Gas Phase Reaction of Nitric Acid with Hydroxyl Radical without and

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Gas Phase Reaction of Nitric Acid with Hydroxyl Radical without and with Water. A Theoretical Investigation Javier Gonzalez and Josep M. Anglada* Departament de Quı´mica Biolo`gica i Modelitzacio´ Molecular, Institut de Quı´mica AVançada de Catalunya, IQAC - CSIC, c/Jordi Girona 18, E-08034 Barcelona, Spain ReceiVed: April 1, 2010; ReVised Manuscript ReceiVed: July 9, 2010

The gas phase reaction between nitric acid and hydroxyl radical, without and with a single water molecule, has been investigated theoretically using the DFT-B3LYP, MP2, QCISD, and CCSD(T) theoretical approaches with the 6-311+G(2df,2p) and aug-cc-pVTZ basis sets. The reaction without water begins with the formation of a prereactive hydrogen-bonded complex and has several elementary reactions processes. They include proton coupled electron transfer, hydrogen atom transfer, and proton transfer mechanisms, and our kinetic study shows a quite good agreement of the behavior of the rate constant with respect to the temperature and to the pressure with the experimental results from the literature. The addition of a single water molecule results in a much more complex potential energy surface although the different elementary reactions found have the same electronic features that the naked reaction. Two transition states are stabilized by the effect of a hydrogen bond interaction originated by the water molecule, and in the prereactive hydrogen bond region there is a geometrical rearrangement necessary to prepare the HO and HNO3 moieties to react to each other. This step contributes the reaction to be slower than the reaction without water and explains the experimental finding, pointing out that there is no dependence for the HNO3 + HO reaction on water vapor. Introduction 1

Nitric acid is an important species in the earth’s atmosphere. It acts as a reservoir of NOx (NOx ) NO + NO2) and it can be removed by dry deposition, by rain out, or by reaction with hydroxyl radical, which converts nitric acid to the reactive NO3 radical.2 Kinetic studies have shown that the HNO3 + HO reaction presents unusual pressure and temperature dependences and that deuterium substitution on nitric acid reduces considerably the rate constant.3–5

HNO3 + HO h HNO3 · · · HO f NO3 + H2O

(1)

These data are consistent with reaction 1, which explains the unusual kinetic behavior.4 It involves, in a first step, the formation of a prereactive hydrogen-bonded complex before the transition state and the formation of the products. This prereactive hydrogen-bonded complex is formed vibrationally excited and can redissociate or form the NO3 + H2O products. In addition, it can also be stabilized by collisions with bath gas and then redissociate or decompose to the reaction products. The reaction shown in eq 1 has also been investigated theoretically, where it has been pointed out that the mechanism is complex and that the prereactive complex has a six-membered ring structure.6–8 Very recently, the prereactive hydrogen-bonded complex has been identified scpetroscopically and its binding energy has been estimated to be 5.3 kcal · mol-1.8 High level theoretical calculations reported in the same study predict a binding energy of 5.9 kcal · mol-1, in very good agreement with the experimental value.8 In the present work, we investigate the effect of a single water molecule in reaction 1 by studying reactions 2 and 3. We will * Corresponding author. E-mail: [email protected].

compare these results with those of reaction 1 that has been also considered for sake of completeness.

HNO3 · · · H2O + HO f NO3 + (H2O)2

(2)

HNO3 + HO · · · H2O f NO3 + (H2O)2

(3)

The study of these reactions is important because in the troposphere there is a great amount of water vapor and it is known that nitric acid forms hydrogen-bonded complexes with water.9 Thus, an important fraction of HNO3 can be found forming a complex with a single water molecule. In addition, the tropospheric concentration of the HO · · · H2O complex10 is estimated to be 5.5 × 10-4 molecule · cm-3 so that its reactivity should be taken into account. Very recently, Carl and co-workers11 performed pulsed-laserphotolysis experiments for the HNO3 + HO reaction in the presence of water vapor and concluded that the rate constant obtained at 298 K showed no dependence on water. This result is very interesting since recent work in the literature proved that water vapor produces a catalytic effect. Thus, VohringerMartinez and co-workers12 have shown that water vapor catalyzes the oxidation of acetaldehyde by a hydroxyl radical. It has been also shown that a single water molecule not only produces a catalytic effect in the HCOOH + HO reaction but also influences their product distribution.13,14 Water vapor also enhances the HO2 self-reaction producing H2O2 and O215,16 or reacts with carbonyl oxides producing carboxylic acids or H2O2 in a nonradical process, a reaction that is also catalyzed by a second water molecule.17–19 In a similar way water vapor produces an important catalytic effect on the gas phase reaction of SO3 with H2O to produce H2SO4.20–22 On the contrary, Allodi and co-workers10 showed that water vapor reduces the oxidative

10.1021/jp102935d  2010 American Chemical Society Published on Web 08/03/2010

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ability of the HO radical with respect to methane, pointing out that this effect is caused by an enhanced stability of the prereactive complex formed. Water vapor is also proven to play an important role, for instance, in the photolysis of sulfuric acid,23 in the decomposition of CF3OH,24 in the oxidation of DMS,25 or in the oxidation of propionaldehyde by hydroxyl radicals.26 Consequently, a deep knowledge of the role that water vapor plays in gas phase reactions of interest in the chemistry of the atmosphere is necessary. In addition, the issue is also interesting because the studied reaction may have implications in the atmospheric HNO3/NO3 cycle and the HNO3 · · · H2O complex may be a precursor for cloud condensation nuclei.27 In this work we will analyze, in a first step, the formation of hydrogen-bonded complexes between HNO3 and HO with H2O. In a second step, we will study the reaction between nitric acid and hydroxyl radical. In a third step, we will report the results of the investigation of reactions 2 and 3, and in the fourth step, a kinetic study will be reported.

