Catalytic Effect of Water, Formic Acid, or Sulfuric Acid on the Reaction

Article pubs.acs.org/JPCA

Catalytic Effect of Water, Formic Acid, or Sulfuric Acid on the Reaction of Formaldehyde with OH Radicals Weichao Zhang,* Benni Du, and Zhenglong Qin College of Chemistry and Chemical Engineering and Jiangsu Key Laboratory of Green Synthetic Chemistry for Functional Materials, Jiangsu Normal University, Xuzhou, Jiangsu 221116, People’s Republic of China S Supporting Information *

ABSTRACT: In this paper, for the hydrogen abstraction reaction of HCHO by OH radicals assisted by water, formic acid, or sulfur acid, the possible reaction mechanisms and kinetics have been investigated theoretically using quantum chemistry methods and transition-state theory. The potential energy surfaces calculated at the CCSD(T)/6-311+ +G(df,pd)//MP2(full)/6-311++G(df,pd) levels of theory reveal that, due to the formation of strong hydrogen bond(s), the relative energies of the transition states involving catalyst are significantly reduced compared to that reaction without catalyst. However, the kinetics calculations show that the rate constants are smaller by about 3, 9, or 10 orders of magnitude for water, formic acid, or sulfur acid assisted reactions than that uncatalyzed reaction, respectively. Consequently, none of the water, formic acid, or sulfur acid can accelerate the title reaction in the atmosphere.

1. INTRODUCTION Formaldehyde (HCHO) is the most abundant carbonyl compound in the atmosphere1 and it is also an important component of photochemical smog.2 On a global scale, the most important source of formaldehyde in the atmosphere is the photochemical oxidation of methane and nonmethane hydrocarbons,3,4 while in and near urban areas, direct emissions such as automobile exhaust gases and industrial processes are typically the dominating source of formaldehyde. As one of the dominant reactive species in the degradation of organic compounds in both the natural and polluted troposphere, OH radicals play an important role in the atmospheric chemistry. Besides photolysis, reaction with OH radicals is the major loss process of HCHO in the daytime. Until now, a large number of experimental5−15 and theoretical studies13,16−21 have been reported on the rate constants and reaction mechanisms for the HCHO + OH reaction. Both experimental and theoretical studies have demonstrated that the formation of HCO + H2O via hydrogen atom abstraction is the dominant reaction pathway, while the formation of HCOOH + H via initial addition followed by rearrangement and decomposition will be negligible. Moreover, using different experimental methods, the rate constants for the title reaction have been studied over different temperature range and the reported rate constants at 298 K are fairly uncertain, ranging from (7.75 ± 1.24) × 10−1211 to 1.4 × 10−11 cm3·mol−1s−1.5 Recently, because of the ability of forming hydrogen bonds, considerable investigations about the possible role of a single water molecule in lowering the transition states energies have been done for the reactions involving OH radicals.22−35 The theoretical studies suggest that the involvement of a single water molecule can reduce the intrinsic reaction barrier; © 2014 American Chemical Society

however, the amount of complex formed in the initial water complexation step will be crucial to the total rate constants.24,29,32−35 Beyond the well-known water, it has been demonstrated theoretically that other molecules such as formic acid36−41 and sulfur acid31,38,42,43 can also play the same role as water to reduce the transition-state energies in the isomerization36−38 or hydrolysis reaction processes.39−43 Compared with water, formic acid and sulfur acid may have better catalytic effects for some reaction systems.38,39,41,42 In this paper, the reaction mechanisms and kinetics for the major reaction pathway of HCHO + OH, viz., H abstraction pathway have been studied theoretically in the presence of water, formic acid, or sulfur acid, respectively. The goal of the present investigation is to elucidate the reaction mechanisms of water, formic acid, or sulfur acid assisted H abstraction reaction pathways and to evaluate the relatively catalytic ability of water, formic acid, and sulfur acid according to the detailed potential energy surfaces. Furthermore, on the basis of kinetic calculations, it will also be clarified that whether the presence of a single water, formic acid, or sulfur acid can enhance the rate constant of HCHO + OH reaction in the atmosphere.

2. COMPUTATIONAL METHODS The geometries of the reactants, products, intermediates, complexes, and transition states were fully optimized with default convergence criteria using second-order Møller−Plesset perturbation theory (MP2)44 in conjunction with the 6-311+ +G(df,pd) basis set. At the same level, the frequencies of Received: March 23, 2014 Revised: June 13, 2014 Published: June 13, 2014 4797

dx.doi.org/10.1021/jp502886p | J. Phys. Chem. A 2014, 118, 4797−4807

The Journal of Physical Chemistry A

Article

Table 1. ZPE (hartree), TCG (hartree), ZPE Corrected Relative Energies (Δ(E + ZPE), kcal/mol), and Gibbs Free Energies (ΔG, kcal/mol) of Various Species Involved in the HCHO + OH Reactions without Catalyst CCSD(T)//MP2(full)

a

CCSD(T)//BH&HLYP

species

ZPE

TCG

Δ(E + ZPEa)

ΔG(298 K)

ZPE

TCG

Δ(E + ZPEb)

ΔG(298 K)

