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Energetics, Thermodynamics and Hydrogen Bonding Diversity in Ammonium Halide Clusters John J. Biswakarma, Vlad Ciocoi, and Robert Q. Topper J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.6b06788 • Publication Date (Web): 22 Sep 2016 Downloaded from http://pubs.acs.org on September 26, 2016

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The Journal of Physical Chemistry

Submitted to Journal of Physical Chemistry A

Energetics, Thermodynamics and Hydrogen Bonding Diversity in Ammonium Halide Clusters John J. Biswakarma, Vlad Ciocoi and Robert Q. Topper* Department of Chemistry, The Cooper Union for the Advancement of Science and Art, 41 Cooper Square, New York NY 10003 USA.

* Corresponding author. Phone (212) 353-4378; fax (212) 353-4341; email: [email protected].

Abstract Contributions from different intermolecular and interionic forces, as well as variations in bond energies, produce size-dependent variations in the structures of acid-base molecular clusters. In this work the structures and interaction energetics of cluster particles with the nominal formulas (NH4X)n , X=(F, Cl, Br) are predicted using either “mag-walking” sawtooth simulated annealing Monte Carlo calculations or model building, followed by M06-2X or RI-MP2 geometry optimization and single-point energy calculations. Whereas the n=1 clusters all exhibit a single hydrogen bond, small (NH4F)n particles (n=2-5) exhibit three distinct types of hydrogen bonds as a function of size (traditional, ion-pair and proton-shared). However, (NH4Br)n and (NH4Cl)n particles (n=2-13) all solely exhibit ion-pair hydrogen bonding, with even values of n exhibiting pronounced relative stability. The computed differential interaction energy of the bromide and chloride systems is generally near the bulk limit of the difference in their accepted lattice energies, despite the fact that their structures do not resemble the bulk crystal structures. Nanoparticle growth reactions are predicted to be thermodynamically spontaneous under standard conditions, with significant size and system dependencies. This work is designed to further our understanding of the nature of hydrogen bonding and other intermolecular forces, particularly within ionic nanocrystallites, as well as the thermodynamics of cluster formation.

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Introduction Airborne particles of ammonium chloride can form as the result of atmospheric processes, particularly in polluted marine environments. 1-8 Chlorides are found throughout the troposphere (generated by natural and anthropogenic sources), and can react with atmospheric nitric and sulfuric acids generated by NOx/SOx pollution to generate HCl (g). The reaction of hydrogen chloride with atmospheric ammonia, which arises from both natural sources (such as bogs, swamps, seaweed and other decaying matter) and anthropogenic sources (including agriculture / livestock activity and landfills) produces ammonium chloride.5 Among other concerns, ammonium and sodium chlorides accelerate the corrosion of zinc, which itself is used for corrosion inhibition.9 At high concentrations and low relative humidity a dispersion of crystalline NH4Cl(s) particles is produced when NH3 (g) and HCl (g) are combined at room temperature.10,11 Conversely, under rarified conditions the formation of a hydrogen-bonded NH3…HCl monomer cluster is observed without proton transfer, connected by a hydrogen bond.12 At intermediate concentrations, the possible formation of airborne particles of the form (NH4Cl)n must also be considered.1,13,14 The physical properties of ammonium halide clusters are also of fundamental interest. Previous studies have predicted that the structures of neutral, cation and anion ammonium chloride clusters are noticeably different than the structure of the bulk phase.13-16 A single water molecule, or even a single electron, halide, ammonium, ammonia, or haloacid is sufficient to catalyze proton transfer in ammonium chloride.17-23 Some unanswered questions to date include: (1) How large do these clusters have to be before their properties resemble those of the bulk solid phase? In our laboratory, previous work on (NH4Cl)n indicated that even n=13 is too small for the ammonium chlorides to converge to the bulk CsCl structure motif.13 However, the CsCl motif was recently predicted to describe much larger ammonium halide nanoparticles when solubilized in a mixture of water and organic matter under certain conditions.14 (2) How do the structures and properties of ammonium halide clusters (NH4X)n vary as the identity of X varies? (3) What size distribution is expected when clusters of the ammonium halides form from ammonia and the haloacid under dry conditions? (4) When aerosolized particles are formed from different reactants than those found in the environment (NH4+ and Cl- instead of NH3 and HCl), 2