Gonzalez and Anglada the partition functions computed at the B3LYP/6-311+G(2df,2p) level of theory. The tunneling correction to the rate constants has been considered and computed by the zero-order approximation to the vibrationally adiabatic PES with zero curvature. In this case, the unsymmetrical Eckart potential energy barrier has been used to approximate the potential energy curve.49 The geometry optimizations at the B3LYP level of theory and the CCSD(T) single point energy calculations have been performed using the Gaussian03 suite of programs.50 TST rate constants and tunneling corrections have been computed using the Polyrate program51 while the (RRKM) calculations have been done using the Unimol program.48 The topological properties of the wave function were obtained with the AIMPAC program package.52 The Molden program53 was also used to visualize the geometrical and electronic features of the different stationary points. Results and Discussion

Technical Details of the Calculations We have used the hybrid density functional B3LYP method28 with the 6-311+G(2df,2p) basis set29,30 to optimize and characterize all stationary points investigated in this work. At this level of theory we have also calculated the harmonic vibrational frequencies to verify the nature of the corresponding stationary points (minima or transition state), to provide the zero point vibrational energy (ZPE) and the thermodynamic contributions to the enthalpy and free energy. Moreover, to ensure that the transition states connect the desired reactants and products, we have performed intrinsic reaction coordinate calculations (IRC).31–33 In addition, anharmonic frequency calculations have been also computed for some of the stationary points investigated in this work, to check the accuracy of the methods employed and also to help a possible identification of the IR spectra of these species. The anharmonic corrections have been evaluated by the second-order perturbative treatment implemented by Barone and co-workers.34,35 With the aim to get more accurate relative energies, we have performed single-point CCSD(T)36–39 calculations at the optimized geometries using the more flexible aug-cc-pVTZ basis set.40,41 To check the reliability of single-determinant-based methods, we have looked at the spin eigenvalue of the unrestricted Hartree-Fock wave function (before and after anhililation) and at the T1 diagnostic42 of the CCSD wave function with regard to the multireference character of the wave function. The corresponding values are reported as Supporting Information showing that the spin contamination is not severe. The reliability of the theoretical approach employed has been also checked by doing additional calculations for the HNO3 + HO reaction. Thus, the corresponding stationary points were reoptimized at MP243–45 and QCISD46 levels of theory employing the 6-311+G(2df,2p) basis set and, additionally, CCSD(T) single point energy calculations with the aug-cc-pVTZ basis set were also carried out at the optimized geometries. For several stationary points of interest, we have also analyzed the bonding features by using the atoms in molecules (AIM) theory by Bader.47 In this case, the wave function derived from the B3LYP/6-311+G(2df,2p) has been used. Finally, we have computed the kinetic properties of the system. For this purposes, we have combined transition state theory (TST), taking into account the tunneling effects, and Rice-Ramsperger-Kassel-Marcus (RRKM) calculations.48 For these calculations we have considered the energies obtained at the CCSD(T)/aug-cc-pVTZ//B3LYP/6-311+G(2df,2p) level and

HNO3 · · · H2O and H2O · · · HO Hydrogen-Bonded Complexes. We have found four different hydrogen-bonded complexes formed with nitric acid and water and our calculated values for their geometrical features and relative stabilities are displayed in Figure 1 and Table 1. Three of these complexes have been recently reported in the literature54,55 and our results compare quite well with the reported values. Therefore, we will consider in this section only the main trends. M1 has a six-membered ring structure and it is stabilized by two hydrogen bonds, one is formed between the hydrogen atom of HNO3 and the oxygen atom of water with a computed bond length of 1.707 Å and the other one is formed between one of the hydrogen atoms of water and the oxygen atom of the HNO3 group with a computed bond distance of 2.424 Å. It is the most stable complex and our computed binding energy is 8.45 kcal · mol-1. This hydrogen bond complex has been investigated experimental and theoretically and in this work we have also computed the anharmonic frequencies for both the M1 complex and the HNO3 reactant. These results can be found in the Supporting Information, and our computed values compare quite well with previous experimental and theoretical results reported in the literature (see footnote c in Table 1).56–58 Each one of other three complexes M2, M3, and M4 has only one hydrogen bond, with larger computed bond lengths compared to those for M1, between 2.169 and 2.210 Å. Accordingly, their computed binding energies are smaller than M1 with values between 1.70 and 1.79 kcal · mol-1 (see Table 1). We have also included in Table 1 and Figure 1 our results on two H2O · · · HO hydrogen-bonded complexes (M5 and M6), whose computed binding energies are 3.77 and 2.33 kcal · mol-1, respectively, in good agreement with previous experimental and theoretical results from the literature (see footnote d in Table 1).10,59–65 At this point it is worth considering the atmospheric importance of these complexes. The results displayed in Table 1 allow us to estimate the equilibrium constants at 298 K for the HNO3 · · · H2O complexes, which has been computed to be 1.32 × 10-19 cm3 · molecule-1, at 298 K for M1 and 6.66 × 10-23, 8.38 × 10-23, and 1.12 × 10-23 cm3 · molecule-1, at 298 K for the M2, M3, and M4 complexes, respectively. With a typical gas phase concentration of H2O of 3.85 × 1017 molecule · cm-3, corresponding to 50% of relative humidity at 298 K, about 5% of the whole HNO3 will be complexed with water as M1, whereas the fraction of the remaining M2-M4 complexes will be unappreciable. The computed equilibrium

