Effect of Formic Acid Addition on Water Cluster ... - ACS Publications

ARTICLE pubs.acs.org/JPCA

Effect of Formic Acid Addition on Water Cluster Stability and Structure Erin G. Goken,† Kaushik L. Joshi,‡ Michael F. Russo, Jr.,‡ Adri C. T. van Duin,‡ and A. W. Castleman, Jr.*,†,§ †

Department of Chemistry, §Department of Physics, and ‡Department of Mechanical and Nuclear Engineering, The Pennsylvania State University, University Park, Pennsylvania 16802, United States ABSTRACT: Computational chemistry simulations were performed to determine the effect that the addition of a single formic acid molecule has on the structure and stability of protonated water clusters. Previous experimental studies showed that addition of formic acid to protonated pure water results in higher intensities of large-sized clusters when compared to pure water and methanol
water mixed clusters. For larger, protonated clusters, molecular dynamics simulations were performed on Hþ(H2O)n, Hþ(H2O)nCH3OH, and Hþ(H2O)nCHOOH clusters, 19
28 molecules in size, using a reactive force field (ReaxFF). Based on these computations, formic acid
water clusters were found to have significantly higher binding energies per molecule. Addition of formic acid to a water cluster was found to alter the structure of the hydrogen-bonding network, creating selective sites within the cluster, enabling the formation of new hydrogen bonds, and increasing both the stability of the cluster and its rate of growth.

’ INTRODUCTION Water clusters have been studied using a wide range of methods, both experimental1
3 and computational.4,5 Studies of water clusters are used to examine the fundamentals of intermolecular interactions such as hydrogen bonding and cluster structure, as well as such phenomena relevant to atmospheric chemistry as solvation and nucleation. Small water clusters are important because they can provide information on the gas-to-particle transition, which is of particular interest in atmospheric chemistry. Water clusters exist in the atmosphere as neutral, protonated, and ionic clusters depending on the region or altitude. Recent flow-tube studies of the mass distributions of protonated water clusters at well-controlled temperatures and their reactions with atmospherically relevant chemical species have been shown to be complementary to direct atmospheric measurements for identifying chemicals in the atmosphere that might contribute to nucleation and particle growth.6 Most experiments on water clusters are performed using ions, either protonated or anionic clusters, as neutral clusters are much more complicated to detect. Under various experimental conditions, including expansion of ionized water vapor,1 nearthreshold vacuum-UV photoionization,2 and thermal flow-tube conditions at cold temperatures,3,6
8 the protonated 21-water cluster stands out as having “magic” characteristics. Magic clusters can be defined as standing out based on mass spectral abundance or the display of an abrupt discontinuity in an otherwise smoothly varying distribution. A more accurate means of determining whether a cluster such as Hþ(H2O)n has magic character is to make an intensity ratio plot using the equation R ¼

IðnÞ Iðn þ 1Þ

ð1Þ

where R is the intensity ratio and I stands for intensity. A large peak in the intensity ratio plot corresponding to a mass peak that stands out in the mass spectrum indicates a magic cluster. The structure of the r 2011 American Chemical Society

magic 21-water cluster and what causes its magic character has long been disputed. The debate about whether the excess proton resides on the surface of the cluster or within the cage is ongoing and will not be discussed in this work. Many explanations have been developed to account for the magic stability of the 21-water magic cluster. Miyazaki et al.4 observed the IR spectra of water clusters ranging from 4 to 27 molecules and reported that the stretching mode for the acceptor
acceptor
donor (AAD) moiety, where a water molecule is accepting hydrogen-bonding character from two other molecules while donating to only one, was the most prominent for the 21molecule cluster. They concluded that this observation implied that the transition from two-dimensional chains to a threedimensional cage structure was complete. Shin et al.5 observed the OH stretching frequencies of clusters ranging from 6 to 27 molecules. Their experiments showed that a doublet stretching feature present for clusters larger than 11 molecules shifted to only a single peak at the 21-molecule cluster, indicating that only one type of OH stretch was present and that all dangling OH bonds were equivalent.5 Both of these considerations focus on the structure of the clusters and how the structure relates to the magic character of the 21-water cluster. The magic character of the 21-water cluster makes it an ideal species for studying the interaction of molecules with water using a flow-tube apparatus. Throughout this work, we compare calculations to specific flow-tube experiments on protonated water clusters, Hþ(H2O)n, where n = 2
30 molecules. Protonated clusters are formed by passing water seeded in helium gas over a wire that has a voltage applied to it. Cluster growth occurs in the main body of the flow tube, where the Received: November 19, 2010 Revised: March 27, 2011 Published: April 20, 2011 4657