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what is the size distribution? This last situation was addressed experimentally by Röllgren and coworkers through the use of thermospray mass spectrometry of NH4+(NH4Cl)n particles24,25 and

was shown to be dominated by n=(1,3,5,6,13), a finding which correlated well with subsequent M06-2X calculations.13 On the other hand, when the reactants are the neutral NH3 and HCl molecules in low concentrations, (NH4Cl)n particles with (n=4,6,8) should predominate.13,23 Given the progress made in characterizing the structures and behaviors of ammonium chloride clusters, our attention is now given to the formation of ammonium fluoride and bromide clusters, which are the main focus of the present work. The broad nature of hydrogen bonding within small inorganic clusters has been the subject of numerous investigations. In this context, Del Bene26 surveyed the literature and found evidence throughout the literature for three kinds of hydrogen bonding interactions in gas-phase hydrogen bonded species: “traditional”, “ion-pair” and “proton-shared.” In this point of view, a traditional hydrogen bond has the form X – H …Y, with the X—H bond only slightly different than that of the isolated X-H species; an ion-pair hydrogen bond resembles X- … +H—Y with the X-Y distance similar to a traditional hydrogen bond but the H-Y distance similar to that of the (HY)+ cation, and a proton-shared hydrogen bond resembles X … H … Y, characterized by a short X-Y distance. In the case of NH3 --- HCl, the hydrogen bonding can be described as traditional, whereas in the case of (NH4Cl)n (n>1) hydrogen bonding is of the ion-pair type.13,15,16,23 Previous theoretical and experimental studies of NH3 --- HBr and NH3 --- HF indicated that they also exhibit traditional hydrogen bonding.27-32 The phase properties of the solid ammonium halides have been studied extensively, and are determined both by Coulombic and ion-pair hydrogen bonding interactions.33 In this work we compare previous structural and energetic predictions for (NH4Cl)n (n>1) to new predictions for (NH4F)n and (NH4Br)n (n>1), examine their structural trends and sizedependent energy variations, and observe to what extent these three kinds of hydrogen bonds are present. In the present work we generally refer to “traditional” hydrogen bonds simply as hydrogen bonds, without modification, while employing the ion-pair and proton-shared descriptions where appropriate. We also compare the asymptotic interaction energies of (NH4Cl)n and (NH4Br)n in order to assess how well the models and methods employed are 3



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describing the average intermolecular forces, as represented by the lattice energies of NH4Cl (s) and NH4Br (s). Finally, we examine trends in the reaction energetics and thermodynamics for homogenous nucleation of these clusters from ammonia and the haloacids. Methods In principle, an individual cluster system can be assembled to form a myriad of minimum-energy structures, and generally only one structure is the global miniumum.34,35 In order to address this complexity, simulated annealing Monte Carlo methods were used to find the lowest minimum-energy structures of (NH4Br)n (n=2-13) particles. A “sawtooth” simulated annealing “mag-walk” Monte Carlo method employing both single-particle moves and BarkerWatts molecular rotation moves was used to generate minimum-energy structures for each particle size.36-39 Mag-walking allows the Monte Carlo algorithm to occasionally fluctuate between structures which are separated by energy barriers. This is achieved by randomly choosing to allow a fluctuation to rotate a molecule by an unusually large rotational angle, or to allow atoms or molecules to translate further apart or closer together than would typically be probable at the simulation temperature.13,34,38 Simulated annealing refers to varying the simulation temperature slowly from a high value to 0K in order to “quench” the system into its lowest energy structure. However, a simulated annealing calculation can sometimes result in a structure which is not the one lowest in energy. To address this, the temperature is varied in a manner that is designed to allow the system to escape this local energy minimum and find other structures which are lower in energy. The particular strategy we used is known as “sawtooth” simulated annealing.39 The temperature varies according to a predetermined sequence, linearly cooling the system each time with successively smaller and smaller uppermost temperatures (and slower cooling rates) within each sawtooth. Here we refer to the combination of mag-walking at each fixed temperature with a sawtooth simulated annealing schedule of temperature variation as the MW-SSA method. In our experience this method is a highly ergodic and computationally efficient method for molecular cluster systems.10 The critical simulation parameters for simulated annealing include the number of translational and rotational move cycles per temperature as well as the number of temperatures and the uppermost temperature. These were varied in order to generate diverse sets of low-lying 4


