the presence of water vapor. Although H2CO3 decomposition has been intensely studied experimentally and theoretically during the last three decades, key questions remain; for example, do other mechanistic pathways contribute to its gas-phase decomposition? In this work, we propose a new mechanism for the catalyzed tropospheric decomposition of H2CO3 by carboxylic acids. Monocarboxylic acids such as formic acid, HCOOH, and dicarboxylic acids such as oxalic acid are considered along with H2CO3 itself. The involvement of an acid causes a dramatic reduction in the barrier height of the reaction and thus provides a facile bimolecular route for decomposition of gaseous H2CO3. The autocatalytic activity of H2CO3 has already been reported,17 including, more recently,18 two additional, more effective, autocatalytic pathways based on different conformations of H2CO3 that result in multiple conformers for the H2CO3 dimer. These reactions are considered in the general context of the catalytic role of organic acids, which is important for several reasons. Both HCOOH and H2CO3 are produced in icy grain mantles upon irradiation with high-energy photons.1,22 Carboxylic acids


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are important components of tropospheric chemistry23 with their concentrations reaching several parts per billion.24 There is a significant literature indicating that acids exert catalytic influence on the gas-phase chemistry mediated by hydrogen atom transfer reactions.25-30 The formation of the H2CO3 dimer has been found theoretically to be a barrierless process.19

O O H O H

O

H 2O

RCO 2H

H O

O

H

O

O

H O

H

H

O

O

H

H

O

R O H O

O O

H O

H O

H O H

Scheme 1. The

O

O

O H

O

H

H

H 2O

H

+

H

H

C O

O

O

O

RCO 2H R

general

mechanistic pathways for the unassisted and the assisted gas-phase decomposition of the syn-anti H2CO3 conformer. Despite the fact that the role of acid catalysis in accelerating the hydrogen atom transfer in the gas and condensed phase is increasingly being recognized, the molecular level insight into the factors that could tune the reactivity of acid catalysis remains elusive. The ability of acid catalysts to enhance the hydrogen atom transfer has been demonstrated by studying either HCOOH-assisted or sulfuric acid-assisted reactions.25-30 Although it is often assumed that organic acids other than HCOOH would produce similar catalytic effect,25,28 their effect has yet


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to be investigated and quantified. Given that dicarboxylic acids are also present in considerable concentrations in the troposphere,31,32,33 they may also catalyze hydrogen transfer chemistry. However, we are not aware of any theoretical study of their catalytic effect on hydrogen atom transfer. Moreover, it remains to be seen whether their mode of catalysis would be similar to that of monocarboxylic acids. In the remainder of this paper, we explore these factors in the context of carbonic acid decomposition.

2. COMPUTATIONAL METHODS Two types of quantum chemical calculations have been carried out to gain a detailed mechanistic insight into the gas-phase decomposition of H2CO3: 1) density functional theory (DFT) calculations, and 2) wavefunction-based calculations including coupled cluster with single and double excitations (CCSD), CCSD(T) that also includes perturbative triple contributions, QCISD, and local pair natural orbital coupled electron pair approximation version 1 (LPNOCEPA/1) calculations. The LPNO-CEPA/1 method is gaining recognition because of its promise to deliver both accuracy and computational efficiency.34 This method, which is based on localization of the occupied orbitals in the reference wavefunction and the spanning of the unoccupied space with highly localized pair natural orbitals, has an accuracy approaching that of CCSD(T).35 DFT, CCSD, CCSD(T) and QCISD calculations were performed using the NWChem36 quantum chemical software while the LPNO-CEPA/1 calculations were carried out with the ORCA37 suite of electronic structure programs. In the first step, we performed a detailed DFT investigation of the unimolecular gasphase decomposition of an H2CO3 molecule. All the structures were fully optimized at the M062X/aug-cc-pVTZ level of theory and the second-order Hessian matrices were calculated to