HCHO + OH RC1 TS1 PC1 TSR-1 IM1 HCO + H2O

0.035844 0.038549 0.034543 0.037612 0.041122 0.043751 0.035260

−0.002067 0.009731 0.006248 0.008068 0.015504 0.018447 −0.004032

0.00 −3.38 −1.14 −32.55 31.83 −21.10 −30.25

0.00 2.41 4.85 −27.24 39.71 −12.94 −31.14

0.036497 0.039182 0.034767 0.038460 0.040777 0.044277 0.03 746

−0.001377 0.010487 0.007426 0.009447 0.014807 0.018967 −0.003468

0.00 −3.39 −1.65 −32.33 27.95 −21.50 −30.21

0.00 2.48 4.89 −26.69 35.60 −13.29 −31.08

ZPE scaled by 0.95.53 bZPE scaled by 0.9335.54

Table 2. ZPE (hartree), the TCG (hartree), ZPE Corrected Relative Energies (Δ(E + ZPE), kcal/mol) and Gibbs Free Energies (ΔG, kcal/mol) of Various Species Involved in the HCHO + OH Reactions with Water CCSD(T)//MP2(full)

a

CCSD(T)//BH&HLYP a

species

ZPE

TCG

Δ(E + ZPE )

ΔG (298 K)

ZPE

TCG

Δ(E + ZPEb)

ΔG (298 K)

HCHO + OH + H2O HCHO···H2O + OH H2O···HO+HCHO HO···H2O + HCHO RC2W TS2W PC2W RC3W TS3W PC3W HCO+H2O+H2O

0.057774 0.060926 0.061329 0.060069 0.064682 0.060403 0.064202 0.063535 0.058896 0.061186 0.057190

0.002229 0.015815 0.014787 0.012297 0.031555 0.029128 0.030852 0.028561 0.024943 0.021695 0.036927

0.00 −3.54 −4.56 −2.44 −9.33 −8.42 −39.30 −6.56 −4.35 −33.71 −30.25

0.00 3.11 1.20 2.51 4.95 6.89 −25.17 6.53 9.24 −23.53 −31.14

0.058644 0.061792 0.061763 0.060922 0.065351 0.060372 0.065055 0.064426 0.059194 0.062083 0.057893

0.003167 0.016391 0.014199 0.013057 0.031582 0.029074 0.031969 0.029748 0.025377 0.023169 0.037997

0.00 −3.55 −4.77 −2.46 −9.36 −9.64 −39.30 −6.67 −5.01 −33.57 −30.21

0.00 2.90 0.32 2.41 4.55 5.60 −24.98 6.63 8.60 −23.03 −31.08


relative energy of transition state TS2W is lower than that of the corresponding prereactive complex RC2W, and similar instances are also found in the formic acid assisted reactions such as TS2F with RC2F, TS2Fa with RC2Fa, and so on. Thus, in this paper, unless otherwise mentioned, we adopt the relative energies with ZPE correction calculated at the CCSD(T)// MP2(full) levels of theory for the subsequent analysis. Conventional transition-state theory (CTST) calculations based on ab initio molecular orbital methods have been performed to evaluate the rate constants for the major reaction pathway of the title reaction without and with catalyst. In this paper, all the electronic structures and energies calculations were performed using the Gaussian 0952 program.

various species were calculated to obtain the zero-point energy (ZPE) and the thermal correction to Gibbs free energy (TCG) and to determine the nature of the stationary points, saddle points, or minima by means of the analysis of the number of imaginary frequencies (NIMAG = 1 or 0, respectively). Connections of the transition states between designated isomers were confirmed by intrinsic reaction coordinate (IRC)45,46 calculations. The geometries optimized at the MP2(full)/6-311++G(df,pd) are used to perform single-point energy calculations for all species using the coupled cluster CCSD(T)47/6-311++G(df,pd) level of theory. In order to give a qualitative assessment of the significance of the multireference wave function, the T1 diagnostic values48,49 have also been calculated at the CCSD(T) level. As shown in Table S1 of Supporting Information, the T1 diagnostic values of various species in our system are smaller than 0.044,48 which means that the multireference character in the CCSD(T) wave functions can be negligible. Furthermore, in order to descript the noncovalent interactions and hydrogen-bonded complexes involved in the title reaction, the BH&HLYP50,51 method in conjunction with the 6-311++G(df,pd) basis set also has been used to optimize the geometries of various species, and the single-point energies also have been given at the CCSD(T)/6-311++G(df,pd)// BH&HLYP/6-311++G(df,pd) (denoted as CCSD(T)// BH&HLYP) levels of theory. It can be seen from Tables 1, 2, 4, and 5, for the HCHO + OH reaction without catalyst, that the relative energies with ZPE correction and the Gibbs free energies of various species calculated at the CCSD(T)// MP2(full) and the CCSD(T)//BH&HLYP levels are almost equal. However, in the case of water-assisted reactions, the