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minimum-energy structures for each cluster size. For each cluster size, ten teeth in the magwalking algorithm were used with twenty temperatures per tooth, and the initial temperature of each simulation was 10000K with the uppermost temperature of each tooth equal to 0.8 of the uppermost value of the previous tooth. At each temperature, the simulation length was on the order of 105 Monte Carlo iterations. For each cluster size of ammonium bromide, the set of structures predicted by MW-SSA simulations using different simulation parameters were analyzed with quantum calculations. It must be emphasized that the simulation parameters were chosen in a manner intended to generate a reasonable diversity of quenched minimum-energy structures for subsequent quantum mechanics calculations, and not solely for the purpose of finding the global minimum-energy structure. The interaction potential energy model used in the MW-SSA calculations was the same type as the one used in previous work on ammonium chloride clusters.13 In this model, interaction energy functions are used to model the van der Waals interactions between each possible pair of atoms between different atoms and molecules within the cluster. In each MWSSA run, the ammonium ions were held rigid. Relaxing this condition and allowing the ammonium to be distorted within an internal harmonic force field was previously shown to have only a small quantitative effect on the structures and energies of the annealed clusters for the ammonium chloride system15 and it is assumed here that similar behavior is exhibited for the ammonium bromide system. During subsequent quantum-mechanical calculations, all atoms were allowed to move and relax according to the computed potential energy surfaces thus generated. Direct quantum-mechanical calculation of the cluster energy during the Monte Carlo calculations is impractical for cluster systems of the size range considered here, especially the larger systems. Following previous work 13,40 the interaction energy function V is assumed to be a pairwise additive function of the distances rij between atoms i and j, and has the form

q q D C  V = ∑∑  i j + Aij exp ( −αij rij ) + 12ij − 6ij  rij rij  i j >i   rij

5


(1)


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The sum is over all distinct interactions between atoms, but interactions within a particular rigid NH4+ molecule are excluded. The first term represents attractive and repulsive Coulombic interactions between atomic partial charges (qi) on the NH4+ molecules and the bromide anions, as well as repulsive interactions between bromide ions. The partial and atomic ion charges used were qH = 0.35, qN = -0.4, and qBr = -1.0 atomic units. The second and third terms and parameters are chosen to represent contributions to the energy due to repulsive interactions between atoms at short and intermediate range, while the final term models contributions due to attractive dispersion forces at intermediate to long range. The parameters for the H-H, N-N and H-N interactions are assumed to be the same as those used in previous work13 except for the Dij parameters, which were further adjusted to prevent divergences of the potential energy to (−∞) at very small interparticle distances while leaving the potential in the interaction region unchanged. The N-Br, Br-Br and H-Br parameters are the same as those used in previous work on NH4Br(s) by Klein et al.40 except for the Dij parameters, which they set equal to zero. For our purposes, these parameters need to be finite and large enough to prevent divergences towards (−∞) while not adding repulsive character to the interaction. The DNBr parameter was determined in the same manner as the H-H, N-N and H-N interactions, i.e., by choosing a value large enough to remove all divergence behavior while leaving the physically accessed interaction region unchanged. DBrBr was calculated using Lennard-Jones parameters presented by Mao and Pappu41. DHBr was determined by initially setting CHBr and DHBr to zero, then solving for the distance at which the modified interaction energy is zero (the “collision radius”), and then setting CHBr back to its original value and increasing DHBr until the distance at which the interaction energy is zero was equivalent to the collision radius found before. All potential parameters used in the present work are summarized in Table S1 of the Supplementary Material for this article. The interaction energy model just described was not used in the study of ammonium fluoride clusters, because it assumes that the particles are made completely of ionic particles. Trial calculations on small particles of (NH4F)n revealed that HF is too weak an acid for the n>1 clusters to consist solely of ionic particles. Therefore, in the case of (NH4F)n clusters (n=2-5), a variety of structures were built and examined individually by subsequent quantum-mechanics 6