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ensure that the optimized structures are either true minima or first-order saddle points. Using the M06-2X-optimized geometries, the barrier heights were also estimated from single point calculations (Y/aug-cc-pVTZ//M06-2X/aug-cc-pVTZ; Y= DFT, CCSD, CCSD(T), QCISD, or LPNO-CEPA/1) as well as by performing full geometry optimizations with a variety of DFT functionals including B3LYP, BP86, O3LYP, MPW1PW91, MPW1K, M06-L, PBE, TPSSh, ωB97X-D, and B97-D. The analysis of barrier heights estimated using the DFT and wavefunction-based methods indicate that the accuracy of the M06-2X/aug-cc-pVTZ method is more than sufficient for these systems (see below and Supporting Information). This was also verified by calculating the energies of three rotational isomers of H2CO3, and the activation barrier of interconversion between the syn-syn and anti-syn H2CO3 isomers (Figure 1), and comparing them with the previously reported data.7,12-17,18,19,20 Calculating and validating the barrier heights for tautomerization of vinyl alcohol, isomerization of methoxy radical, and hydrolysis of sulfur trioxide and formaldehyde, key gas-phase hydrogen transfer processes, with previously published data further supports the choice of method, M06-2X/aug-cc-pVTZ. To understand the role of catalysis in the gas-phase decomposition of H2CO3, we considered water, H2CO3, and various monocarboxylic and dicarboxylic acids as potential catalysts. In order to account for entropic effects, all the calculated reaction profiles are reported in terms of Gibbs free energies under atmospheric conditions of 298.15 K and 1 atm. The factors influencing the catalytic activity of an acid were specifically explored by studying a variety of monocarboxylic acids with different electron-donating and withdrawing groups, including HCOOH, acetic acid, monochloroacetic acid, dichloroacetic acid, trichloroacetic acid, H2CO3, propionic acid, and butyric acid. The dicarboxylic acids considered were oxalic acid and malonic


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acid. To illustrate the broad implications of our findings, we also studied the monocarboxylic acid assisted tautomerization of vinyl alcohol and isomerization of methoxy radical (Scheme 2).

Scheme 2. Two additional hydrogen atom transfer reactions namely tautomerization of vinyl alcohol and isomerization of methoxy radical studied in the present work. Note that the oxalic acid monomer has four stable conformations with three capable of catalyzing the H2CO3 decomposition (Figure S7). However, in the present study, only two of the catalytically active oxalic acid conformations are examined in the decomposition. In establishing a relationship between the catalytic activity of a monocarboxylic acid and its acid dissociation constant (pKa), the experimentally determined pKa values were used.

3. RESULTS AND DISCUSSION 3.1. Unimolecular H2CO3 Decomposition. As little experimental information in the form of conformer-specific spectroscopic signatures is available on the gas-phase structure of H2CO3,7-8 the potential energy landscape of its conformers and the mechanism of its unimolecular decomposition have been extensively explored theoretically.7,12-17,18,19,20 In the first step, we also applied our chosen theoretical method, M06-2X/aug-cc-pVTZ to study these two key components of H2CO3 chemistry. The ability to accurately describe these events is generally considered to be the prerequisite for any appropriate theoretical method for addressing the


7


H2CO3 chemistry. Although, the syn-syn conformer of the H2CO3 is the most stable, it corresponds to the inactive H2CO3 conformation, which must undergo a conformational change to allow access to its active syn-anti conformation prior to decomposition. The estimated free energy difference of

10.3 10

anti-anti

TS

9.1

8

Free Energy [kcal/mol]

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6

O C H 4

2

1.4 syn-anti 0

0.0 syn-syn

-2

Figure 1. M06-2X/aug-cc-pVTZ calculated free energy landscape (298.15 K, 1 atm) of the H2CO3 conformers. 1.4 kcal/mol between the syn-syn and syn-anti H2CO3 isomers, and the free energy barrier of 9.1 kcal/mol for their interconversion (Figure 1) are in very good agreement with the literature values of 1.0-1.9 kcal/mol and 10.3-10.5 kcal/mol.6,7,8,18 The calculated transition state for the isomerization of the syn-syn H2CO3 has a single negative frequency of 551 cm-1 which corresponds to the motion of H-O vector around the C-O bond axis and is indicative of a true saddle point. The calculated structural parameters and the rotational constants for the syn-anti