3. RESULTS AND DISCUSSION 3.1. H-Abstraction Reaction Pathways of HCHO + OH Assisted by Water. As described in the Introduction, a number of theoretical studies have been done for the Habstraction reaction pathway of HCHO + OH. In this section, the H-abstraction reaction of HCHO by OH radicals without water has been involved to investigate the possible catalytic effect of water. Furthermore, the initial addition reaction pathway also has been studied. The geometries of various species, including reactants, reactant complexes (RC), intermediates (IM), transition states (TS), product complexes (PC), and products, involved in these processes calculated at MP2(full) and BH&HLYP levels of theory are shown in Figures S1-a and S1-b, respectively (Supporting Information). The ZPE, TCG, relative energies with ZPE correction (Δ(E + ZPE)), and the Gibbs free energies (ΔG) of various species 4798



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energy of −3.38 kcal/mol, and our results are in reasonable agreement with the theoretical study calculated at the B3LYP/ 6-311++G(3df,3pd) level by Aloisio and Francisco.55 TS1 lies below the initial reactants by 1.14 kcal/mol, and the barrier of it is 2.24 kcal/mol relative to RC1. As shown in Figure 1, the relative energies of TS1 and RC1 are lower than that of the initial reactants, while on the free energy potential energy surface, as can be seen from Table 2, both RC1 and TS1 lie above the reactants. However, these results are not in contradiction, and the corresponding description can be seen from the similar acetaldehyde + OH system.32 For the addition pathway, it can be seen from Figure 1 that in the formation of adduct intermediate IM1 the reaction must climb up to TSR-1 at 31.83 kcal/mol above reactants, which is consistent with the previous theoretical results.13,19,21 The high barrier of TSR-1 will make the formation of IM1 unfeasible under atmospheric conditions, and the subsequent reactions involving IM1 will not be discussed. In the presence of water, due to the case that the simultaneous collision of isolated HCHO, OH, and H2O molecules is unlikely, the reaction would occur through the formation of a two-body complex first, and then it collides with the third species to form three-body complexes. Figures S1-a and S1-b (Supporting Information) show the optimized structures of species involving water at MP2(full) and BH&HLYP levels, respectively. The suffix “W” has been added to denote the species involved in the reactions with water. The relative energies with ZPE correction and the Gibbs free energies calculated at both methods together with the potential energy surface for the title reaction with water are shown in Table 2 and Figure 2, respectively. Three two-body complexes, viz. HCHO···H2O, H2O···HO, and HO···H2O, have been found in the entrance channel, and the binding energies of them are −3.54, −4.56, and −2.44 kcal/

calculated at the CCSD(T)//MP2(full)) and CCSD(T)// BH&HLYP levels of theory are listed in Table 1. The T1 diagnostic values and the absolute energies of various species involved in this paper are shown in Table S1 (Supporting Information). According to the relative energies of CCSD(T)//MP2(full)) with ZPE correction, the schematic potential energy surface (PES) of HCHO + OH without catalyst is depicted in Figure 1.

Figure 1. Potential energy surface of the HCHO + OH reaction without catalyst at the CCSD(T)//MP2(full)+ZPE × 0.95 level.

Similar to previously theoretical studies on the HCHO + OH reaction,13,19,21 for the most favorable product pathway of producing HCO + H2O, it occurs by the formation of a hydrogen-bonded complex RC1 in the reaction entrance, followed by the direct hydrogen abstraction transition state TS1 and the product complex PC1. In RC1, the H atom of OH radicals is appointed to the O atom of HCHO with a binding

Figure 2. Potential energy surface of the HCHO + OH reaction with water at the CCSD(T)//MP2(full)+ZPE × 0.95 level. 4799



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Table 3. Equilibrium Constants(cm3 Molecule−1) and Concentrations (Molecules cm−3) of Relevant Two-Body Complexes Involved in the HCHO + OH Reactionsa complex

RC1

HCHO···H2O

H2O···HO

HCHO···FA-I

FA−OH-II

HCHO···SA

SA−OH-I

Keq [complex]

4.66 × 10−22 3.7 × 10−3

7.54 × 10−23 4.6 × 107

3.67 × 10−21 2.8 × 104

4.11 × 10−21 2.7 × 103

6.09 × 10−22 1.2 × 10−3

7.72 × 10−19 2.5 × 102

9.23 × 10−20 3.7 × 10−4

a

Water concentration (7.7 × 1017 molecules cm−3) at 100% relative humidity;56,57 formaldehyde concentration (8.0 × 1011 molecules cm−3) taken from ref 58, hydroxyl radicals concentration (1.0 × 107 molecules cm−3) taken from ref 59, formic acid concentration (2.0 × 1011 molecules cm−3) taken from ref 60, and sulfur acid concentration (4.0 × 108 molecules cm−3) taken from ref 61.