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calculations as described in the next section, starting either from (NH4Br)n / (NH4Cl)n structures but with F substituting all Br/Cl atoms, or from a variety of plausible arrangements for combinations of NH3 / HF and/or NH4+/F- pairs. In the MW-SSA simulations, the temperatures are sometimes sufficiently high that individual ions could evaporate from the system during the annealing schedule. Because this study does not focus on characterizing evaporative processes, a constraint potential that is only measurable when ions move too far away from the center of the cluster is added to the interaction potential.42 The constraint potential ensures that molecules cannot evaporate from the cluster at the initial, unphysically high temperatures of the simulated annealing calculations, but is vanishingly small near the center of mass so that it has no effect on the cluster structures. The constraint potential used in the present work is N

VC ( ri ) = κ ∑ i =1

(

r ur r i − R cm RC

)

20

(2)

where N = the number of ions, Rcm is the vector locating the center of mas of the cluster, ri is a vector locating the center of mass of each ion, RC is a radial scaling parameter (which ranged from 15.0 to 30.0 Bohr depending on the size of the cluster), and κ is an arbitrary constant with units of energy (κ = 1 Hartree in the calculations presented here).

The quantum-mechanical calculations presented here were variously completed using Gaussian 09,43 Q-Chem44 and SPARTAN 14.45 All calculations pertaining to ammonium fluoride clusters were performed at the RI-MP2/aug-cc-pVTZ level of theory.46-48 This method and basis set combination was used in part because previous calculations of the NH3 --- HF system at the MP2/aug-cc-pVDZ level of theory showed good agreement with experiment.31 Kawahara et al. showed that MP2/aug-cc-pVTZ calculations of the (F-H-F)− system geometry and binding energy agree well with both experiment and QCISD(T)/aug-cc-pVQZ calculations.49 The structures were subjected to frequency calculations following geometry optimization to ensure that they corresponded to minimum-energy structures. In the case of the ammonium bromide and chloride clusters, a different strategy was employed. Following each simulated annealing run, the minimum-energy structures of each 7



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(NH4Br)n cluster were subjected to quantum-mechanical geometry optimization and frequency calculations using the B3LYP50,51 or M06-2X52,53 density functional theory methods. Previous work on ammonium chloride clusters showed that the M06-2X method gave reliable predictions of geometries and energetics when n>1, but that B3LYP performed somewhat less well.13 Numerical integrations within the density functional calculations were carried out using an EML(128,302) grid.54 The results of various calculations for the monomer, dimer and tetramer cluster systems were compared to the results of certain individual calculations that were considered as benchmark values, as well as the limited experimental data which was available. Specifically, the gas-phase NH3---HBr monomer is the only ammonium bromide cluster system for which experimental27 and theoretical55,56 values are available in the literature. Some of this data is summarized in Table 1, as well as selected additional calculations we have carried out using the RI-MP2, B3LYP and M06-2X methods. Overall, for the monomer cluster geometry optimizations at the RI-MP2 level produced good agreement with both experiment and CCSD calculations from this and previous work. The density functionals tested here did slightly less well; this behavior was previously noted for the NH3---HCl system.13 In addition, the lowest energy (NH4Br)2 structure predicted by MW-SSA simulations was refined with equilibrium geometry calculations using various functionals, basis sets, and calculation settings in order to determine which would be sufficient for accurately describing ammonium bromide cluster structures. The results are shown in Table 2. As in previous work,13 the N---Br distance attained from CCSD/6-311++G(2df,2p) geometry optimization calculation was used as a benchmark. It was observed that M06-2X/6-31G(d,p) equilibrium geometry calculations generated an average N---Br distance of 3.180 Å, which agrees well with the average N---Br distance predicted by the CCSD calculation (3.186 Å). This behavior is also similar to that previously observed for (NH4Cl)2 .13 The cubic (NH4Br)4 cluster, which is also composed of fully ionized particles, was also refined with equilibrium geometry calculations using various functionals and basis sets. Here the N---Br distance obtained from RI-MP2/6-311++G(2df,2p) geometry optimization calculation was used as a benchmark. Once again, M06-2X/6-31G(d,p) calculations predicted accurate structures of the ammonium bromide dimer cluster, agreeing with the average N-Br bond length 8