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H2CO3 conformer (Table S1) are also in good accord with the previous calculations17 as well as the experimental data of Mori et al.7 The decomposition of gaseous H2CO3 is a single step, high-energy 1,3 hydrogen transfer. The reaction involves the concerted cleavage of both the C-OH bond that has the syn OH group along with the anti O-H bond, and is mediated by a four-membered sterically constrained transition state. The DFT-calculated zero point energy-corrected barrier height for the uncatalyzed unimolecular decomposition is 41.0 kcal/mol (Figure 2), in excellent agreement with the previously reported CCSD(T) values of 41.0-43.6 kcal/mol.7,12-13,15,17,18 Note that we considered a variety of DFT functionals. Several, including B3LYP and BP86, underestimated the barrier height of the reaction by 4.0-5.0 kcal/mol (Table S2). The analysis of the zero-point uncorrected barrier heights from the DFT and wavefunction-based methods indicate that M062X/aug-cc-pVTZ is sufficiently accurate for these systems. It predicts a barrier of 44.9 kcal/mol, in close accord with the CCSD(T)/aug-cc-pVTZ//M06-2X-aug-cc-pVTZ value of 44.0 kcal/mol (Table S3). In the M06-2X calculated transition state, the transferring hydrogen atom is nearly equidistant from both the oxygens involved in the reaction while the C-OH bond is significantly elongated to 1.63 Å. There is a single negative frequency of 1733 cm-1 associated with the transition state geometry that corresponds to the translational motion of hydrogen atom between the two non-carbonyl oxygens. The tautomerization of vinyl alcohol,25 isomerization of methoxy radical,26 hydrolysis of sulfur trioxide,27,30,38 and hydrolysis of formaldehyde39 are some of the most important unimolecular and bimolecular gas-phase reactions. The barrier heights for these reactions are also faithfully reproduced with this method, which indicates its broad utility for studying the gas-phase hydrogen transfer chemistry (Table S4).


9


40

O C H

TS

41.0

30


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20

10

0

0.0

Int

-10

-9.2

H 2O + CO 2 -12.1

P -20

Figure 2. M06-2X/aug-cc-pVTZ calculated free energy profile (298.15 K, 1 atm) for the unimolecular gas-phase decomposition of a syn-anti H2CO3 molecule.

3.2 Bimolecular H2CO3 Decomposition 3.2.1 Water-Catalysis. The role of water catalysis on the gas-phase H2CO3 decomposition has been previously examined using electronic structure methods.12,13 We have recalculated the potential energy surface showing the effect of a single water molecule on the reaction in order to facilitate the comparison between acid-assisted and water-assisted decomposition on an equal


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theoretical basis. The M06-2X/aug-cc-pVTZ calculated free energy profile and the optimized geometries of key stationary points for the water-assisted reaction are shown in Figure 3. The present DFT calculations reproduce the previously reported12,13 catalytic effect of water. The presence of a single H2O molecule lowers the reaction free energy barrier by 17.1 kcal/mol. We note that it is important to consider the entropic contributions that disfavor the formation of the water-H2CO3 complex. Thus, here and in the following analyses, we report free energy profiles; see Table 1. The calculated catalytic effect reducing the barrier by 18.9 kcal/mol in electronic energy relative to the water-H2CO3 complex, is in reasonable agreement with the 16.4 kcal/mol previously found at the CCSD(T)/aug-cc-pVDZ//MP2/aug-cc-pVDZ/B3LYP/6-31+G(d) level of theory.12,13 Although we have not investigated the catalytic effect of an H2O cluster on the decomposition reaction, Loerting et al. found a maximum catalytic effect of 22.7 kcal/mol in the calculated barrier height of the reaction when catalyzed by an H2O trimer,13 indicating that the effect of additional waters is limited. 3.2.2. Monocarboxylic Acid Catalysis. Since the basis of the catalysis by water is the shuttling of hydrogen atoms, it is interesting to investigate if a carboxylic acid, such as HCOOH, would act similarly. Indeed, our calculations find that HCOOH catalyzes H2CO3 decomposition by a similar mechanism and to a much greater degree. The calculated free energy profile along with key stationary points is shown in Figure 3. In contrast to the water-assisted reaction, the formation of prereaction complex, Int1, in the HCOOH-assisted reaction is 4.7 kcal/mol exoergonic. This is due to the formation of two sterically favorable hydrogen bonds between the substrate and the catalyst. The calculated reaction free energy barrier for the HCOOH-assisted decomposition is only 8.7 kcal/mol relative to the separated reactants, which is a dramatic reduction from both the uncatalyzed (∆G‡ = 41.0 kcal/mol) and H2O-catalyzed (∆G‡ = 23.9


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Table 1. M06-2X/aug-cc-pVTZ calculated zero point-corrected energies, ∆E, and free energies, ∆G, (in kcal/mol) of various species involved in the uncatalyzed and catalyzed gas-phase decomposition of a H2CO3 molecule. Energies are reported with respect to the separated reactants.