Reaction of Nitric Acid with Hydroxyl Radical

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Figure 1. Relevant geometrical parameters, obtained at the B3LYP/6-311+G(2df,2p) level, for the reactants, products, the HNO3 · · · H2O complexes, and the H2O · · · HO complexes.

constant at 298 K, for the H2O · · · HO (M5) complex is 4.37 × 10-21 molecule · cm-3, in very good agreement with the 5.91× 10-21 molecule · cm-3 estimated by Allodi and et al.10 Reaction between HNO3 and HO Radical. A theoretical investigation on this reaction has been already reported in the literature,6 and we have reinvestigated it to compare with the same reaction with a single water molecule, as will be reported below. Our theoretical results compare quite well in general, with those results reported previously in the literature, and in the present work we have only considered the three elementary reaction paths having the lowest energy barriers, which have more significance. A schematic picture of the potential energy surface is reported in Figure 2. Figure 3 displays the most relevant geometrical parameters of the stationary points whereas

Table 2 contains the corresponding zero point vibrational energy, entropy, energy, enthalpy, and free energy values. As usual in many reactions in the gas phase, each elementary reaction path considered in this study begins with the formation of a prereactive hydrogen-bonded complex occurring before the transition state and the product formation. Regarding the prereactive hydrogen-bonded complex region, we have found four stationary points, two of them correspond to minima and the other two correspond to transition states connecting these two minima. Cr1 (X 2A′′) is the most stable minimum, and Figure 3 shows that it has a planar six-membered ring structure having two hydrogen bonds. The unpaired electron is mainly localized over the oxygen of the hydroxyl radical moiety, perpendicular to the symmetry plane, and consequently does

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TABLE 1: Zero Point Vibrational Energies (ZPE in kcal · mol-1), Entropies (S in au), and Relative Energies, ZPE Corrected Energies, Enthalpies, and Free Energies (in kcal · mol-1) for the HNO3 · · · H2O Hydrogen-Bonded Complexesa,b compound

ZPE

S

∆E

∆(E+ZPE)

∆H(298K)

∆G(298K)

HNO3 + H2O M1c M2 M3 M4 H2O + HO M5 (H2O · · · HO)d M6 (H2O · · · HO)

29.93 32.02 31.06 31.12 31.06 18.7 20.8 20.1

108.7 79.9 91.3 91.3 90.7 87.7 66.7 70.5

0.00 -10.53 -2.83 -2.97 -2.89 0.00 -5.89 -3.68

0.00 -8.45 -1.70 -1.79 -1.77 0.00 -3.77 -2.33

0.00 -8.90 -1.44 -1.56 -1.50 0.00 -4.47 -2.62

0.00 -0.33 3.75 3.62 3.86 0.00 1.79 2.50

a In the case of M1, the ZPE correction includes anharmonic effects. b Values computed at CCSD(T)/aug-cc-pVTZ//B3LYP/6-311+G(2df,2p) with enthalpy and free energy corrections obtained at B3LYP/6-311+G(2df,2p). c For M1, the ∆(E+ZPE) values from the literature are -7.5 and -8.1 kcal · mol-1, respectively (see refs 54 and 55). d For M5 the ∆E values from the literature are -7.45, -5.49, -6.4, and -5.6 kcal · mol-1, respectively (see ref 59, 63, 64, and 79), and the ∆(E+ZPE) values from the literature are -3.97 and -3.6 kcal · mol-1, respectively (see refs 10 and 65).

Figure 2. Schematic potential energy surface for the HNO3 + HO reaction.

not participate in the hydrogen bond interaction. This hydrogenbonded complex has been recently studied.8,66 It has been identified by IR spectroscopy and their experimental binding energy has been estimated to be 5.3 kcal · mol-1.8 In the same work, the binding energy has been computed to be 5.9 kcal · mol-1 (at the CCSD(T)/CBS basis set (CBS stands for complete basis set), extrapolated to the aug-cc-pV∞Z basis set) in very good agreement with the experimental value. Our calculations, taking into account the anharmonic effects on the ZPE, predict a binding energy of 6.32 kcal · mol-1, which is in good agreement with the previous experimental and calculated data. For this complex we have also computed the anharmonic frequencies, and our computed values (3497 and 3172 cm-1

for modes ν1 and ν2) compare very well with the experimental frequencies (3517 and 3260 cm-1, respectively).8 The remaining computed frequencies are contained in the Supporting Information and displayed in Figure 6 below. The secondary minimum, complex Cr2, has a five-membered ring structure and its computed binding energy is 3.96 kcal · mol-1 (∆(E+ZPE) value). The topological analysis of its wave function indicates the existence of only one hydrogen bond (O2NOH · · · OH), but there is also a bonding interaction between the oxygen of the hydroxyl radical moiety and one oxygen of the nitric acid, which are separated by 2.418 Å, a value that is shorter than twice the oxygen atom van der Waals radius (see Figure 3). The topological analysis of the wave function at the



Figure 3. Relevant geometrical parameters, obtained at the B3LYP/6-311+G(2df,2p) level, for the stationary points of the HNO3 + H2O reaction.