dx.doi.org/10.1021/jp1110746 | J. Phys. Chem. A 2011, 115, 4657–4664

The Journal of Physical Chemistry A clusters undergo ∼105 collisions. These collisions cause the clusters to grow and break apart at a specific rate, meaning that the clusters detected by the channeltron electron multiplier represent an averaged mass distribution, or a thermalized distribution, of the clusters present in the flow tube. A reactant gas is typically introduced into the flow tube some distance away from the ionization source and the detector in order to allow the reactant molecules to interact with already-formed water clusters and the reacted clusters to undergo enough collisions to be considered thermalized. The reacted cluster species can be compared to pure-water cluster distributions to provide information about possible reaction mechanisms and products under certain conditions. There are three likely reaction channels that are potentially operative for water-cluster ion
molecule studies: association, proton transfer, and switching. Recent flow-tube studies of formic acid
water mixed clusters and methanol
water mixed clusters6 were performed because of interest generated from calculations presented by Aloisio et al.9 that examined the changes in the hydrogen-bonding network of small neutral water clusters upon the addition of formic acid. Further, formic acid has been shown to enhance the uptake of sulfuric acid by water.10 In this work, similar small cluster calculations were performed and compared to experimental flow-tube mass spectrometry data and to literature values;6,9 the calculations presented here include small neutral pure-water, formic acid
water, and methanol
water clusters. To further examine the differences between the formic acid
water mixed clusters and the methanol
water mixed clusters and to determine whether incorporation of formic acid into the cluster causes a structural change on a larger size scale than studied using density functional theory (DFT) in this work, numerical modeling of protonated water clusters ranging from 20 to 28 molecules was performed using the ReaxFF reactive forcefield model. These larger, protonated cluster calculations are necessary to more directly compare the results with the experimental flow-tube studies of protonated clusters. The ReaxFF force-field method allows moderately large systems (up to 4000 atoms on a single processor, >106 atoms in a parallel environment) to be modeled at low computational cost while still retaining near-quantum-mechanical (near-QM) accuracy. ReaxFF is a bond-order-dependent reactive force field and is capable of modeling the breaking and formation of bonds during molecular dynamics simulation. The parameters used within this force field are developed by fitting against experimental and QM calculations. The ReaxFF reactive force field was initially developed for hydrocarbons11,12 and has been extended for many other organic and inorganic systems.13
18

’ EXPERIMENTAL METHODS Density Functional Theory. In a prior study, Aloisio et al.9

performed QM calculations on small neutral pure-water clusters (with between one and four molecules), as well as clusters with the same numbers of molecules that had one formic acid molecule replacing one water molecule within the cluster structure. They performed an extensive study of the various basis sets involved in geometrical optimization in DFT. In this work, we present calculations performed using the Gaussian 03 suite of programs19 employing the B3LYP/6-311þþG(d,p) basis set, which was the highest level of theory Aloisio et al.9 presented for their geometry calculations. In addition, only the most stable

ARTICLE

cage structures calculated by Aloisio et al.9 are compared in the present work. ReaxFF Force-Field Method. The ReaxFF system is based on a balance of energies Esystem ¼ Ebond þ Eval þ Etors þ Eover þ Eunder þ Elp þ EH-bond þ EvdWaals þ ECoulomb

ð2Þ

The partial contributions in eq 2 include bond energies (Ebond), valence-angle energies (Eval), torsion-angle energies (Etors), energy to penalize overcoordination of atoms (Eover), energy to stabilize undercoordination of atoms (Eunder), lone-pair energies (Elp), hydrogen-bond energies (EH-bond), and terms to handle nonbonded Coulomb (ECoulomb) and van der Waals (EvdWaals) interaction energies. All of the energy contributions, excluding the last two terms of eq 2, depend on the bond order. This bond-order dependence allows for smooth transitions between bond breaking and formation during the dynamic modeling. More detailed descriptions of each individual energy term and the ReaxFF method can be found in refs 11
13. ReaxFF Force-Field Parameterization. The ReaxFF potential was reoptimized to incorporate the effect of formic acid on the cooperative hydrogen bonding of water molecules. The initial force-field parameters of H/O/C interactions were extensively optimized using quantum data describing reactive and nonreactive interactions relevant to water. This includes equations of state for water dimers, proton-transfer barriers, and crystal ice. For the proton-transfer reactions, we used a H2O/H3Oþ dimer at various O 3 3 3 O distances (2.4, 2.6, 2.8, 3.0, 3.2, and 3.4 Å). The DFT data (generated at the X3LYP/6-311þþG** level of theory) indicate that the global minimum for this dimer is at an O 3 3 3 O distance of about 2.8 Å, in which case a 5 kcal/mol barrier is observed for proton migration.20 Upon compression of the O 3 3 3 O distance, this barrier disappears, whereas extension of the O 3 3 3 O distance leads to a steep increase in the proton migration barrier. These DFT results are accurately reproduced by ReaxFF. Furthermore, ReaxFF was tested against the reaction energy of the self-ionization of water in a [H2O]8 cluster. For this system, Svozil and Jungwirth reported that the [H3O]þ[OH]
[H2O] system is 25.5 kcal/mol higher in energy than [H2O]8, with a small reaction barrier separating the ionized state from the neutral cluster.21 ReaxFF accurately reproduces these results (ΔE = 24.0 kcal/mol, barrier = 0.5 kcal/mol). A further description of the water force field will be provided elsewhere.22 For the work described here, additional complexes between formic acid and water molecules [(HCOOH
(H2O)n, where n = 1, 2] were included in the optimization. These data points were taken from Aloisio et al.9 The training set was further extended with QM data describing the energy barrier for the protonation of formic acid in the presence of a single water molecule. A single-parameter-based parabolic extrapolation method was used to optimize the force-field parameters against the QM data present in the training set.11 Molecular Dynamics Method. All molecular dynamics (MD) simulations in this study were performed on protonated clusters. An MD-NVT-based anneal simulation method was used to obtain the most stable configuration of each cluster. The velocity Verlet method was used for integrating governing equations of motion. The Berendsen thermostat was employed to control system temperature.23 Each anneal cycle consisted of heating the cluster from 0 K to Tmax in 4 ps, equilibrating the cluster at Tmax for 2 ps, cooling the cluster from Tmax to 0 K in 4 ps, and 4658