Catalyst None Water Formic acid Acetic acid Monochloroacetic acid Dichloroacetic acid Trichloroacetic acid Propionic acid Butyric acid Oxalic acid Malonic acid Succinic acid Carbonic acid (D1syn-anti) Carbonic acid (D2syn-anti) Carbonic acid (Dsyn-syn)

Int1 ∆E -7.6 -15.0 -17.0 -11.7 -10.9 -10.4 -18.2 -18.0 -9.8 -9.6 -6.1 -7.2 -13.4 -11.9

TS ∆G 0.6 -4.7 -6.7 -2.3 -0.5 0.0 -7.5 -7.1 0.7 1.0 3.2 2.7 -2.9 -1.4

∆E 41.0 14.5 -2.5 -4.7 0.3 1.1 2.0 -5.9 -5.6 3.5 4.0 1.7 19.3 -1.2 0.3

Int2 ∆G 41.0 23.9 8.7 6.5 10.8 12.5 14.0 5.8 6.2 15.0 15.8 13.5 29.7 10.3 11.7

∆E -6.6 -12.1 -19.6 -20.7 -16.8 -16.6 -16.3 -22.0 -21.8 -14.7 -14.2 -16.3 -19.7 -16.7 -16.4

∆G -9.2 -5.7 -11.7 -12.1 -10.6 -7.3 -7.8 -13.9 -12.3 -5.6 -4.5 -7.5 -14.0 -9.0 -7.5

P ∆E -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -4.4 -7.3 -4.4 -4.4

∆G -12.1 -12.1 -12.1 -12.1 -12.1 -12.1 -12.1 -12.1 -12.1 -12.1 -12.1 -12.1 -22.9 -12.1 -12.1

kcal/mol) reactions. This dramatic catalytic effect is because HCOOH effectively converts a single 1,3 hydrogen shift reaction into two 1,2 hydrogen shifts. As a result, an expanded eightmembered ring transition state is formed in the HCOOH-mediated decomposition that is sterically less encumbered than the four- or six-membered cyclic transition states involved in the uncatalyzed and H2O-catalyzed reactions, respectively. Moreover, the pre- and post-reaction complexes involved in the HCOOH-assisted reaction are almost two times more stable than the


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25

23.9

O C H

20

TS

15.2

15

10 TS


1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


8.7

5

0.6 0.0

0

Int 1

-5

-10

-4.7 Int 2

-5.7

HCOOH + H 2O -11.7 + CO2 Int 2 -12.1 P

-15

Int 1

H 2O + H 2O + CO2

-12.1 Acid catalysis

Water catalysis

P

Figure 3. M06-2X/aug-cc-pVTZ calculated free energy profile (298.15 K, 1 atm) of formic acidcatalyzed (left) and water-catalyzed (right) gas-phase decomposition of H2CO3. ones formed in the H2O-assisted reaction due to the presence of stronger hydrogen-bonding interactions. Interestingly, the catalytic efficiency of a single HCOOH molecule is even higher than that of the best H2O cluster, i.e., HCOOH lowers the H2CO3 decomposition electronic energy barrier by 69% compared to a maximum of 52% for water clusters.13 Though the general structure of the transition state involved in the HCOOH-catalyzed and (H2O)3-catalyzed decomposition is nearly identical, there is a significant entropic penalty for bringing four bodies


13


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together in the (H2O)3-catalyzed decomposition which inhibits the catalytic potential of an H2O cluster. Since several monocarboxylic acids, e.g., acetic and propionic acid, are also present in appreciable amounts in the troposphere,23 it is instructive to investigate how the structure of the organic acid changes the catalytic effect on the H2CO3 decomposition. Although recent theoretical studies25-30 have extensively explored the catalytic role of HCOOH in atmospheric hydrogen atom transfer chemistry, the possible involvement of monocarboxylic acids other than HCOOH has not received attention. Thus, we have also examined the effect of other carboxylic acids on the H2CO3 decomposition. The calculations reveal that different monocarboxylic acids do not necessarily produce similar catalytic effects as has been assumed previously; rather the catalytic activity of a given monocarboxylic acid directly correlates with its acid dissociation constant, pKa, as shown in Figure 4 (see also Figures S1-S6 and Table 1). Among all the acids considered, propionic acid produces the maximum catalytic effect, lowering the free energy barrier by 86%, from 41.0 to 5.8 kcal/mol. The origin of this catalytic effect is electronic in nature as the transition state structure of all the acid-catalyzed H2CO3 decompositions is found to be essentially constant (Table 1). The nature of the substituent on the carbonyl carbon of the acid influences its catalytic potency. That is, an electron-withdrawing group (e.g., chlorine) reduces the electron density at the carbonyl oxygen and thus decreases the hydrogen atom accepting ability of the acid, while an electron-donating group (e.g., methyl) enhances the nucleophilicity of the carbonyl oxygen and thus improves the catalytic efficiency of the acid. For this reason, chloroacetic acid (∆G‡ = 10.8 kcal/mol; pKa = 2.9) is less effective than HCOOH (∆G‡ = 8.7 kcal/mol; pKa = 3.7), which in turn is less effective than acetic acid (∆G‡ = 6.5 kcal/mol; pKa =4.7) in catalyzing the H2CO3 decomposition.