Table 4. ZPE (Hartree), the TCG (Hartree), ZPE Corrected Relative Energies (Δ(E + ZPE), kcal/mol), and Gibbs Free Energies (ΔG, kcal/mol) of Various Species Involved in the HCHO + OH Reactions with Formic Acid CCSD(T)//MP2(full)

a

CCSD(T)//BH&HLYP a

species

ZPE

TCG

Δ(E + ZPE )

ΔG (298 K)

ZPE

TCG

Δ(E + ZPEb)

ΔG (298 K)

HCHO + OH + FA HCHO···FA-I + OH HCHO···FA-II + OH HCHO···FA-III + OH FA···OH-I + HCHO FA···OH-II + HCHO FA···OH-III + HCHO RC2F TS2F PC2F RC2Fa TS2Fa PC2Fa RC2Fb TS2Fb PC2Fb RC2Fc TS2Fc PC2Fc RC3F TS3F PC3F HCO + H2O + HCOOH

0.070219 0.073009 0.071473 0.071457 0.073211 0.072856 0.072443 0.075364 0.071492 0.075278 0.074762 0.070935 0.074382 0.075062 0.071041 0.074607 0.074077 0.070926 0.074047 0.075308 0.070492 0.075225 0.069635

0.008236 0.024991 0.020122 0.020339 0.023280 0.020707 0.020195 0.037618 0.036357 0.037790 0.035664 0.033354 0.034399 0.037022 0.035014 0.036033 0.033690 0.033579 0.033742 0.036436 0.033427 0.037370 0.046109

0.00 −7.70 −3.21 −2.50 −2.38 −3.59 −2.39 −12.30 −11.02 −40.47 −7.69 −7.57 −38.70 −8.57 −7.55 −38.06 −5.88 −5.57 −36.42 −10.33 −8.13 −41.13 −30.25

0.00 1.15 3.51 4.35 5.28 2.66 3.79 3.07 5.87 −24.94 6.81 7.77 −24.76 6.60 8.77 −23.23 7.79 9.91 −22.70 4.33 7.51 −25.83 −31.14

0.071730 0.074637 0.073282 0.073107 0.074908 0.074334 0.073921 0.077444 0.072171 0.076918 0.076481 0.071578 0.076132 0.076662 0.071727 0.075846 0.075751 0.071264 0.075253 0.077104 0.071651 0.076918 0.070979

0.009823 0.027086 0.023122 0.022534 0.025178 0.022694 0.021598 0.040637 0.037131 0.039948 0.037882 0.034773 0.037498 0.039299 0.035283 0.037059 0.036492 0.033648 0.034830 0.039854 0.035531 0.039937 0.047467

0.00 −7.70 −3.09 −2.44 −2.77 −3.72 −2.38 −11.60 −12.25 −40.94 −7.88 −8.78 −38.49 −8.55 −8.53 −37.92 −5.77 −6.65 −36.32 −10.41 −8.92 −40.94 −30.21

0.00 1.43 4.35 4.73 5.01 2.83 3.72 4.39 4.63 −25.08 6.94 6.97 −23.70 7.06 7.45 −23.24 8.61 8.58 −22.69 5.29 7.26 −25.08 −31.08


require no or little energy. Thus, RC2W can be formed directly via the association of HCHO···H2O with OH radicals. Starting from RC2W, with the H atom shifting from HCHO to the O atom of OH moiety further, the final products of HCO with H2O will be formed via direct hydrogen abstraction transition state TS2W and product complex PC2W. Both RC2W and TS2W are almost planar conformations. With the assistance of a single water in the hydrogen-abstraction process, the relative energy of TS2W is drastically reduced to −8.42 kcal/mol and the barrier of it is only 0.91 kcal/mol relative to RC2W. Obviously, the formation of hydrogen bonds involving the water molecule contributes to the reduction of the relative energy and barrier of TS2W. In addition, the interchange between the two HCHO···H2O + OH and H2O···HO + HCHO reactant channels also has been considered. As shown in Table 2, the free energy of TS2W is 3.78 and 5.69 kcal/mol larger than that of the two entry channels reactants, which means that the interchange between HCHO···H2O + OH and H2O···HO + HCHO will be feasible.42 Starting from RC1 + H2O or HCHO···H2O + OH reactants, another three-body complex RC3W will be formed. According to the binding energies, the partition functions calculated at the

mol, respectively, at the CCSD(T)//MP2(full) level. As shown in Figure 2, beginning with the HCHO···H2O + OH or H2O··· HO + HCHO reactants, the same three-body complex RC2W will be formed with the water acting as both hydrogen bond acceptor and donor simultaneously. RC2W has a sevenmembered-ring structure, and the binding energy of it is −9.33 kcal/mol. It is worth mentioning that in the formation of RC2W via HCHO···H2O complex, the C−H···O hydrogen bond must be broken. Thus, similar to the instances of HOCl + OH28 and H2O2 + OH29 with water, another three-body complex and transition state should be existence before the formation of RC2W. Despite numerous attempts, no corresponding complex and transition state have been found at both MP2(full) and BH&HLYP methods. Furthermore, the B3LYP method also has been used to search the corresponding species due to its reliability in studying the bond interchange involving hydrogen bond.28 However, all these efforts are still in vain. The failure of locating these species may be due to that in the HOCl + OH + H2O28 and H2O2 + OH + H2O29 systems, the broken bond is the relatively strong O−H···O hydrogen bond, while in the HCHO···H2O complex, the C−H···O hydrogen bond (2.652 Å) is so weak that the breaking of it will 4800



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Figure 3. Potential energy surface of the HCHO + OH reaction assisted by formic acid at the CCSD(T)//MP2(full)+ZPE × 0.95 level.