dx.doi.org/10.1021/jp1110746 |J. Phys. Chem. A 2011, 115, 4657–4664

The Journal of Physical Chemistry A

ARTICLE

finally equilibrating the cluster again at 0 K for 2 ps, where Tmax represents the maximum temperature. All annealing cycles were simulated with a time step of 0.1 fs and a thermostat coupling constant of 100. Each structure was subjected to 82 such anneal cycles to find the most stable cluster configuration. For water clusters [Hþ(H2O)n] and formic acid
water mixed clusters [Hþ(H2O)n(HCOOH)], a maximum temperature of 160 K was used. For methanol clusters [Hþ(H2O)n(CH3OH)], the maximum temperature used was 110 K. A lower value of maximum temperature was selected for methanol clusters because, at higher temperatures, methanol has the tendency to evaporate from the water cluster because of its weaker binding characteristics.

’ RESULTS AND DISCUSSION Protonated pure-water distributions at cold temperatures, below ∼153 K, display a magic peak at the 21-molecule cluster. Through comparisons of previous experimental studies for methanol in our group and experiments and calculations in the literature, it was shown that methanol reacts with water through a switching reaction mechanism.24,25 Methanol can replace a water molecule in the cluster structure and still retain the magic-cluster characteristics, as evidenced by flow-tube studies and confirmed by more recent IR studies.24,25 The formic acid
water mixed clusters do not retain a similarly shaped cluster distribution compared to that of the pure-water clusters, although it is hypothesized that the formic acid also replaces water molecules within the cluster structure through a switching-like reaction. Previous studies have shown that the formic acid spectrum closely resembles the theoretical spectrum, with a doublehumped shape that is expected in the case of nucleation.6 As was the case for formic acid, methanol undergoes a switching-like reaction with water clusters. Methanol is composed of a polar
OH group that is able to hydrogen bond within the cluster network and a nonpolar
CH3 group that can readily replace a dangling hydrogen.24 Because there are 10 dangling hydrogen bonds, it is believed that up to 10 methanol molecules could replace waters in the cluster without seriously disrupting the stable magic-cluster structure. (Note replacement of waters in the cluster cage by up to nine methanol molecules has been observed.)24 However, in the case of formic acid, there is an ability to form more than one hydrogen bond with the cluster for each individual formic acid molecule. This additional hydrogenbonding capability is believed to disrupt the hydrogen-bonding network. We have suggested that this disruption is sufficient to alter the structure of the protonated 21-molecule cluster and cause it to lose its magic character.6 Neutral-Cluster Calculations. DFT Geometry Calculations. DFT geometry optimization calculations presented in this work were performed on small neutral pure-water, formic acid
water, and methanol
water mixed clusters. These calculations were performed for the neutral clusters for two reasons. First, Aloisio et al.9 used the Gaussian 98 suite of programs, and because the present approach utilizes the Gaussian 03 suite of programs,19 it was critical to ensure that our calculations were comparable to those presented in the prior literature. Second, simulations on the mixed methanol
water cluster system were necessary to compare our experiments to the conclusions of Aloiso et al.9 and to determine whether methanol has a significant impact on the water
water hydrogen bonds in small neutral clusters. Similar calculations were performed in a previous study.26 The values

Figure 1. Calculated bond lengths and angles for a neutral four-water cluster. All four of the water molecules are equivalent in terms of bond angles and bond lengths.