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To explore the generality of these results, we also studied the acid-assisted tautomerization of vinyl alcohol and the isomerization of a methoxy radical in the presence of various monocarboxylic acids (Scheme 2). Although the role of the acid catalysis in these reactions has been recently reported,25,26 the effect of acids other than HCOOH was not examined. As mentioned earlier, our theoretical method reasonably reproduces the barrier heights for these reactions and thus, possesses the necessary chemical accuracy. Similar to prior theoretical studies, our calculations suggest a significant catalytic role of HCOOH in the hydrogen atom transfer chemistry. But in addition to that, the present calculations also find that the acid catalysis is indeed tunable, i.e., just as for H2CO3 decomposition, there exists a direct correlation between the catalytic effectiveness of an acid and its pKa (Figure 4; Tables S5-S6). Interestingly, the correlation between the free energy barrier and the pKa, as measured by the slope of a linear fit to the data, ∆G‡ = α pKa + β, in Figure 4 is nearly the same for all these reactions. The data suggest a slightly larger effect of the pKa of the carboxylic acid on the tautomerization of vinyl alcohol (α = -1.28) than the H2CO3 decomposition (α = -0.99) or isomerization of methoxy radical (α = -0.96).


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Figure 4. M06-2X/aug-cc-pVTZ calculated reaction free energy barriers versus pKa for the acidcatalyzed H2CO3 decomposition (top panel), tautomerization of vinyl alcohol, (middle panel), and isomerization of a methoxy radical (bottom panel).


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We also analyzed our calculated data for the H2CO3 decomposition using the Hammett equation, one of the most widely used linear free energy relations for quantifying the effect of substituents on reaction mechanisms.40 The estimated Hammett correlation is shown in Figure 5 for the acid-catalyzed decomposition of a H2CO3 molecule. The calculated free energy barriers for the substituted HCOOH-catalyzed reaction exhibit a linear relationship with the Hammett constant values of the acids, which provides corroborating evidence that substitution at the carbonyl carbon tunes the acid catalysis. To the best of our knowledge, this is the first theoretical study elucidating that the nature of a monocarboxylic acid also plays a key role in determining its catalytic activity in the context of any hydrogen atom transfer reaction.

Figure 5. Hammett correlation between the M06-2X/aug-cc-pVTZ calculated reaction free energy barriers of the acid-catalyzed H2CO3 decomposition and σ-values of the acids. 3.2.3. Dicarboxylic Acid Catalysis. Since dicarboxylic acids are common organic pollutants in the urban, industrial, and rural air,31 it is natural to enquire about their role in H2CO3 decomposition. As oxalic acid is the simplest and most common dicarboxylic acid in the Earth’s atmosphere,32,33 we first analyzed the effect of a single oxalic acid molecule on the potential


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energy surface of the H2CO3 decomposition. Note that the oxalic acid monomer exists in multiple conformations, with three of them being catalytically active for H2CO3 decomposition (Figure S7). However, we have only explored two of its catalytically active conformations. The calculations reveal that the free energy barrier of the oxalic acid-catalyzed reaction is significantly reduced to 15.0 kcal/mol, which reflects a lowering of 8.9 and 26.0 kcal/mol relative to the water-catalyzed and the uncatalyzed reactions, respectively (Figure 6 and Table 1). Although a single oxalic acid conformer lowers the barrier less than a monocarboxylic acid or an H2CO3 conformer (see below), its catalytic effect is still appreciably higher than that of water. The relatively lower catalytic efficacy of an oxalic acid conformer is due to the presence