of HCO + 2H2O via HCHO···H2O and TS2W will be the major reaction channel. 3.2. H-Abstraction Reaction Pathways of HCHO + OH Assisted by Formic Acid. In formic acid (FA), there are two different oxygen atoms (carbonyl oxygen and hydroxyl oxygen) and two different hydrogen atoms (formyl hydrogen and acidic hydrogen). Thus, in the entrance channel, various possible structures for HCHO···HCOOH (denoted as HCHO···FA) complexes and HCOOH···OH (denoted as FA···OH) complexes can be formed. The optimized geometries and the energies of various species involved in the formic acid assisted reaction obtained at both methods are shown in Figure S2-a and S2-b (Supporting Information) and Table 4, respectively, with the suffix “F” denoting the species involved in the reactions with formic acid. The corresponding potential energy surface is given in Figure 3. Three possible HCHO···FA complexes have been found. Among them, the most stable one is the seven-membered-ring HCHO···FA-I complex, which is held together by an O−H···O hydrogen bond and a weak C−H···O interaction with a binding energy of −7.70 kcal/mol. For the other two HCHO···FA complexes, viz. HCHO···FA-II and HCHO···FA-III, both of them are six-membered-ring structures and only two weak C− H···O interactions are formed between the HCHO and HCOOH moieties. Accordingly, compared with HCHO···FAI, HCHO···FA-II and HCHO···FA-III have smaller binding energies of −3.21 and −2.50 kcal/mol, respectively. Three FA···OH complexes, viz., FA···OH-I, FA···OH-II, and FA···OH-III, have been found, and the binding energies of them are −2.38, −3.59, and −2.39 kcal/mol, respectively. It is

MP2(full) level and the average atmospheric concentrations of each species, the equilibrium constants and the concentrations of two-body complexes can be obtained theoretically, and they are listed in Table 3. It can be seen from Table 3 that the equilibrium constants of RC1 and HCHO···H2O are 4.66 × 10−22 and 7.54 × 10−23 cm3 molecule−1, and the atmospheric concentration of them are 3.7 × 10−3 and 4.6 × 107 molecules cm−3, respectively. Moreover, the smaller binding energy of RC1 than that of HCHO···H2O will result in the shorter lifetime of it. All these results indicate that the formation of RC3W via RC1 + H2O will be negligible. In RC3W, the OH and H2O subunits are separate from each other, while in RC2W, the OH and H2O moieties are hold together by one hydrogen bond. Accordingly, RC3W has higher energy of 2.77 kcal/mol than that of RC2W. Subsequently, RC3W can go through TS3W to form the product complex PC3W in the exit channel. Except for the H2O subunit, TS3W has similar structure to that of TS1. As shown in Figure 2, TS3W lies 4.07 kcal/mol above the energy of TS2W. As a consequence, the reaction pathway via RC3W and TS3W will not be competitive with that via RC2W and TS2W at normal temperature. It can also be seen from Figure 2 that for the hydrogen abstraction reactions of HCHO + OH assisted by water, the pathway via H2O···HO should be more feasible due to the larger binding energy of it. However, as listed in Table 3, the lower concentration of H2O···HO (2.8 × 104 molecules cm−3) at 298 K than that of HCHO···H2O (4.6 × 107 molecules cm−3) will make this pathway unfavorable, and the production 4801



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Table 5. ZPE (Hartree), the TCG (Hartree), ZPE Corrected Relative Energies (Δ(E + ZPE), kcal/mol), and Gibbs Free Energies (ΔG, kcal/mol) of Various Species Involved in the HCHO + OH Reactions with Sulfur Acid CCSD(T)//MP2(full)

a

CCSD(T)//BH&HLYP

species

ZPE

TCG

Δ(E + ZPEa)

ΔG(298 K)

ZPE

TCG

Δ(E + ZPEb)

ΔG(298 K)

HCHO + OH + SA HCHO···SA + OH SA···OH-I + HCHO SA···OH-II + HCHO RC2S TS2S PC2S RC3S TS3S PC3S HCO + H2O + SA

0.075836 0.078815 0.078610 0.078453 0.081720 0.076965 0.081554 0.081321 0.076145 0.081026 0.075252

0.010357 0.027383 0.024878 0.024513 0.042908 0.038299 0.041643 0.040215 0.036020 0.039637 0.047471

0.00 −11.26 −8.30 −6.84 −16.05 −14.10 −43.23 −13.25 −11.31 −43.85 −30.25

0.00 −2.35 −0.84 0.49 0.87 2.76 −27.01 2.22 4.61 −28.57 −31.14

0.077203 0.080020 0.080065 0.079897 0.082452 0.077347 0.082632 0.082458 0.076868 0.082325 0.076452

0.011825 0.028728 0.026516 0.026097 0.041449 0.038192 0.042649 0.041441 0.037077 0.041627 0.047601

0.00 −11.37 −8.27 −6.80 −15.44 −15.18 −43.23 −13.53 −12.05 −43.82 −30.21

0.00 −2.42 −0.73 0.58 0.08 1.28 −27.07 1.98 3.99 −28.12 −31.08


Figure 4. Potential energy surface of the HCHO + OH reaction assisted by sulfur acid at the CCSD(T)//MP2(full)+ZPE × 0.95 level.