TABLE 2: Zero Point Vibrational Energies (ZPE in kcal · mol-1), Entropies (S in au), and Relative Activation and Reaction Energies, ZPE Corrected Energies, Enthalpies, and Free Energies (in kcal · mol-1) for the HNO3 · · · HO Reactiona compound

ZPEa

Sa

∆Eb,e

∆(E+ZPE)b

∆H(298K)b

∆G(298K)b

HNO3 + HO

21.85

106.2

CR1 (2A′′)c,f,g CR2g TS1g TS2g TS3g CP1 NO3 + H2Od

23.14 23.62 21.83 19.87 26.18 20.88 20.01

80.7 77.9 72.8 69.9 76.6 93.4 108.3

0.00 (0.00) -7.62 -5.73 2.55 8.80 8.26 -14.27 -13.13 [-13.64]

0.00 (0.00) -6.32 -3.96 2.54 6.82 12.59 -15.24 -14.96 [-15.46]

0.00 (0.00) -6.62 -4.52 1.31 5.33 11.76 -14.21 -14.37 [-14.88]

0.00 (0.00) 0.97 3.91 11.27 16.13 20.58 -10.41 -14.99 [-15.51]

a

Values computed at B3LYP/6-311+G(2df,2p). b Values computed at CCSD(T)/aug-cc-pVTZ//B3LYP/6-311+G(2df,2p) with enthalpy and free energy corrections obtained at B3LYP/6-311+G(2df,2p). c For CR1 the ZPE, enthalpy, and entropy corrections take into account the anharmonic effects. d Values in brackets have been computed at CCSD(T)/aug-cc-pVQZ//B3LYP/6-311+G(2df,2p) with enthalpy and free energy corrections obtained at B3LYP/6-311+G(2df,2p). e ∆E values (in kcal · mol-1) computed at CCSD(T)/aug-cc-pVTZ//MP2/ 6-311+G(2df,2p) are -7.57, +5.95, +9.11, +9.11, and -13.15 for CR1, TS1, TS2, TS3, and NO3 + H2O, respectively. ∆E values (in kcal · mol-1) computed at CCSD(T)/aug-cc-pVTZ//QCISD/6-311+G(2df,2p) are -7.58, +2.71, +8.73, +9.18, and -13.07 for CR1, TS1, TS2, TS3, and NO3 + H2O, respectively. f Values reported in the literature are -5.9 kcal · mol-1 (∆(E+ZPE) and -7.4 kcal · mol-1 (∆E value), see ref 8). g At the G2M level of theory the ∆E computed values are (in kcal · mol-1) -8.1 for CR1, -5.31 for CR2, 1,3 for TS1, 5.9 for TS2, and 3.5 for TS3 (see ref 6).

bond critical point (bcp) gives the following values: F ) 0.0252 au and 32F ) 0.1064 au (F and 32F stand for the density and the Laplacian of the dednsity at the bcp) pointing out that this interactionhasabondingcharacter,asoccursfortheHCOOH · · · HO complex.67 The transition state TSCr1Cr2 connects these two minima whereas TSCr2Cr2 connects the two possible forms of the Cr2 complex, with the HO moiety being above or below the HNO3 plane. In fact, TSCr2Cr2 has a planar structure similar to that for Cr1, but in this case the electronic state is a

2

A′. That is, the unpaired electron, which is mainly localized over the oxygen of the hydroxyl radical moiety, lies on the molecular plane. The geometrical parameters of these transition states are drawn in the Supporting Information. Regarding the reaction mechanism, we have considered three elementary reactions that involve the interaction between the hydroxyl radical and the ONOH moiety of nitric acid. From an electronic point of view, these three elementary reactions have the same features as discussed for the gas phase oxidation of

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HCOOH and H2SO4 by the HO radical,68–70 so that we can anticipate that there are two of these elementary reactions producing NO3 + H2O whereas the products of the third reaction are HNO3 and HO, that is, the same as the reactants so that this is a silent reaction. Figure 2 shows that the reaction path having the lowest energy barrier occurs through TS1 (see Figure 3) and our calculations predict this stationary point to lie 2.54 kcal · mol-1 (∆(E+ZPE) value) above the energy of the separate reactants, which compare with other results from the literature.6 In TS1, the HO radical moiety is oriented in such a way that the unpaired electron interacts with the lone pair of the oxygen atom of the NO moiety and provokes a shift of one electron of the lone pair of the oxygen atom of the NO group to the oxygen of the hydroxyl radical moiety and simultaneously, the proton of the nitric acid is transferred to the hydroxyl radical in what is known as a proton coupled electron transfer process (pcet).69 The topological analysis of the wave function (F ) 0.0424 au and 32F ) 0.1855 au) confirms this O · · · O interaction. Moreover, the atomic spin population analysis indicates that the unpaired electron is shared between O6 (0.676) and O3 (0.328) (see Figure 2 for the atom numbering), in a similar way as has been discussed for the HCOOH + HO reaction.68,69 Figure 2 shows that the process occurring through TS2 involves a double proton transfer mechanism so that the reaction products are the same species as the reactants. Please note that this process could be identified by using deutered species. Figure 3 shows that the transition state has a planar six-membered ring structure, possessing C2V symmetry (2B1 electronic state). The unpaired electron lies perpendicular to the molecular plane and is mainly localized over the oxygen of the hydroxyl moiety. Our calculations predict this transition state to lie 6.82 kcal · mol-1 above the energy of the separate reactants. The elementary process having the highest energy barrier occurs via TS3. Figure 3 shows that this transition state has a planar structure (Cs, 2A′) and the process involves the hydrogen atom abstraction (hat) of nitric acid by the hydroxyl radical, as it is indicated by the analysis of the corresponding wave function. Accordingly, the spin population shows that the unpaired electron is shared between O6 (0.661) and O4 (0.309). Our calculations predict TS3 to lie 12.59 kcal · mol-1 above the energies of the separate reactants, which contrasts with the 3.5 kcal · mol-1 reported by Xia and co-workers.6 The high energy barrier computed for this transition state can be associated with a lack of hydrogen bond interaction between the hydrogen of the hydroxyl radical moiety and the oxygen of nitric acid. As our results predict some differences with respect to the previous results from the literature, we have performed additional calculations to check the reliability of the theoretical approach used in this work. Thus, we have performed geometry optimizations for the reactants, the CR1 prereactive complex and the transition states and the most stable prereactive complex at MP2 and QCISD levels of theory, employing the 6-311+ G(2df,2p) basis set. At the optimized geometries, we have also performed single point energy calculations at CCSD(T)/augcc-pVTZ level of theory. In the case of the MP2 stationary points, we have also carried out frequency calculations to check the character of the stationary points. The corresponding energetic results are displayed in footnote e of Table 2, and the values obtained at the best level of theory, namely CCSD(T)/ aug-cc-pVTZ//QCISD/6-311+G(2df,2p), compare quite well with those obtained at CCSD(T)/aug-cc-pVTZ//B3LYP/6311+G(2df,2p), confirming the reliability of the last theoretical approach. The CCSD(T)/aug-cc-pVTZ//MP2/6-311+G(2df,2p)