Figure 6. M06-2X/aug-cc-pVTZ calculated transition states for the oxalic acid-, malonic acid-, and succinic acid-assisted decomposition of a gas-phase H2CO3 molecule (left panel) and their free energy barrier dependence plotted as a function of pKa and intramolecular =O⋅⋅⋅H bond length (right panel). Also see Figure S8. of an intramolecular hydrogen bond (OH = 2.05 Å) that exists between its two carboxyl groups and hampers the hydrogen transfer from the H2CO3 to the oxalic acid. The larger free energy barrier of 15.8 kcal/mol for the next larger dicarboxylic acid, malonic acid-assisted reaction, in


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which the intramolecular hydrogen bond is stronger (OH = 1.91 Å), provides further support. In addition, we studied the decomposition reaction using the alternate conformations of oxalic acid and malonic acid in which the hydrogen bond-forming hydroxyl hydrogen is rotated away from the carbonyl oxygen of the carboxyl group taking part in the reaction (Figure S8). In that case, the free energy barriers for the oxalic acid- and malonic acid-assisted reaction are lowered by 1.5 and 8.3 kcal/mol. The relatively greater lowering calculated for the malonic acid-assisted reaction is due to the fact that not only the intramolecular hydrogen bond is disrupted, but the distance between the hydroxyl group and the carbonyl oxygen of the active carboxylic group is also significantly increased to ~ 6.0 Å. Interestingly, as shown in Figure 6, the catalytic effect of a dicarboxylic acid does not follow a direct correlation with its pKa, in contrast to the monocarboxylic acids, but satisfies an inverse correlation with the strength of the intramolecular hydrogen bond. These results suggest that, in addition to the pKa, the location of the second carboxyl group plays a key role in determining the catalytic efficacy of a dicarboxylic acid towards the hydrogen transfer reaction. 3.2.4. Carbonic Acid Autocatalysis. The autocatalytic decomposition of gaseous H2CO3 has previously been studied,17,18 and here, we have recalculated the autocatalytic reaction path for all the possible catalytically active dimer H2CO3 conformations to directly compare with our results for other acids. Since H2CO3 exists as three different rotational isomers (see Figure 1), there are only three catalytically competent conformations (D1syn-anti, D2syn-anti, Dsyn-syn) of a H2CO3 dimer (Scheme 3) that can actually assist in its own decomposition. The present calculations reproduce the earlier trends17,18 i.e., the D1syn-anti is the least effective whereas the D2syn-anti and Dsyn-syn are equally more effective towards the decomposition reaction. Interestingly, the D2syn-anti and Dsyn-syn conformations are even catalytically superior to a water


19


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cluster. The estimated free energy barrier for the decomposition of D2syn-anti and Dsyn-syn is dramatically reduced from 41.0 kcal/mol to 10.3 and 11.8 kcal/mol, respectively (Figures 7 and S9). This lowering of the barrier by 71-75% is significantly larger than that for the best H2O cluster and dwarfs the modest 28% lowering calculated for the decomposition of D1syn-anti, (∆G‡ = 29.7 kcal/mol). The mechanistic possibility of an autocatalytic reaction is supported by a theoretical study indicating that the formation of a H2CO3 dimer is essentially a barrierless process.19 It is important to mention that recently Ghoshal and Hazra predicted the autocatalytic decomposition of D2syn-anti or Dsyn-syn to be an effectively barrierless process.18 According to their MP2/aug-cc-pVTZ calculations, these decompositions have a submerged barrier (by 0.2 and 1.7 kcal/mol) relative to the separated reactants; at the CCSD(T) level, similar, but positive barriers (of 1.8 and 0.4 kcal/mol) were calculated. The present DFT calculations yield barriers of -1.2 and 0.3 kcal/mol relative to separated reactants (Table 1), in excellent agreement with these prior MP2 and CCSD(T) results. However, as noted above, the data in Table 1 also indicate that these reactions have significant (>10 kcal/mol) free energy barriers (Figure 7). This indicates that electronic energies should be interpreted with caution due to entropic effects associated with the formation of the prereaction complex for these systems that can significantly influence the kinetics.