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predicted by the RI-MP2 calculations to within less than 0.3% (see Table 2). The M06-2X/631G(d,p) theoretical level was therefore chosen for all of the equilibrium geometry calculations presented here for the bromides and chlorides. The M06-2X/6-311++G(2df,2p) level was chosen for all subsequent single-point energy calculations, because energy calculations are inherently more sensitive to the size of the basis set. These are the same levels of theory used in previous work on ammonium chloride clusters.13 As discussed in the Results, calculations of the changes in cluster interaction energy using this method agree well with confirmatory calculations at the CCSD(T)/aug-cc-pVTZ//M06-2X/6-31G(d,p) level of theory.

Using the pair potential parameters described previously, MW-SSA calculations were used to generate minimum-energy structures for each cluster size. To minimize the amount of time spent running quantum calculations, a winnowing strategy was used to reduce the number of computations performed. First, structures deviating by less than 40kJ/mol from the lowest energy structure determined by the MW-SSA simulations were chosen for single-point energy calculations. For clusters of size less than n=10, M06-2X/6-31G(d,p) single-point energy calculation were performed for the structures chosen from the MW-SSA simulations. The exception to this is the pentamer cluster, for which M06-2X/6-311++G(2df,2p) single-point energy calculations were used because it was found that there was some sensitivity to the basis set and grid density used in this one case. For clusters of size 10 ≤ n ≤ 12 the 6-311++G(2df,2p) basis was used for the single-point energy calculations. This was done because it was suspected that these systems would be more sensitive to the size of the basis set, and also because there was a greater number of possible structures that were close in energy; it was presumed that a more diffuse and polarized basis set would lead to more well-defined differences between the energies of the trial structures in question. For n=13, 6-31G(d,p) single-point energy calculations were used to analyze and rank the multiple structures obtained from the MW-SSA simulations. Next, only those structures deviating by less than 10kJ/mol from the lowest energy structure determined from these single-point energy calculations were chosen for the final geometry optimization calculations (M06-2X/6-31G(d,p)) and subsequent single-point energy calculations (M06-2X/6-311++G(2df,2p)). Some structures were arbitrarily chosen for further analysis for further examination, even if they were not energetically favorable. Changes in relative energy 9



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less than 20 kJ/mol occurred for individual structures when subjecting them to M06-2X/631G(d,p) single-point energy calculations. However, changes in relative energy associated with increasing the size of the basis set (changing from 6-31G(d,p) to 6-311++G(2df,2p)) were at most 7 kJ/mol. Normal mode frequency and moment of inertia calculations were carried out at the M062X/6-31G(d,p) level for all of the chloride and bromide clusters reported here. These calculations were used to predict enthalpies, entropies and Gibbs free energies of reaction for the growth of chloride and bromide clusters, as described in the next section.

Results and Discussion For n=1, all three system types consist of an ammonia molecule and an HX molecule, i.e., (NH3)(HX). These systems all exhibit a single hydrogen bond, with H-X distances similar to those of the isolated HX molecules. The structures of the clusters for (NH4Br)n , n=2-13 obtained from simulated annealing and subsequent density functional theory calculations are shown in Figure 1. In many cases these structures are similar to those previously identified for (NH4Cl)n . However, there are also significant differences when n = (7,10,11). The n=7 bromide cluster is a clathrate-like cage structure, whereas in previous work13 it was found that the n=7 chloride cluster resembles a distorted n=6 cluster with an edge-attached ion pair. When n=10, the chloride cluster resembles n=8 with two ion pairs attached, whereas the n=10 bromide cluster is again a clathrate-like cage structure. Finally, the n=11 chloride cluster is planar but somewhat stellate in character, whereas n=11 bromide resembles the n=9 cluster but with an edge-attached ion pair. Although the bromide and chloride clusters are similar to one another for n < 7, there are significant differences between the fluoride clusters and those formed from the other halides when n > 1. The n=2 chloride and bromide clusters consist of two ammonium molecules and two halide anions (NH4X)2, with two ion-pair hydrogen bonds. However, the n=2 fluoride cluster consists of two ammonia and HF molecules, i.e., (NH3)2(HF)2, with two hydrogen bonds and no protons transferred from the relatively weak acid molecules (HF) to ammonia (Figure 2). This is reflected in the fact that the dimer H---F distance from RI-MP2 calculations (0.997 Å) is only 8.1% larger than the computed H----F distance for isolated hydrogen fluoride (0.922 Å) and just 10