worth noting that at the MP2(full) level, FA···OH-I has the largest binding energy of −5.88 kcal/mol among these three complexes, and our result is consistent with previous theoretical studies by Anglada62 and Iuga et al.35 The hydrogen abstraction reactions of HCHO by OH radicals assisted by formic acid are in a manner analogous to that discussed above involving one water molecule. Because of the complexity in the entrance channel, more reaction pathways will be open in the presence of formic acid. First, with the collision of OH with the HCHO···FA-I complex or HCHO with FA···OH-II complex, three-body complex RC2F will be formed. It can be seen from Figure S2-a (Supporting Information) that in the formation of RC2F starting from HCHO···FA-I complex, with the association of OH radicals, a new four-membered-ring structure is formed,

and it does not change the original seven-membered-ring structure largely. Furthermore, the C−H···O hydrogen bond in the HCHO···FA moiety changes only from 2.407 Å of HCHO···FA-I to 2.566 Å of RC2F; that is to say, RC2F can be formed directly via the association of HCHO···FA-I with OH radicals without breaking the C−H···O hydrogen bond. RC2F lies 12.30 kcal/mol below the initial reactants. In RC2F, both the carbonyl and the hydroxyl groups are involved in the ring configuration. After RC2F, the reaction proceeds via transition state TS2F and product complex PC2F to form the final products. Compared to TS2W, the significant change in TS2F is the shorter O−H···O hydrogen bond (1.794 Å) formed between the HCOOH and HCHO subunits, which suggests stronger hydrogen bond interactions in the formic acid assisted complex. In addition, when moving from a seven4802



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involving it unimportant, and thus this reaction pathway will not be discussed further. Moreover, it should be interesting to point out that in the atmosphere, sulfuric acid is found hydrated with several water molecules and the abundance of different hydrates depends significantly on the temperature and relative humidity (RH).63,64 For example, under the conditions of T = 298.15 K, RH = 20%, 100%, and [H2SO4] = 5 × 107 molecules cm−3, the concentration of sulfuric acid monohydrate64 is 1.9× 107 and 2.4× 107 molecules cm−3, respectively. This indicates that the formation of sulfuric acid monohydrate will be more easily than that of HCHO···SA. Once formed, RC2S is involved in the most feasible reaction pathway via RC2S → TS2S → PC2S to form the corresponding products. TS2S possesses twisted nine-membered-ring configuration. Compared with RC2F and TS2F, RC2S and TS2S have shorter O−H···O hydrogen bonds (1.581 and 1.681 Å, respectively) formed between the H2SO4 and HCHO subunits, which in turn result in larger binding energy of −16.05 kcal/mol for RC2S and lower relative energy of −14.10 kcal/mol for TS2S, respectively. For the other reaction pathway, viz., HCHO···SA+OH → RC3S → TS3S → PC3S, similar to the instance of water or formic acid assisted reaction, TS3S has higher relative energy of 2.79 kcal/mol than that of TS2S and thus it can not play an important role in the formation of product. From the discussion given above, it can be seen that in the presence of water, formic acid, or sulfur acid, the barrier for the H abstraction process can be reduced compared with the case without catalyst. For the waterassisted reaction, the barrier is reduced to 0.91 kcal/mol, and for formic acid and sulfur acid assisted reactions, the barriers are 1.28 and 1.95 kcal/mol, respectively. Although the barriers of TS2F and TS2S are higher than that of TS2W, the relative energies of RC2W, RC2F, and RC2S together with TS2W, TS2F, and TS2S decrease gradually with the replacement of water by formic acid or sulfur acid; thus, further kinetic study should be done to evaluate the possible catalytic effect of water, formic acid, or sulfur acid on the title reaction in the atmosphere. 3.4. Kinetics and Atmospheric Implications. For the most feasible hydrogen abstraction pathways of the HCHO + OH reaction assisted by water, formic acid, or sulfur acid (which are represented by the red line in Figure 2, Figure 3, and Figure 4, respectively), the rate constants of them have been studied using classic transition state theory at 298 K. The methodology used in this paper has already been described in detail in previous publications.65−67 Briefly, for the HCHO + OH reaction without catalyst, it can occur according to the two-step mechanism proposed in eq 1:

membered-ring TS2W to a nine-membered-ring TS2F, the strain energy will also be reduced. Accordingly, TS2F has a lower relative energy of −11.02 kcal/mol. The energy barrier of TS2F is 1.28 kcal/mol relative to RC2F, which is slightly higher than that of reaction assisted by water. Of course, as shown in Table 3, because of the lower atmospheric concentration of 1.2 × 10−3 molecules cm−3 for FA···OH-II than that of HCHO··· FA-I (2.7 × 103 molecules cm−3), the reaction pathway via FA···OH-II will not contribute to the final formation of product. Furthermore, TS2F lies 4.72 and 3.21 kcal/mol higher in free energy than that of OH + HCHO···FA-I and HCHO + FA··· OH-II reactants, which indicates that the interchange between the two reactant channels is plausible. As shown in Figures S2-a and S2-b (Supporting Information), besides RC2F, two other eight-membered-ring complexes RC2Fa and RC2Fc together with seven-membered-ring complex RC2Fb can also be formed via the interaction of twobody complexes with the third species (where the species with small letters a, b, or c as a suffix denoting the isomers of the most stable conformer RC2F). However, the corresponding transition states TS2Fa, TS2Fb, and TS2Fc are much higher in energy than that of TS2F. For instance, TS2Fa, which has the lowest relative energy among these three species, lies 3.45 kcal/ mol higher in energy than that of TS2F. Obviously, these reaction pathways cannot compete with that one via TS2F and they will not be discussed at length. Similar to the formation of RC3W, with the replacement of H2O by HCOOH, complex RC3F will be formed by bimolecular encounter involving HCHO···FA-I complex with OH radicals. Passing through TS3F with a barrier of 2.20 kcal/ mol, the reaction can proceed to form product complex PC3F before the final dissociation products of HCO with H2O. Due to the formation of stronger hydrogen bonds, the relative energies of RC3F and TS3F are about 4 kcal/mol lower than that of RC3W and TS3W, respectively. However, the higher energy of 2.89 kcal/mol for TS3F than that of TS2F suggests that the reaction pathway via TS3F will not be competitive with the major pathway via RC2F and TS2F for the title reaction assisted by formic acid. 3.3. H-Abstraction Reaction Pathways of HCHO + OH Assisted by Sulfur Acid. Sulfur acid has C2 symmetry, and the two OH groups are equivalent. As shown in Figures S3-a and S3-b (Supporting Information), three two-body complexes, viz., HCHO···SA(SA denoting sulfur acid), SA···OH-I, and SA···OH-II, can be formed in the entrance channels with binding energies of −11.26, −8.30, and −6.84 kcal/mol (listed in Table 5), respectively. As shown in Figure S3-a and Figure 4, in the presence of sulfur acid, with the OH radicals approaching to the HCHO··· SA complex from below, the three-body complex RC2S can be formed directly with a binding energy of −4.79 kcal/mol relative to the HCHO···SA + OH entry channel. In RC2S, the OH radical is involved in the formation of a new fourmembered-ring configuration, and the HCHO···SA moiety is still in a seven-membered-ring structure. It should be noted that starting from SA···OH-I complex, RC2S can not be formed directly due to the existence of two O−H···O hydrogen bonds in it, and additional steps should be involved in this pathway. However, Table 3 shows that the concentration of SA···OH-I is only 3.7 × 10−4 molecules cm−3, which is much smaller than that of HCHO···SA complex (2.5 × 102 molecules cm−3). The very small amount of SA···OH-I will make the pathway

k1

k2

HCHO + OH HooI RC → products k −1

(1)

If k1 and k−1 are the forward and reverse rate constants for the first step and k2 corresponds to the second step, according to the steady-state conditions,68 the rate constant for this process is given by k=

k1 k2 k −1 + k 2

(2)

Because of the very loose transition state, the entropy change in k−1 is much larger than in the formation of products. Consequently, k−1 is considerably larger than k2,68−71 and a pseudoequilibrium assumption can be applied to the formation 4803



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Table 6. Calculated Rate Constant (k, cm3 molecule−1 s−1) for the HCHO+OH Reaction without and with Catalyst at 298 K Keq 6

reaction HCHO + OH HCHO···H2O + OH HCHO···FA-I + OH HCHO···SA + OH

Y complex −23

−5

7.54 × 10 4.11 × 10−21 7.72 × 10−19

5.81 × 10 8.22 × 10−10 3.09 × 10−10

Keq 7 4.66 2.49 2.14 2.36

× × × ×

[X]a

k8 −22

10 10−21 10−21 10−22

7.91 1.79 4.21 1.29

× × × ×

k′b

k

10

10 1011 1010 1011

7.70 × 10 2.00 × 1011 4.00 × 108 17

−10

4.46 × 10 9.01 × 10−11 3.04 × 10−11

3.69 2.59 7.39 9.40

× × × ×

10−11 10−14 10−20 10−21

a

Water concentration at 100% relative humidity;56,57 formic acid concentration taken from ref 60 and sulfur acid concentration taken from ref 61. bk′ = Keq 7k8.

where [HCHO···X] = Keq6[HCHO][X]. Because k−7 is larger than k8, eq 10 can be represented as

of the reactant complex. Accordingly, eq 2 can be represented as k=

k1 k 2 = Keqk 2 k −1

[RC2X] =

(3)

where Keq and k2 are the equilibrium constant of the first step and the rate constant of the second step in the reactions, and they can be given by eqs 4 and 5, respectively. Keq =

Q RC ⎛ E − Ereactants ⎞ k1 ⎟ exp⎜ − RC = ⎠ k −1 Q reactants ⎝ RT

⎛ E − E RC ⎞ k T QTS ⎟ k2 = B exp⎜ − TS ⎠ h Q RC ⎝ RT

d[P] = k 8Keq7Keq6[HCHO][X][OH] dt

(4)

k = k 8Keq7Keq6[X]

k′ = Keq7k 8

(6)

(7)

k8

(8) 72

39

According to Fliegl and Sinha, the above reaction sequence is typically viewed as one involving the formation of the RC2X (RC2W, RC2F, or RC2S) prereactive collision complex, which then undergoes unimolecular reaction. From the energy profile, it can be seen that reaction 8 is the rate-determining step, and the rate can be expressed as d[P] = k 8[RC2X] dt

(9)