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O

O

O

H

H

H O

O

O

H

H

H

H O

O

O

O

O

H O

O H

D1 syn-anti

D2 syn-anti

O

O H

H O

O

O

H

D syn-syn

Scheme 3. Three catalytically competent conformations of the H2CO3 dimer are shown. One of the H2CO3 monomers is in the same conformation, i.e., syn-anti, in all three dimer conformations and the subscript notation represents the conformation of the other H2CO3 monomer. The high catalytic activity of the D2syn-anti and Dsyn-syn conformations is due to the fact that H2CO3 acts as a true catalyst in these decompositions, i.e., it mediates the hydrogen transfer and is recovered at the end of the reaction, whereas the D1syn-anti pathway involves the decomposition of both H2CO3 molecules. This latter reaction involves the cleavage of an additional C-O bond that significantly raises the free energy barrier for the reaction. Moreover, the reactant H2CO3 dimer complexes involved in the dissocation pathways of D2syn-anti and Dsyn-syn are tightly held (∆E = 11.9 and -13.4 kcal/mol) because of the stronger hydrogen bonding interactions and their formation is favorable (∆G = -1.4 and -2.9 kcal/mol) whereas the Int1 of the D1syn-anti dimer has a relatively low binding energy of 7.2 kcal/mol, leading to a positive free energy of formation (∆G = 2.7 kcal/mol). 3.2.5. Rate Constant Estimates. Given the ability of organic acids to lower the activation barrier for the H2CO3 decomposition, it is useful to examine the possible tropospheric impact of the acid-catalyzed reactions investigated in this study by comparing their rate constants


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to that for the uncatalyzed and water-catalyzed reactions. We have used transition state theory (TST) to estimate the bimolecular rate constants for the reaction

+ + + where M represents the catalyst. The rate constant is then given by:

= , =

‡ ‡ ! "∆$ / & ℎ

where kB is Boltzmann’s constant, T is temperature, h is Planck’s constant, '( ‡ is the zero pointcorrected barrier height relative to the separated reactants, and ‡ , , and are the partition functions for the transition state, carbonic acid, and catalyst, respectively, evaluated within the rigid rotor-harmonic approximation.41 Anharmonicity associated with low frequency modes may be significant, but is expected to be a smaller factor than that associated with typical errors in the electronic structure estimates of '( ‡ .42 Tunneling effects have been included based on the Boltzmann-averaged one-dimensional Eckart barrier transmission factor, .43 We note that a large tunneling effect is found for the uncatalyzed reaction (~2000), but tunneling appears to play a minor role in the relative rate constants for the catalyzed reaction ( ~3.8; 0123 ~1 − 1.4. While we are primarily interested in the relative rate constants for different catalysts, we note that the estimated rate constant for the uncatalyzed reaction is k(T) = 1.2 × 10-14 s-1, in reasonable agreement with the experimental value of 1.2 × 10-13 s-1; the disagreement may reflect the absence of multi-dimensional tunneling effects in our estimate.12 Of particular interest is the relative effect of water and organic acids on the carbonic acid decomposition in the atmosphere. We can examine this by comparing the effective reaction rate constant for H2CO3 decomposition


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788 due to reactions with a catalyst M, = 9:.

For the concentrations [M],

Vereecken et al.44 have summarized estimates of concentrations of various species in different environments based on literature reports, with 9 : ≈ 2.4 × 10=> − 6.1 × 10=> molecules/cm3 and 9@ABC: ≈ 5 × 10=E − 1 × 10== molecules/cm3.

The latter is consistent with reports of

9: ≈ 1.3 × 10== molecules/cm3 and 9 : ≈ 1.1 × 10== molecules/cm3 in an urban area.45 In the following we have taken these values as well as 9 : = 6.1 × 10=> molecules/cm3 and 9@ABC: ≈ 5 × 10=E molecules/cm3 for the other carboxylic acids. Using these data, the estimated rate constant for the water-catalyzed reaction is then 788

= 8.0 × 10"> s-1, representing an enhancement in the H2CO3 decomposition rate constant by a factor of ~7 × 10> , consistent with previous esimates.12 However, taking the rate constant for formic acid as representative, the contribution of organic acids to carbonic acid 788

decomposition is = 1.3 × 10" s-1, an increase of a factor of ~10= over the uncatalyzed reaction and, more interestingly, of ~10G over the water-catalyzed reaction. The 788

enhancement is even larger for acetic acid, where

= 5.2 × 10"= s-1. The effect

would be similar for the other, more effective organic acids such as propionic and butyric acid, while the less potent acids, e.g., trichloroacetic acid and the dicarboxylic acids, give contributions to the effective rate constant that are on the same order as the water-catalyzed reaction. Overall, these results suggest that organic acids in the atmosphere should play a larger role than water in H2CO3 decomposition.