Figure 2. Calculated structure for neutral (H2O)3CH3OH, along with calculated bond lengths and angles. All three of the water molecules are roughly equivalent in terms of bond angles and bond lengths. Addition of a methanol molecule shortens the water
water hydrogen bonds when compared with those in pure water.

we obtained were virtually the same as those reported in the literature.9,26 Comparison of the bond lengths between the clusters reveals that addition of methanol also shortens the water
water hydrogen bonds but to a lesser extent than for the addition of formic acid. Figure 1 shows the O
H bond lengths and H
O
H bond angles of the water molecules contained in the four-molecule clusters. For the pure-water four-molecule cluster, all of the O
H bonds contained in the hydrogen-bonding network of the cluster are consistent; in addition, the O
H bonds that represent the dangling hydrogen bonds are also consistent. A slight stretching of the O
H bonds within the hydrogen-bonding network is seen, corresponding to a slight shortening of the O
H bonds that are not within the network, the dangling O
H 4659

dx.doi.org/10.1021/jp1110746 |J. Phys. Chem. A 2011, 115, 4657–4664

The Journal of Physical Chemistry A

Figure 3. Calculated structure for (H2O)3CHOOH, along with bond lengths and bond angles. The water
water hydrogen-bond lengths are decreased when compared to those in both pure water 4 and the methanol
water mixed cluster. Note that one of the water molecules has a larger bond angle and a shorter O
H bond within the hydrogenbonding network, making it not equivalent to other bonds in the same molecule, which is different from the cases of pure water and methanol
water.

bonds. The lengthening of the bonds within the hydrogenbonding network corresponds to an increase in the size of the H
O
H bond angle, which is shown to be consistent across all four water molecules. Figure 2 shows that the water molecules in the methanol
water four-molecule cluster have characteristics similar to those in the pure-water cluster. All of the O
H bond lengths within the cluster cage are roughly equivalent, and the O
H bond lengths not comprising the cage are also approximately equivalent to one another. The H
O
H bond angles for the methanol
water cluster are significantly smaller than those for the pure-water cluster and are closer to the bond angle of a pure-water monomer, but all three H
O
H bond angles are similar for this cluster. When the bond lengths and bond angles are examined for the formic acid
water cluster containing four molecules in Figure 3, however, the O
H bond lengths in the water hydrogen-bonded to the carbonyl group are found to be noticeably different from those in the other two water molecules. Corresponding to this difference in bond lengths, the H
O
H bond angles are different, with one water molecule being similar to the waters in a pure cluster and one water resembling those observed in the methanol mixed cluster. Taking these values into account, the four waters in the purewater cluster appear to be equivalent in their ability to form new hydrogen bonds and add to the hydrogen-bonding network. In the case of the methanol mixed cluster, the three waters are all equivalent in their ability to form new hydrogen bonds. For the formic acid mixed cluster, two water molecules are roughly equivalent in bond lengths and bond angle, but one water molecule is noticeably different. It is possible that this inequality of the waters produces selective molecules for forming new hydrogen bonds and adding to the cluster hydrogen-bonding network. For instance, the water closest to the carbonyl group on

ARTICLE

the formic acid is donating more hydrogen-bonding strength to the two pairs of free electrons on the oxygen and is thus less likely to donate to another hydrogen bond. It is more likely to accept hydrogen bonding from another water molecule, suggesting that it might have a slight negative character. The two lone pairs on the carbonyl group act as acceptors of hydrogen bonding and could also simply form another hydrogen bond. The third possible selective site arises from the stronger donation of hydrogen bonding by the
OH group of the formic acid to the water closest to it. It can be observed in all of the calculated structures for formic acid that a slight double-bonding character forms between the
OH oxygen and the carbon molecules, which results in an extended bond between that oxygen and hydrogen. As a result, the hydrogen is closer to the water molecule than any of the other hydrogen bonds observed, giving that water a slight H3Oþ character. The donation of positive character has a direct correlation to the slight negative character of the water closest to the carbonyl group, inducing a slight dipole on the neutral water cluster. This dipole produces several additional selective sites for adding waters to the hydrogenbonding network, which could explain why our experimental data show that formic acid
water mixed clusters selectively form larger cluster sizes. Also, the addition of more than one formic acid molecule would increase the number of selective addition sites, causing further growth of large clusters. An induced dipole is not the only way that formic acid can contribute to a higher rate of growth of water clusters. An examination of the four-molecule clusters shows the number of potential hydrogen-bonding sites in each cluster. A pure-water cluster with four molecules will have four dangling hydrogen molecules that can act as four hydrogen-bond donors. In addition for each water molecule, one of the two lone pairs on the oxygen is not involved in the hydrogen-bonding network; these electron pairs can then act as four hydrogen-bond donors. This means the (H2O)4 cluster has eight potential hydrogen-bonding sites. The methanol
water four-molecule cluster shows the same number of bond acceptors, but the
CH3 group takes the place of one of the bond donors, suggesting that a (H2O)3CH3OH cluster has only seven sites for potential hydrogen-bond formation. Formic acid has two oxygen molecules, with only one lone pair occupied in the hydrogen-bonding network of the (H2O)3CHOOH cluster. The formic acid
water mixed cluster has six potential hydrogen-bonding sites from the three waters in the cluster plus three potential hydrogen-bond acceptors from the formic acid, making a total of nine potential hydrogen-bonding sites. This increased number of hydrogen-bonding sites also likely contributes to the increased growth observed in formic acid
water mixed clusters. To better compare these calculations to previous experimental data, we would need to study systems both on a larger scale and also for protonated clusters. However, protonated water clusters of small size, including four-molecule clusters, have a twodimensional structure made up of dangling chains where the neutral clusters form three-dimensional cages at sizes of three molecules and larger. With increasing sizes, the chains observed for protonated clusters begin to form cyclic structures, but a full three-dimensional cage does not form until the 21-molecule cluster. IR experiments have shown these distinct differences in the hydrogen-bonding network of the neutral and ionic clusters at sizes as small as three molecules and as large as 100 molecules.4,5,27 The two-dimensional structures cannot be used to compare the difference in water
water hydrogen bonds in a 4660