Gonzalez and Anglada are not so reliable. TS1 differ by 3.4 kcal · mol-1 from the result obtained with the best theoretical method as the MP2 approach predicts a too short O3-O6 bond distance (see Supporting Information). Moreover, the MP2 approach predicts a too parabolic potential energy surface for TS3, as indicated by its computed imaginary frequency (-4138.8 cm-1), making the ZPE and thermodynamic corrections unreliable. Finally, Table 2 shows that our computed reaction energy and enthalpy (at 298 K) are -14.96 and -14.37 kcal · mol-1, respectively, at the CCSD(T)/aug-cc-pVTZ//B3LYP/6311+G(2df,2p) level of theory, and -15.46 and -14.88 kcal · mol-1, respectively, at the CCSD(T)/aug-cc-pVQZ//B3LYP/ 6-311+G(2df,2p) level of theory, which still differs in 2.2 kcal · mol-1 for the experimental estimate (∆H(298K) ) -17.1 kcal · mol-1).71 Effect of a Single Water Molecule on the Potential Energy Surface. We have studied the effect of a single water molecule on the title reaction by considering that (a) HNO3 can form a stable hydrogen-bonded complex with H2O and then this complex reacts with HO radical (reaction 2) or (b) HNO3 reacts with a previously formed H2O · · · HO radical complex (reaction 3). In a previous section we have already pointed out that M1 (Figure 1) is the only HNO3 · · · H2O complex of atmospheric significance and therefore only the reaction of M1 with HO has been considered. Moreover, the energy and features of two H2O · · · HO complexes (M5 and M6) have been also presented. Figure 4 shows a schematic potential energy surface of this reaction whereas Figure 5 contains the most relevant geometric parameters of the stationary points. Table 3 contains the ZPE, S, and energy, enthalpy, and free energy values. As for the naked HNO3 + HO reaction described above, the reaction between M1 (HNO3 · · · H2O) and HO begins with the formation of hydrogen-bonded complexes, which occur before the transition states and the product formation. We have found three minima and two transition states located in the prereactive hydrogen-bonded region. In a first step, the hydrogen atom of the hydroxyl radical interacts with one of the lone pair of the water moiety in M1 (HNO3 · · · H2O) forming the CR1a complex, which is computed to be 1.58 kcal · mol-1 more stable than the M1 + HO reactants at 0 K. The next step involves the formation of the seven-membered ring complex CR2a, with a calculated binding energy of 6.11 kcal · mol-1. The process occurs through the TSCR1a transition state, which lies 1.27 kcal · mol-1 above CR1a and involves the breaking of the O2NOH · · · OH2 hydrogen bond and the forming of the O2NOH · · · OH hydrogen bond, respectively (see Figure 5). Finally, we have also found the seven-membered ring CR3a complex. Please note from Figure 4 that both CR1a and CR2a can also be formed by interaction between HNO3 and the H2O · · · OH (M5) reactants, whereas CR3a is formed by interaction between HNO3 and the H2O · · · OH (M6) reactants, respectively. The binding energies of CR2a and CR3a with respect to M5 and M6, (H2O · · · OH) are 10.74 and 12.75 kcal · mol-1, respectively. With the aim of helping a possible experimental identification of CR2a, we have computed the anharmonic vibrational frequencies of this complex and their corresponding values are reported in Figure 6, along with the anharmonic vibrational spectra of CR1. A look in Figure 6 shows clearly that CR2a could be easily identified by the two vibrational bands at 3134 and 2726 cm-1, and the band at 2726 cm-1 can be considered as a signature of this complex. These two bands correspond to the two possible combinations of the stretching of the HO corresponding to the hydroxyl radical moiety and nitric acid moiety respectively. A



Figure 4. Schematic potential energy surface for the HNO3 + HO reaction with a single water molecule.