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4.1% larger than the H---F distance within the n=1 monomer cluster (0.958 Å). Table 3 contains a summary of critical atom-atom distances for the ammonium fluoride cluster systems. The n=3 fluoride cluster is particularly unusual (Figure 3) in that it consists of two NH3 and HF molecules connected by hydrogen bonds (rHF =1.024 Å) and a pair of species wedged between them which exhibits a proton-shared hydrogen bond with rHF =1.309 Å, i.e., [(NH3…HF)2(H3N…H…F)]. It is important to emphasize that this is structure is truly an energy minimum, verified by vibrational frequency calculations; in fact, the lowest frequency vibration does not involve any proton transfer coordinates. In contrast, within the n=3 chloride and bromide clusters all three pairs of molecules exhibit complete proton transfer to form completely ionic structures, to which the fluoride cluster is otherwise similar in geometry. It should also be noted that in the fluoride clusters, rHF increases with n even when the proton has not yet transferred. This signifies a gradual size-dependent increase in competition between the energy cost of breaking the covalent H-F bond with the energy lowering which could be obtained by the attractive ion-ion interactions which accompany proton transfer. When n=4, all three system types (F,Cl,Br) form distorted cubes consisting of protontransferred ion pairs, (NH4X)4 , linked by ion-pair hydrogen bonds. The tetramer fluoride cluster has rHF = 1.591 Å (Figure 3), which is significantly larger than the anomalous proton-shared bond in the trimer. The computed N---F distance (2.612 Å) is similar to the experimental value for the wurtzite form of solid NH4F (2.66 Å57). The n=5 chloride and bromide clusters are also similar to one another (forming small clathrate-like cage structures). However, the n=5 pentamer fluoride cluster (Figure 3) consists of a distorted cube of proton-transferred ion pairs with a hydrogen bonded NH3-HF pair attached to one edge of the cube, i.e., (NH4F)4(NH3…HF). This structure is 23.7 kJ/mole lower in energy at the RI-MP2/aug-cc-pVTZ level of theory than the minimum-energy geometry corresponding to the lowest-energy structure adopted by the X=Cl,Br clusters (in which all five protons are transferred) with F substituted for (Br,Cl). Clearly, the fluoride clusters exhibit a rich diversity of hydrogen bonding situations. Moreover, a larger number of acid-base pairs is required for these systems to be near the bulk limit than for the chloride and bromide systems, all three of which consist solely of ion pairs in the solid phase. 11



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The variations in the different types of hydrogen bonding in the fluoride clusters can be effectively visualized by examination of the highest occupied molecular orbital with sigma character (σ-HOMO) for each system. Following Rundle58 and Pimentel59, if we consider a hydrogen bond as a 3-center, 4-electron bond, a perfectly symmetric hydrogen bond would be expected to exhibit a symmetric σ-HOMO with nonbonding character, as would an ion-pair hydrogen bond. However, an asymmetric hydrogen bond would yield pronounced amplitude in the σ-HOMO on the less electronegative species.49,60,61 To examine these predictions more closely, the HOMOs for all five fluoride systems are displayed in Figures 4 and 5. As expected, in Figure 4 we see that for n=1 and 2 the HOMO has pronounced amplitude on the ammonia molecules, as well as for the two exterior hydrogen-bonded species in the case of n=3. However, the interior proton-shared pair exhibits a nearly symmetric σ-HOMO amplitude between the two species. Figure 5 shows that the n=4 species, which exhibits ion-pair hydrogen bonding, displays a σ-HOMO with nonbonding character as expected, whereas the n=5 species orbital shows the character expected of an asymmetric hydrogen bond between the two edge-attached species. One property of particular interest is the cluster’s ionic interaction energy (Vn0), which refers to the difference in electronic energies between the products and reactants of the following reaction: n NH4+ + n X− (NH4X)n