dx.doi.org/10.1021/jp1110746 |J. Phys. Chem. A 2011, 115, 4657–4664

The Journal of Physical Chemistry A

ARTICLE

Figure 5. Binding energies per molecule of protonated clusters for pure water, formic acid
water mixed clusters, and methanol
water mixed clusters.

Figure 4. Binding energies of formic acid
water complexes: (a) (H2O)HCOOH, (b) (H2O)2HCOOH, (c) (H2O)3HCOOH.

cage structure for small ionic clusters. To gain more insight into structural changes in the ionic clusters, ReaxFF calculations were performed on ionic clusters of 20
28 molecules, as this method is much less computationally expensive than DFT calculations. Protonated-Cluster Calculations. Force-Field Optimization. The structures of all of the complexes between formic acid and water molecules that were used in the training set can be found in Aloisio et al.9,28 The force field predicts that the Z conformation of formic acid is more stable than the E conformation by 4.007 kcal mol
1, which is in excellent agreement with the experimental result29 of 4.0 kcal mol
1. Parts a and b of Figure 4 show that the trained force-field parameters reproduce the QM results adequately for the energies of the complexes between formic acid and water molecule. The worst agreement is for the FAZ3 complex, for which the force field overestimates the stability. Given the relative instability of the FAZ3 complex, we believe that this discrepancy will not significantly affect the ReaxFF results. With this optimized force field, we computed the binding energies of formic acid complexes with three water molecules. It should be noted that these data points [(H2O)3HCOOH complexes] were not used for optimizing the force field, but instead were used to test the accuracy of the optimized force field. Figure 4c shows that the force-field predictions of binding energies are in excellent agreement with the QM calculations performed by Aloisio et al.9 Molecular Dynamics Simulations. Figure 5 shows the calculated binding energies of the protonated clusters as a function of

Figure 6. Oxygen/hydrogen RDFs of protonated clusters of the forms Hþ(H2O)n, Hþ(H2O)nHCOOH, and Hþ(H2O)nCH3OH, where the total number of molecules in the clusters ranges from 20 to 25 molecules.

cluster size for pure water, methanol
water, and formic acid
water clusters. For all three types of clusters, the binding energy per molecule decreases as the cluster size increases. For water clusters Hþ(H2O)n, the binding energy peaks at n = 21, indicating the existence of a clathrate-like (three-dimensional cage structure) magic cluster. A similar trend is observed for methanol
water mixed clusters, with a peak at n = 21 indicating that the
CH3 group of methanol interacts weakly with other water molecules of the cluster. However, for the formic acid
water mixed clusters, we do not observe any peak in the binding energy at n = 21. The overall binding energies of formic acid
water mixed clusters are considerably higher than those of the other two types of clusters studied. This shows that formic acid 4661

dx.doi.org/10.1021/jp1110746 |J. Phys. Chem. A 2011, 115, 4657–4664

The Journal of Physical Chemistry A

Figure 7. Oxygen/hydrogen RDFs of neutral water clusters compared to the RDFs of protonated water clusters in the size range of 20
25 molecules.