23


25 23.9

O C H

20

13.5

12.2

15 11.7


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10.3

1.4

TS

TS

10

5

0.0

0

-1.4 Int 1

Int 1

-2.9

-5 Int 2

-10

H 2CO 3 + H 2O + CO2

H 2CO 3 + H 2O + CO2

Int 2

-12.1 P

-15

-7.5

-9.0

-12.1 D2 syn-anti

D syn-syn

P

Figure 7. M06-2X/aug-cc-pVTZ calculated free energy profiles (298.15 K, 1 atm) of gas-phase decomposition of D2syn-anti (left) and Dsyn-syn (right) conformations of a H2CO3 dimer. The blue horizontal line refers to the free energy barrier of water-catalyzed decomposition.

4. CONCLUSIONS A potential catalytic route for the gas-phase decomposition of H2CO3 via reaction with H2O, H2CO3, and a variety of organic acids has been investigated using DFT calculations. The results provide new insight into the decomposition mechanism of tropospheric H2CO3. The organic acids appreciably lower the free energy barrier to H2CO3 decomposition because they effectively


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convert a 1,3 hydrogen atom transfer reaction into two 1,2 hydrogen atom shifts. The stereo environment of the transition state influences the catalytic effect. A water-catalyzed reaction, due to the formation of a six-membered transition state, yields the smallest catalytic effect while, an acid-catalyzed reaction is mediated by a less sterically congested eight-membered transition state and is the more favorable decomposition route. Among the family of monocarboxylic acids examined here, the nature of the substituent on the carbonyl carbon determines the catalytic activity. Using the calculated free energy barriers, a direct correlation between the catalytic efficiency of an acid and its pKa is observed. Similar reactivity patterns observed for the acidassisted tautomerization of vinyl alcohol and the isomerization of methoxy radical, two key tropospheric reactions indicate the wider implications of these results. On the other hand, the catalytic efficacy of a dicarboxylic acid is significantly affected by the presence and location of the second carboxyl group. The present theoretical calculations add to a growing library of gasphase hydrogen transfer reactions that are catalyzed by organic acids and may have broad implications in understanding and utilizing the catalytic power of organic acids in promoting atmospherically and industrially important hydrogen transfer reactions. ASSOCIATED CONTENT Supporting Information. Calculated structural parameters, conformations, free energy reaction profiles and thermodynamic data. This material is available free of charge via the Internet at http://pubs.acs.org. AUTHOR INFORMATION Corresponding Author *E-mail: [email protected]


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Funding Sources This work is funded by NIFA/USDA grant no. 2011-10006-30362. Notes The authors declare no competing financial interest.

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(36) Valiev, M.; Bylaska, E. J.; Govind, N.; Kowalski, K.; Straatsma, K. P.; van Dam, H. J. J.; Wang, D.; Nieplocha, J.; Apra, E.; Windus, T. L.; de Jong, W. A. NWChem: A Comprehensive and Scalable Open-source Solution for Large Scale Molecular Simulations. Comput. Phys. Commun. 2010, 181, 1477-1489. (37) ORCA V2.8.0, an ab initio, DFT, and semiempirical SCF-MO package developed by F. Neese, Bonn University, Germany; available online from http://www.thch.unibonn.de/tc/orca/. (38) Morokuma, K.; Muguruma, C. Ab Initio Molecular Orbital Study of the Mechanism of the Gas Phase Reaction SO3 + H2O: Importance of the Second Water Molecule. J. Am. Chem. Soc. 1994, 116, 10316-10317. (39) Hazra, M. K.; Francisco, J. S.; Sinha, A. Gas Phase Hydrolysis of Formaldehyde to Form Methandiol: Impact of Formic Acid Catalysis. J. Phys. Chem. A 2013, 117, 1170411710. (40) Hansch, C.; Leo, A.; Taft, R. W. A Survey of Hammett Substitutent Constants and Resonance and Field Parameters. Chem. Rev. 1991, 91, 165-195. (41) We have also estimated the effective rate constants assuming the reactants are in equilibrium with the pre-reaction complex, Int1, which is then characterized by a 788 unimolecular rate constant for forming the products. This yielded values 10-25

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TOC GRAPHICS


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Organic Acids Tunably Catalyze Carbonic Acid Decomposition - The

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