(R1)

This quantity can be calculated for all three clusters types, but since it is only meaningfully called an “interaction energy” when the cluster consists solely of interacting cations and ions, we only considered X=(Cl,Br). The interaction energies for (NH4Cl)n were presented in previous work13 but have been recalculated here using the same basis sets and methods and employing the EML-(128,302) numerical integration grid, which has a small (< 2 kJ/mole) effect on the interaction energy. These energies are presented for (NH4Br)n and (NH4Cl)n in Table 4. In principle, as n becomes sufficiently large the structure should converge to that of a bulk particle, and the magnitude of the interaction energy per ion pair should approach the lattice energy of solid NH4X. 12


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The currently accepted lattice energies of NH4Br(s) and NH4Cl(s) at 0K are respectively 665 kJ/mol and 698 kJ/mol.62,63 In terms of these energies, we see that even n=13 is not large enough for the interaction energy to correspond well to the bulk limit for either system type. Examining the cluster structures, we see that although the structure of bulk ammonium bromide is the CsCl motif, the large-n structures discovered in the particles most resembles the NaCl motif. However, we do see that the interaction energy per ion pair is consistently larger for (NH4Cl)n than for (NH4Br)n. Moreover, as shown in Figure 6 the difference in interaction energy per ion pair between the chloride and bromide clusters quickly approaches the difference in the experimentally determined lattice energies (-33 kJ/mole). In fact many of the individual differences are quite close to -33 kJ/mole, with prominent exceptions at n = (1, 7). In the case of n = 1, the system consists of a van der Waals-bonded molecule between NH3 and HBr with no proton transfer, and so we expect the interaction energy to be very different from the bulk limit. The large deviation from the bulk limit at n = 7 may be attributed to the fact that the structures of the chloride and bromide systems are qualitatively dissimilar.

The interaction energies were further analyzed by computing difference in energy between subsequent cluster sizes, ∆Vn, which is defined as ∆Vn = Vn-1 – Vn . Peaks in a plot of ∆Vn as a function of n indicate cluster sizes which are relatively stable towards the addition of an ion pair, which tends to correlate with the distribution of particles formed from ionic reactants. This same method of analysis was used to successfully interpret the observed peaks and trends in the electrospray mass spectrum of [(NH4Cl)nNH4+] in previous work.13 Figure 7 shows peaks at even values of n for both the bromide and chloride systems, indicating that these are energetically favored over odd values of n. We see that for the chloride clusters the greatest relative stability is observed at n=4; however, for the bromides although n=4 is relatively stable, n=6 and n=8 are similar in stability to n=4. This may simply be attributable to a larger dispersion interaction between ammonium and bromide than between ammonium and chloride which is better optimized in the even-numbered species. All three of the structures are structurally similar to one another for both the bromide and chloride clusters, and can be thought of as adding two or four ion pairs to the top of the n=4 cube. 13



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Page 14 of 37

In order to further assess the accuracy of the ∆Vn predictions, additional calculations at the CCSD(T)/aug-cc-pVTZ//M06-2X/6-31G(d,p ) level were carried out for the n=1-3 ammonium bromide clusters.64 These calculations yielded ∆V1 = 0.2486 Hartree (+0.4% higher than M06-2X, for which ∆V1 = 0.2476) and ∆V2 = 0.2341 (-0.3% lower than the M06-2X prediction of 0.2347)..The quality of these results is consistent with work by Herb et al.65 in which they used single-point CCSD(T) calculations to assess the quality of PW91 density functional theory calculations for ammonium hydrogen sulfate clusters. Mardirossian and HeadGordon66 recently considered the performance of 14 of the “Minnesota” functionals and verified that the M06-2X functional generally performs well for the description of the energetics of intermolecular forces.

The thermodynamics of the formation of the clusters via the addition of molecular reactants to sequentially form each product cluster, represented by the reaction R2, was analyzed:

(NH4X)n-1 (g) + NH3 (g) + HX (g) (NH4X)n (g) .