strengthens the hydrogen-bonding network and makes the clusters more stable. This strengthening is likely related to the higher number of potential hydrogen-bonding sites discussed earlier. By increasing the stability of the clusters above the stability of pure water and providing more sites for potential cluster growth, formic acid likely increases the chances of the clusters to nucleate, enhancing the possibility of particle growth. To further compare the large protonated cluster structures to the hypothesis presented by Aloisio et al.9 that formic acid shortens the water
water hydrogen bonds, the radial distribution function (RDF) of the hydrogen
oxygen pair was examined for protonated clusters of various sizes (20, 21, 23, 24, and 25 total molecules) containing formic acid and methanol. For calculating the RDF, the most stable configuration was selected for each type of cluster. It should be noted that the RDF was calculated for the entire cluster and that the contributions from both water and solute molecules were considered in evaluating the function value. In contrast to most nonreactive force fields, ReaxFF does not use atom typing, which means that all hydrogens, irrespective of their bonding environment, are described with the same parameter set. Hydrogen bonding occurs when the H 3 3 3 O separation is around 180 pm, and hence, only that portion of the RDF is shown in Figures 6 and 7. Figure 6 examines the effect of formic acid and methanol on the hydrogen-bonding network present inside the protonated clusters. The RDF distributions of all of the clusters show two peaks in the 1.7
1.9-Å region. The first peak is observed around 1.74 Å, and the second peak is near 1.85 Å. The RDF variations of pure-water and methanol
water mixed clusters are very similar to one another; each of these two RDF calculations shows that the second peak of the two present is predominant. However, for formic acid clusters, the first of the two peaks is more prominent for the clusters containing 20, 21, and 25 molecules. A reverse trend is observed for the [Hþ(H2O)22HCOOH] cluster and the [Hþ(H2O)23HCOOH] cluster, which show a single peak at

ARTICLE

1.85 Å. These results indicate that the presence of formic acid alters the hydrogen-bonding network and reduces the hydrogenbond length in specific configurations. Figure 7 shows the effect that addition of a proton has on the radial distribution function of pure-water clusters by comparing the RDFs of neutral clusters to the RDFs of protonated clusters. The distribution indicates that the presence of a proton slightly reduces the magnitude of the RDFs for Hþ(H2O)20 and Hþ(H2O)21 clusters, making the distributions appear more flat near the 1.8-Å bond length. When compared with neutral clusters, MD results indicate that the presence of the proton does not have any significant effect on the hydrogen-bond length. When the larger protonated clusters are examined closely, it is clear that the pure 21-water cluster has 10 dangling hydrogen bonds. These dangling hydrogen molecules (AAD) along with the ADD water molecules with the lone pairs of the oxygen pointing toward the outside of the cluster mean that this water cluster has a set number of sites for additional hydrogen bonds to form through accepting or donating hydrogen-bonding character. Methanol replaces the dangling hydrogen molecules with a methyl group that is unlikely to form additional hydrogen bonds, decreasing the number of available sites for water molecules to add to the cluster. Formic acid, however, adds additional sites for potential hydrogen-bond formation, increasing the potential of the cluster to add water molecules and grow. This corroborates the findings discussed earlier for the small neutral clusters. From the MD anneal simulations, the most stable configurations were extracted for each type of water cluster. These stable configurations for the clusters containing 21 molecules are shown in Figure 8. The structure of the methanol
water mixed cluster shows that the
CH3 group replaces the dangling hydrogen and remains on the outside of the cluster. On the contrary, formic acid becomes further incorporated into the hydrogen-bonding network by forming multiple hydrogen bonds with the surrounding water molecules and moves inside the cluster. Each molecule replaces an
OH bond from a water; the
CH3 group of methanol does not interact with the cluster structure, whereas the carbonyl group of formic acid forms an additional bond with the cluster structure. This additional bond disrupts the shape and configuration of the cluster from that of a pure-water cluster, thereby affecting its stability. Given the different natures of the formic acid and methanol interactions with the water cluster, we chose to examine the evaporation of molecules from the protonated clusters of 21 molecules. MD simulations provided an estimated temperature at which a molecule would be lost by evaporation from the cluster being studied. Evaporation was considered to have become irreversible when a molecule had moved far enough away from the cluster to be unable to re-form its bonds with the cluster. The methanol molecule evaporated from the methanol
water molecule at ∼160 K. A water molecule evaporated from the purewater cluster at ∼270 K. A water molecule evaporated from the formic acid
water cluster at ∼278 K. Methanol is clearly more weakly bound to the cluster, as it evaporates within a temperature range about 100 K lower than the other two clusters. This weak interaction could explain why methanol
water clusters maintain the hydrogen-bonding network of pure water with little structural change. The difference in evaporation temperature between the pure-water and formic acid
water clusters is within the uncertainty of the MD simulations. However, the fact that a water molecule rather than the formic acid molecule evaporates from the formic acid
water mixed cluster is an important result and 4662

dx.doi.org/10.1021/jp1110746 |J. Phys. Chem. A 2011, 115, 4657–4664

The Journal of Physical Chemistry A

ARTICLE

Figure 8. Most stable structures found for the 21-molecule protonated clusters, including (a) Hþ(H2O)21, (b) Hþ(H2O)20HCOOH, (c) Hþ(H2O)20CH3OH.

shows that formic acid interacts more strongly with the hydrogen-bonding network of the cluster than in the case of pure water.