full list of the computed anharmonic frequencies of HO, H2O, HNO3, CR1, CR2a, and CR3a is reported in the Supporting Information. Regarding the reaction mechanism occurring after the CR2a and CR3a hydrogen-bonded complexes, we anticipate here that the electronic and geometrical features of the different stationary points are very similar to those described recently for reaction of formic acid with hydroxyl radical catalyzed by single water molecule.13 Table 3 and Figure 4 show that the reaction path having the lowest energy barrier occurs through TS1a, which has a five-membered ring structure and resembles very much TS1 of the naked reaction (see Figures 2 and 3, respectively). As discussed above for TS1, this process involves a pcet mechanism and here the water molecule interacts, through a hydrogen bond, with the hydrogen atom of the hydroxyl radical. Our calculations predict TS1a to lie 2.25 kcal · mol-1 above the energy of the reactants, so that the water molecule produces a stabilizing effect of about 0.30 kcal · mol-1 with respect to the naked reaction (see Table 2 and Figure 2). This small stabilizing effect is produced by the small charge transfer associated to the hydrogen bond interaction in the same way as discussed in the case of the water catalyzed HCOOH + HO reaction.13 Figure 4 shows that, in the exit channel, the reaction proceeds through CP2a, which occurs before the formation of the most stable complex CP3a and the NO3 + (H2O)2 products. The reaction path occurring through TS1b involves also a pcet mechanism in which an electron is transferred from one oxygen atom of the HNO3 moiety to the oxygen atom of the hydroxyl radical moiety and, simultaneously, there is a double proton transfer, form the nitric acid moiety to the water moiety and from the water moiety to the hydroxyl radical moiety (see Figures 4 and 5). Our calculations predict this transition state to lie very high in energy (8.43 kcal · mol-1 above the M1 plus HO reactants;

see Figure 4 and Table 3) in a way similar to that described for the equivalent process in the HCOOH + HO reaction with water.13 The elementary process involving a hydrogen atom abstraction (hat) mechanism takes place through TS3a and is computed to lie 3.68 kcal · mol-1 above the M1 + HO reactants. Comparing this energy barrier with that of the naked reaction (see above), it appears that the water molecule produces a stabilization of 8.91 kcal · mol-1. This stabilization effect is caused by the existence of two hydrogen bonds in TS3a (it has an eightmembered ring structure where the water molecule interacts with one oxygen atom of the HNO3 moiety and the hydrogen atom of the HO moiety), in clear contrast with the reaction without water, where no stabilization by hydrogen bond was found (see TS3 above). Finally, Figures 4 and 5 show that the elementary reaction occurring through TS2a involves a three proton transfer mechanism between nitric acid, hydroxyl radical, and water so that the products are the same species as the reactants. The results displayed in Table 3 and Figure 4 indicate that TS2a lies 7.24 kcal · mol-1 above the energy of the M1 + HO reactants, a value greater than those of all reactant channels. From a technical point of view, it was very difficult to find TS2a. Any attempt to find it using the 6-311+G(2df,2p) basis set converged to the lowest transition state TS3a, and we have located it by using the 6-311+G(d,p) basis set. Kinetics of the Reactions. Table 4 contains the results of a theoretical study for the HNO3 + HO reaction without and with water, carried out between 200 and 350 K at 0.025 and 1 atm of pressure, respectively. More detailed information regarding the computed rate constants for each elementary path can be found in the Supporting Information. For the reaction without water we have followed the kinetic model shown in Scheme 1 that has been developed by Brown

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Figure 5. Relevant geometrical parameters, obtained at the B3LYP/6-311+G(2df,2p) level, for the stationary points of the HNO3 + H2O reaction with a single water molecule.

and co-workers4 and that has also been reported by Smith and co-workers.72 Following this scheme, these authors have shown that the negative temperature dependence and the low pressure dependence of the reaction rate can be explained by taking into account that the prereactive complex can react before being thermalized by the surrounding bath gas, depending on the pressure. In this model Kh is the unimolecular rate constant for the vibrationally excited prereactive complex (CR), Kd is the unimolecular rate constant for the stabilized CR, Ke is the CR equilibrium constant, Kc and K-c account for the rate of vibrationally satabilization/destabilization of CR, and Ka and K-a account for the rate of formation of the vibrationally excited CR. In the RRKM calculations the ka and k-a, values have been obtained over a Varshni potential,73 which is a modified Morse potential, and it is used because the potential energy surface in this region is very flat. The reaction is also supposed to happen in a N2 bath simulated with a Lennard-Jones potential with parameters σ ) 3.98 Å and ε/K ) 189, which have been taken from the HNO3 case.74 For the kinetic study, we have used the

temperature range between 200 and 350 K and two different pressures, namely, 0.025 and 1 atm for low and high pressure, respectively. These values have been chosen to compare the computed rate contants with the experimental ones. Table 4 indicates that our calculations predict the rate constant at 298 K to be 0.3 × 10-13 cm3 · molecule-1 · s-1, which is in reasonable agreement with experimental values of 1.2 × 10-13 cm3 · molecule-1 · s-1 reported by Brown et al.5 At 1 atm pressure, our computed value is 1.1 × 10-13 cm3 · molecule-1 · s-1, which compares quite well with the range (1.26-1.64) × 10-13 cm3 · molecule-1 · s-1 reported from experiments at different pressures.11,75–77 The variation of the rate constant with the temperature at the two pressures considered is also displayed in Figure 7, showing a divergent behavior at low temperatures in good agreement with the experimental results.4 The second part of our kinetic study refers to possible effect of a single water molecule on the kinetics of the HNO3 + HO reaction. As discussed in the previous section and shown in Figure 4, the potential energy surface is now much more



TABLE 3: Zero Point Vibrational Energies (ZPE in kcal · mol-1), Entropies (S in cal/(mol K)), and Relative Activation and Reaction Energies, ZPE Corrected Energies, Enthalpies, and Free Energies (in kcal · mol-1) for the Reaction between HNO3 and HO Assisted by a Single Water Moleculea compound