Applying a steady-state approximation to RC2X and assuming that it is in equilibrium with the reactants and by assuming that the equilibrium of reaction 6 is not inferred by reaction 7, then [RC2X] =

k 7[HCHO···X][OH] k −7 + k 8

(14)

From Table 6, it can be seen that for the reactions starting from HCHO···X complex with OH radicals, the rate constants k′ are about 12.1, 2.4, or 0.8 times of that reaction without catalyst when X denoting H2O, HCOOH, or H2SO4, respectively. This seems that, compared to the reaction without catalyst, the rate constants will be larger for the reaction assisted by water or formic acid or comparative for the reaction assisted by sulfur acid. Considering the formation of the two-body complexes in reaction 6, the rate constants k calculated according to eq 13 and the Y complex values for the water, formic acid, or sulfur acid assisted reactions are also listed in Table 6. It can be seen from Table 6 that the reaction rate constant assisted by water (100% relative humidity, i.e., the maximum possible water concentration) is slower by about 3 orders of magnitude than that uncatalyzed reaction due to the small amounts of the twobody complexes formed between HCHO with catalyst. For example, the Y complex value is only 0.0058% for the water assisted reaction at 298 K. As for the reactions assisted by formic acid or sulfur acid, the HCHO···FA and HCHO···SA complexes have larger stability than that of HCHO···H2O, which in turn results in larger equilibrium constant of Keq6. However, the concentrations of HCOOH and H2SO4 are much lower than that of H2O in the atmosphere, which then makes the rate constants of them to be 7.39 × 10−20 and 9.40 × 10−21 cm3 molecule−1 s−1 at 298 K, respectively. Accordingly, it can be stated that the hydrogen abstraction pathway of HCHO +

k7

RC2X → products

(13)

where Keq6 and Keq7 are the equilibrium constants for reactions 6 and 7, respectively, k8 is the rate constant of reaction 8, and [X] is the typical troposphere concentration of H2O, HCOOH, or H2SO4. Additionally, the quantity of Keq6[X] represents the fraction of HCHO···X complex formed in the initial complexation step, viz. Y complex = [HCHO···X]/[HCHO] = Keq6[X]. If reaction 6 is not taken into account, the rate constants for the title reaction assisted by catalyst can be represented as

k6

k −7

(12)

Finally, the rate constant k for the overall reaction is obtained by the following expression

HCHO + X (X = H 2O, FA, or SA)

HCHO···X + OH HooI RC2X

(11)

Consequently, eq 9 can be expressed as

In eqs 4 and 5, QTS, QRC, and QReactants are the partition function of the TS, RC, and the reactants, and Ereactants, ERC and ETS are the total energies of the reactants RC and TS at 0 K with the ZPE corrections, respectively. As shown in Table 6, the rate constant calculated at 298 K for the title reaction without catalyst is 3.69 × 10−11 cm3 molecule−1 s−1, which is slightly larger than the experimental results5−15 ranging from 7.7 × 10−12 to 1.4 × 10−11 cm3 mol−1s−1. For the HCHO+OH reactions assisted by water, formic acid or sulfur acid, the following three steps have been considered:

k −6

k −7

= Keq7Keq6[HCHO][X][OH]

(5)

HooI HCHO···X (X = H 2O, FA, or SA)

k 7Keq6[HCHO][X][OH]

(10) 4804



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OH reaction assisted by water, formic acid, or sulfur acid is of minor importance responsible for the formation of HCO + H2O in the atmosphere.

4. CONCLUSIONS For the purpose of investigating the effect of catalyst on the mechanism and kinetics for HCHO + OH reaction in the atmosphere, the hydrogen abstraction pathways of forming HCO + H2O in the presence of water, formic acid or sulfur acid have been studied at the CCSD(T)/)//MP2(full) and CCSD(T)/)//BH&HLYP levels of theory. The calculational results reveal that for the major reaction pathway, the introduction of a single water, formic acid, or sulfur acid will dramatically reduce the energy of the corresponding transition state, while the corresponding ΔG values are still larger than the initial reactants. Moreover, the kinetic calculations show that the rate constants for these major reaction pathways with catalyst are much smaller than that reaction without catalyst, which means that the effect of these catalysts on the title reaction will be negligible in the atmosphere due to the small amounts of the two-body complexes formed between HCHO with catalyst.

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ASSOCIATED CONTENT

* Supporting Information S

Optimized geometries of reactants, reactant complexes (RC), intermediates (IM), transition states (TS), product complexes (PC), and products involved in the title reaction without and with catalyst, the T1 diagnostic values, the absolute energies of various species, and complete refs 3, 4, 52, and 61. This material is available free of charge via the Internet at http:// pubs.acs.org.

■

AUTHOR INFORMATION

Corresponding Author

*Tel: +86-516-83403165. E-mail: [email protected]. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work is jointly supported by the Natural Science Foundation for Colleges and Universities in Jiangsu Province, People’s Republic of China (Contract Grant No. 10KJB150017), the Doctoral Scientific Research Foundation of Jiangsu Normal University (Contract Grant No. 13XLR003), and a Project Funded by the Priority Academic Program Development of Jiangsu Higher Education Institutions (PAPD).

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Catalytic Effect of Water, Formic Acid, or Sulfuric Acid on the Reaction

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