’ CONCLUSIONS Presented in this work are computational results that have been compared to previous experimental results from a flow-tube apparatus and demonstrate distinct differences in the reaction of formic acid with water when compared to the reaction of methanol with water. Formic acid is a chemical species of interest in the atmosphere and was compared to methanol because the interaction between methanol and water clusters has been wellstudied.24
26 Because the formic acid
water mixed cluster species had very different spectral characteristics, particularly the loss of the magic 21-molecule cluster, DFT and ReaxFF calculations were performed to determine the structural changes caused by the integration of either a methanol molecule or a formic acid molecule into the water cluster. Neutral-Cluster Calculations. We performed DFT calculations on small neutral clusters that were compared to those in the prior literature. Our calculations for pure-water clusters of up to four molecules and water clusters with one formic acid molecule of sizes up to four molecules matched those reported in the literature. We also performed calculations on clusters of the same size with methanol incorporated into the cluster cage. It was determined that, whereas methanol affected the water
water hydrogen-bond lengths in these small neutral clusters to a small degree, this change was not as strong as that seen in the formic acid case. Further, it was hypothesized that formic acid can create a slight dipole in the neutral clusters, causing them to have a slightly positive side and a slightly negative side—both of which could act as selective sites for further addition of water molecules to the cluster. In addition to these selective sites, formic acid has more potential sites for new hydrogen bonds than either water or methanol. Methanol can form hydrogen bonds at the two lone pairs of electrons on the oxygen and at the hydrogen of the O
H group, a total of three potential hydrogen bonds. A water molecule has two O
H groups as well as the two lone pairs, a total of four potential hydrogen bonds. Formic acid, however, has two oxygen molecules and thus four lone pairs of electrons to act as hydrogen-bond acceptors and one O
H group to act as a hydrogen-bond donor, for a total of five sites to form potential hydrogen bonds. The increased number of hydrogen-bonding sites, as well as the selective sites caused by the induced dipole, contribute to the increased growth observed in the flow-tube reactions of formic-acid mixed clusters over pure water and methanol.

Protonated-Cluster Calculations. ReaxFF calculations were used to determine the most stable structures for protonatedcluster systems of pure water, methanol, and formic acid for the range in cluster sizes encompassing the magic 21-molecule cluster. The optimized structures showed that formic acid interacts with the hydrogen-bonding network of the water cluster in multiple places, thus causing a structural change that is not observed with methanol. The ReaxFF calculations showed that, whereas pure water clusters and methanol
water mixed clusters exhibit a peak in binding energy per molecule at 21 molecules, formic acid does not. In addition, the formic acid
water mixed clusters were found to have a higher overall binding energy per molecule, indicating that they are more stable than the other two systems. We conclude that the change to the hydrogen-bonding network caused by the formic acid molecule stabilizes the water clusters, as indicated by the increased binding energy of 15.82 kcal/mol per molecule as compared to 15.12 kcal/mol per molecule for pure water. This increased stability based on binding energy, the increased number of potential sites for hydrogen bonding upon addition of formic acid to the cluster, and the strength of the association of formic acid with the hydrogen-bonding network are all likely to lead to enhanced growth of the water clusters, resulting in nucleation of water molecules at higher temperatures than are seen for pure water and an increased potential for particle growth in the atmosphere.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected].

’ ACKNOWLEDGMENT Financial support from the Atmospheric Sciences Division and the Experimental Physical Chemistry Division of the U.S. National Science Foundation, Grant ATM-0715014, is gratefully acknowledged. ’ REFERENCES (1) Searcy, J. Q.; Fenn, J. B. J. Chem. Phys. 1974, 61, 5282–5289. (2) Nagashima, U.; Shinohara, H.; Nishi, N.; Tanaka, H. J. Chem. Phys. 1986, 84, 209–214. (3) Gilligan, J.; Castleman, A. W., Jr. J. Phys. Chem. A. 2001, 105, 5601–5605. (4) Miyazaki, M.; Fujii, A.; Ebata, T.; Mikami, N. Science 2004, 304, 1134–1137. (5) Shin, J.-W.; Hammer, N.; Diken, E.; Johnson, M.; Walters, R.; Jaeger, T.; Duncan, M.; Christie, R.; Jordan, K. Science 2004, 304, 1137–1140. 4663