ZPE

S

∆E

∆(E+ZPE)

∆H(298K)

∆G(298K)

M1 · · · HO HNO3 + M5 (H2O · · OH) HNO3 + M6 (H2O · · OH) CR1a TSCR1a CR2a CR3a TS1b TS1a TS3a TS2ab CP1a CP2a CP3a NO3 + (H2O)2

37.33 37.34 36.64 39.04 38.39 39.03 38.94 36.93 37.00 35.79 35.69 38.60 38.64 36.99 35.60

122.5 130.28 134.08 99.7 95.4 95.3 95.0 85.9 92.1 90.7 84.9 98.9 101.6 107.72 132.62

0.00 4.62 6.88 -3.30 -1.34 -7.81 -8.06 8.83 2.59 5.22 8.88 -7.98 -6.78 -12.33 -7.81

0.00 4.63 6.29 -1.58 -0.27 -6.11 -6.46 8.43 2.25 3.68 7.24 -6.71 -5.47 -12.67 -9.54

0.00 4.36 6.31 -1.93 -0.89 -6.71 -7.02 6.69 1.28 2.60 5.23 -6.81 -5.43 -11.97 -9.00

0.00 1.91 2.85 4.87 7.17 1.40 1.17 17.58 10.34 12.09 16.43 0.22 0.79 -7.56 -12.02

a Values computed at CCSD(T)/aug-cc-pVTZ//B3LYP/6-311+G(2df,2p) with enthalpy and free energy corrections obtained at B3LYP/6-311+G(2df,2p). b Values obtained at CCSD(T)/aug-cc-pvtz//B3LYP/6-311+G(d,p).

Figure 6. Computed anharmonic spectra for the CR1 (dotted line) and CR2a (full line) complexes.

TABLE 4: Rate Constants (in cm3 · molecule-1 · s-1) for the HNO3 + HO Reaction without and with Water Computed at 0.025 atm (LoP) and 1 atm (HiP) of Pressure HNO3 + OH

SCHEME 1: Schematic Model for the Kinetic Study of the HNO3 + HO Reaction

HNO3 · · · H2O + OH

T (K)

P ) 1 atm

P ) 0.025 atm

P ) 1 atm

200 220 240 260 280 298 350

3.2 × 10-12 1.9 × 10-12 9.2 × 10-13 5.3 × 10-13 2.0 × 10-13 1.1 × 10-13 5.3 × 10-14

1.9 × 10-12 1.2 × 10-12 4.8 × 10-13 1.7 × 10-13 6.1 × 10-14 3.0 × 10-14 2.2 × 10-14

2.5 × 10-18 6.3 × 10-18 1.5 × 10-17 3.2 × 10-17 6.7 × 10-17 1.2 × 10-16 2.4 × 10-16

complex. The reaction begins with a complex prereactive region, with two hydrogen-bonded complexes, CR1a and CR2a, hich are connected through the transition state TSCR1a. This step involves a geometric rearrangement that plays a crucial role in the reaction, as in CR1a, and in M1 too, the hydrogen atom of the HNO3 moiety forms a hydrogen bond with the oxygen atom

of water, which hampers the possible oxidation by the hydroxyl radical. Through the formation of CR2a, both the hydroxyl radical and the HNO3 moieties are prepared to interact to each

9160



Figure 7. Variation of the rate contant for the HNO3 + HO f NO3 + H2O reaction with themperature and pressure. The solid line corresponds to low pressure, and the dashed line corresponds to high pressure.

TABLE 5: Unimolecular Rate Constants (in s-1) and Tunneling Factors (ZCT Approximation) for the Processes through the Different Transition States in the Reaction with Watera T (K)

KTSCR1a (CR1a f CR2a)

KTSCR1a (CR2a f CR1a)

KTS1a

200 220 240 260 280 298 320

3.02 × 10 5.11 × 1010 6.84 × 1010 8.79 × 1010 1.09 × 1011 1.30 × 1011 1.57 × 1011

1.98 × 10 8.24 × 106 2.73 × 107 7.55 × 107 1.82 × 108 3.64 × 108 7.74 × 108

1.42 × 10 1.01 × 104 5.19 × 104 2.07 × 105 6.79 × 105 1.72 × 106 4.67 × 106

a

10

6

3

κ

KTS3a

25.0 12.5 7.6 5.3 4.1 3.4 2.8

2.49 × 10 2.40 × 102 1.58 × 103 7.79 × 103 3.06 × 104 8.96 × 104 2.83 × 105

κ 1

2178.4 472.1 147.9 60.9 30.7 18.9 11.9

Processes through TSCR1a have no tunneling since the energy available is always greater than the barrier.

other. The computed free energy value for CR1a (displayed in Table 3) suggest that this complex is shifted to the reactants side and the rate constant is given by eq 4

kI )

k1 k ) Keqk2 k-1 2

(4)

where Keq is the equilibrium constant given by eq 5.