dx.doi.org/10.1021/jp1110746 |J. Phys. Chem. A 2011, 115, 4657–4664

The Journal of Physical Chemistry A

ARTICLE

(6) Goken, E. G.; Castleman, A. W., Jr. J. Geophys. Res.-Atmos. 2010, 115, D16203. (7) Castleman, A. W., Jr.; Holland, P.; Keesee, R. J. Chem. Phys. 1978, 68, 1760–1764. (8) Zhang, X.; Mereand, E.; Castleman, A. W., Jr. J. Phys. Chem. 1994, 98, 3554–3557. (9) Aloisio, S.; Hintze, P.; Vaida, V. J. Phys. Chem. 2002, 106, 363–370. (10) Nadykto, A.; Yu, F. Chem. Phys. Let. 2007, 435, 14–18. (11) van Duin, A. C. T.; Dasgupta, S.; Lorant, F.; Goddard, W. A., III. J. Phys. Chem. A 2001, 105, 9396–9409. (12) van Duin, A. C. T.; Strachen, A.; Stewman, S.; Zhang, Q.; Xu, X.; Goddard, W. A., III. J. Phys. Chem. A 2003, 107, 3803–3811. (13) Chenoweth, K.; van Duin, A. C. T.; Goddard, W. A., III. J. Phys Chem. A 2008, 112, 1040–1053. (14) Chenoweth, K.; van Duin, A. C. T.; Persson, P.; Cheng, M. J.; Oxgaard, J.; Goddard, W. A., III. J. Phys. Chem. C 2008, 112, 14645–14654. (15) Cheung, S.; Deng, W.; van Duin, A. C. T.; Goddard, W. A., III. J. Phys. Chem. A 2005, 109, 851–859. (16) J€arvi, T. T.; Kuronen, A.; Hakala, M.; Nordlund, K.; van Duin, A. C. T.; Goddard, W. A., III; Jacob, T. Eur. J. Phys. B 2008, 66 (1), 75–79. (17) Nielson, K. D.; van Duin, A. C. T.; Oxgaard, J.; Deng, W. Q.; Goddard, W. A., III. J. Phys. Chem. A 2005, 109, 493–499. (18) Ojwang, J. G. O.; van Santen, R.; Kramer, G. J.; van Duin, A. C. T.; Goddard, W. A., III. J. Chem. Phys. 2008, 129, 244506. (19) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Montgomery, J. A., Jr.; Vreven, T.; Kudin, K. N.; Burant, J. C.; Millam, J. M.; Iyengar, S. S.; Tomasi, J.; Barone, V.; Mennucci, B.; Cossi, M.; Scalmani, G.; Rega, N.; Petersson, G. A.; Nakatsuji, H.; Hada, M.; Ehara, M.; Toyota, K.; Fukuda, R.; Hasegawa, J.; Ishida, M.; Nakajima, T.; Honda, Y.; Kitao, O.; Nakai, H.; Klene, M.; Li, X.; Knox, J. E.; Hratchian, H. P.; Cross, J. B.; Bakken, V.; Adamo, C.; Jaramillo, J.; Gomperts, R.; Stratmann, R. E.; Yazyev, O.; Austin, A. J.; Cammi, R.; Pomelli, C.; Ochterski, J. W.; Ayala, P. Y.; Morokuma, K.; Voth, G. A.; Salvador, P.; Dannenberg, J. J.; Zakrzewski, V. G.; Dapprich, S.; Daniels, A. D.; Strain, M. C.; Farkas, O.; Malick, D. K.; Rabuck, A. D.; Raghavachari, K.; Foresman, J. B.; Ortiz, J. V.; Cui, Q.; Baboul, A. G.; Clifford, S.; Cioslowski, J.; Stefanov, B. B.; Liu, G.; Liashenko, A.; Piskorz, P.; Komaromi, I.; Martin, R. L.; Fox, D. J.; Keith, T.; Al-Laham, M. A.; Peng, C. Y.; Nanayakkara, A.; Challacombe, M.; Gill, P. M. W.; Johnson, B.; Chen, W.; Wong, M. W.; Gonzalez, C.; Pople, J. A. Gaussian 03, revision C.02; Gaussian, Inc.: Wallingford, CT, 2004. (20) Xu, X.; Goddard, W. A. , III. Proc. Natl. Acad. Sci. U.S.A. 2004, 101, 2673–2677. (21) Svozil, D.; Jungwirth, P. J. Phys. Chem. A 2006, 110, 9194–9199. (22) van Duin, A. C. T.; Bryantsev, V.; Su, J.; Goddard, W. A., manuscript in progress. (23) Berendsen, H. J. C.; Postma, J. P. M.; Van Gunsteren, W. F.; Dinola, A.; Haak, J. R. J. Chem. Phys. 1984, 81, 3684–3690. (24) Suhara, K.; Fujii, A.; Mizuse, K.; Mikami, N.; Kuo, J. J. Chem. Phys. 2007, 126, 194306. (25) Zhang, X.; Castleman, A. W., Jr. J. Chem. Phys. 1994, 101, 1157–1164. (26) van Erp, T. S.; Meijer, E. J. Chem. Phys. Let. 2001, 333, 290–296. (27) Mizuse, K.; Fujii, A.; Mikami, N. J. Chem. Phys. 2007, 126, 231101. (28) Rablen, P. R.; Lockman, J. W.; Jorgensen, W. L. J. Phys. Chem. A 1998, 102, 3782–3797. (29) Hurtmans, D.; Herregodts, F.; Herman, M.; Lievin, J.; Campargue, A.; Garnache, A.; Kachanov, A. A. J. Chem. Phys. 2000, 113, 1535–1545.

4664

dx.doi.org/10.1021/jp1110746 |J. Phys. Chem. A 2011, 115, 4657–4664