Keq )

QCR1a -(EC-ER)/RT e QM1QOH

(5)

Because of the complexity of the whole reaction, k2 is computed using eq 6 according to the unified statistical model.78

1 1 1 ) + k2 kTSCR1a kTS1a

(6)

In Table 4 we have collected the computed rate constant, which shows that the water assisted reaction is up to 4 orders of magnitude slower than the naked reaction. This result explains the experimental finding by Carl and co-workers11 pointing out that there is no dependence for the HNO3 + HO reaction on water vapor. For the sake of completeness, we have collected in Table S3 of the Supporting Information the values of each individual step. The analysis of these results shows that the existence of TSCR1a makes the kinetics more complicated. The equilibrium is now accomplished between reactants and CR1a

and, even if the passage from M1 + OH to CR1a is quite fast, as can be seen in Table S3, the overall rate constant is let down by the two TS processes so that the kinetics of the reaction is slower. The second important point is to consider the reaction beginning from the HNO3 + H2O · · · HO (M5) entrance channel. In this case, a look on the free energy values from Table 3 points clearly out that, going through either CR1a or CR2a, the reaction will produce HNO3 · · · H2O (M1) + HO, but not NO3 + H2O. This conclusion can be easily deduced by looking at the unimolecular rate constants involving the CR2a f CP2a and CR2a f CR1a steps that are displayed in Table 5. For sake of completeness, we have included the equilibrium constants of the CR1a and CR2a complexes in Table S3. Summary and Conclusions In this work we have investigated the gas phase reaction of HNO3 + HO without and with water employing high level theoretical methods. The reaction without water begins with the formation of a prereactive complex before the transition states and the release of the products. For this reaction we have considered three different kinds of elementary processes involving a proton coupled electron transfer mechanism (TS1), a double proton transfer process (TS2), and a hydrogen atom transfer reaction (TS3). TS1 and TS3 lead to the formation of NO3 + H2O products while the process through TS2 produces no net reaction. Our calculations predict TS1 to lie 2.54 kcal · mol-1 above the energy of the reactants whereas TS2 and TS3 have higher energy barriers, lying 6.82 and 12.59 kcal · mol-1, respectively, above the reactant channel.

Reaction of Nitric Acid with Hydroxyl Radical With the addition of a single water molecule the potential energy surface is much more complex and we can consider up to three entrance reaction channels, namely, hydroxyl radical plus a previously formed HNO3 · · · H2O (M1) complex or HNO3 plus each of the two H2O · · · HO complexes (M5 and M6). Starting from the M1 complex, the hydroxyl radical adds to the oxygen atom of the water moiety (CR1a) and, after a reorganization of the hydrogen bonds, the seven-membered ring hydrogen-bonded complex CR2a is formed. This geometrical rearrangement is necessary to prepare the HO and HNO3 moieties to react to each other. Then, the reaction proceeds through four reaction paths involving proton coupled electron transfer mechanisms (TS1a and TS1b), a hydrogen atom transfer mechanism (TS3a), and a multiproton transfer mechanism (TS2a). Compared to the naked reaction, a single water molecule produces a slight stabilization of 0.30 kcal · mol-1 for the pcet mechanism (TS1a) and a large stabilization of 8.91 kcal · mol-1 for the hat mechanism (TS3a), both being attributed to a hydrogen bond interaction. The results of the kinetic study for the naked reaction show a quite good agreement of the behavior of the rate constant respect to the temperature and to the pressure with the experimental results from the literature. The reaction with water vapor is computed to be slower than the reaction without water. This fact is due to the geometrical rearrangement occurring in the prereactive hydrogen bonding region, which makes the kinetics more complicated and, in the end, slows the whole reaction process. This result explains the experimental finding showing that there is no dependence for the HNO3 + HO reaction on water vapor. Acknowledgment. This research has been supported by the Spanish Direccioń General de Investigacioń Cientı´fica y Tećnica (DGYCIT, grant CTQ2008-06536/BQU) and by the Generalitat de Catalunya (Grant 2009SGR01472). The calculations described in this work were carried out at the Centre de Supercomputacio´ de Catalunya (CESCA) and Centro de Supercomputacioń de Galicia (CESGA). J.G.A. acknowledges the CSIC for the JAE-DOC contract. Supporting Information Available: Tables containing the computed harmonic and anharmonic frequencies of some species considered, equilibrium constants for the reactants of the reaction with water, and further kinetic constants for the reaction between nitric acid and hydroxyl radical. Figures showing geometrical parameters of additional stationary points discussed in this work. This material is available free of charge via the Internet at http:// pubs.acs.org. References and Notes (1) Wespes, C.; Hurtmans, D.; Herbin, H.; Barret, B.; Turquety, S.; Hadji-Lazaro, J.; Clerbaux, C.; Coheur, P. F. J. Geophys. Res. 2007, 112, D13311. (2) Wayne, R. P. Chemistry of Atmospheres, 3rd ed.; Oxford University Press: Oxford, U.K., 2000. (3) Margitan, J. J.; Watson, R. T. J. Phys. Chem. 1982, 86, 3819– 3824. (4) Brown, S. S.; Burkholder, J. B.; Talukdar, R. K.; Ravishankara, A. R. J. Phys. Chem. A 2001, 105, 1605–1614. (5) Brown, S. S.; Talukdar, R. K.; Ravishankara, A. R. J. Phys. Chem. A 1999, 103, 3031–3037. (6) Xia, W. S.; Lin, M. C. J. Chem. Phys. 2001, 114, 4522–4532. (7) Aloisio, S.; Francisco, J. S. J. Am. Chem. Soc. 1999, 121, 8592– 8596. (8) O’Donnell, B. A.; Li, E. X. J.; Lester, M. I.; Francisco, J. S. Proc. Natl. Acad. Sci. U.S.A. 2008, 105, 12678–12683. (9) Vaida, V.; Headrick, J. E. J. Phys. Chem. A 2000, 104, 5401–5412.

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JP102935D

Gas Phase Reaction of Nitric Acid with Hydroxyl Radical without and

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