(R2)

Reaction R2 might be expected to describe cluster formation under conditions of low concentration and relative humidity. This reaction is different than the one considered by Tao and coworkers, in which they considered the energetics of neutral molecule addition before proton transfer occurs.23 Conversely, the formation of ammonium halide clusters under conditions of high concentrations (but still low humidity) might also be described by

n NH3 (g) + n HX (g) (NH4X)n (g) .

(R3)

For purposes of comparison, similar reactions were considered in a theoretical study of water nucleation by Shields and coworkers.67 In that work, the nucleation reaction analogous to R2 (H2O + (H2O)n-1 (H2O)n) underwent a transition from endergonic to exergonic behavior as the temperature decreased from the standard value, with standard reaction enthalpies ranging from 14


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-12.5 to -56.8 kJ/mol as a function of n.67,68 In the present work the computed enthalpy, entropy and free energy of reactions R2 and R3 for selected X=(Cl,Br) clusters at (298.15K, 1 atm) are provided in Table 5, and Figures 8 and 9 display the standard Gibbs free energy of these reactions as a function of n. Both reactions are strongly exothermic. For example, ∆H for reaction R2 (X=Cl) ranges between -100 and -200 kJ/mol. For reaction R2, the Gibbs free energy plots show clear variation as a function of n for both systems, with strongly exergonic values at even values of n, even at the standard temperature. Overall this behavior is primarily driven by the relatively large enthalpies of reaction which are large enough to offset the increases in the entropy terms which occur as n increases. In the case of R3, although there is some weak size variation the general trend is a marked decrease of the Gibbs free energy as a function of n. Despite the large decreases in the entropy of reaction for each successive n, the increase in the magnitude of the reaction enthalpy more than offsets this effect. These results are consistent with the fact that small clusters can stabilize at room temperature when the initial concentrations are low, but crystalline dispersions are observed when they are high.11,19

Conclusions A study of the periodic variation of the halides in cluster systems of the type (NH4X)n has revealed complex and interesting structures, particularly in the examination of the size-dependent properties of ammonium fluoride clusters. The competition between intramolecular and intermolecular forces as a function of cluster size reveals that at certain critical sizes, the energy cost of proton transfer between ammonia and the hydrogen halides and the energy stabilization gained by the formation of hydrogen bonds must compete with the stabilization gained by the interactions between component ions formed by proton transfer, which are dominated by Coulombic interactions and ion-pair hydrogen bonds. For clusters formed from the combination of ammonia with the strong haloacids (HCl, HBr), proton transfer occurs completely when n>1. In the case of ammonium chloride, the addition of a single NH4+ or a single Cl- is enough to catalyze proton transfer,13 as is a single molecule of NH3 or HCl.23 In marked contrast, clusters formed from a weak haloacid (HF) show a diversity of proton-transfer and hydrogen-bonding behaviors for systems at least as large as n=5. In addition to chlorides, anthropogenic bromides and fluorides are also present in the atmosphere, and this work indicates that bromides may also 15



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form ammonium clusters under similar conditions to those where ammonium chloride clusters may be observed.1-3,69,70 Our work indicates that the formation of ammonium halides from molecular ammonia and (HCl, HBr) in the gas phase is generally exothermic and exergonic at room temperature, with notable size-dependent variations in the reaction enthalpies and free energies. As previously noted, the crystal structure of solid NH4Cl and NH4Br is the CsCl motif, but solid NH4F takes on a wurtzite structure similar to H2O.33,57 Solid NH4Cl and NH4Br are so similar in structure and intermolecular forces that they can form solid solutions,33 and the study of mixed NH4Br/NH4Cl clusters might thus prove interesting. Similarly, H2O can be incorporated into solid NH4F due to the similarities in their solid-state structures, but only up to about 10%.71,72 It would be interesting to know what size range of ammonium fluoride clusters is required to obtain structures which are similar to the wurzite crystal structure for NH4F(s), and what the energetic and hydrogen-bonding properties of mixed clusters of the type (NH4F)m(H2O)n would be in comparison to (NH4Cl)m(H2O)n. Moreover, the presence of water as a catalyst and as a nano-droplet and/or aerosol solvent phase for the formation of ammonium chloride nanoparticles under atmospheric conditions of temperature and relative humidity should be further investigated.14 Future work should include simulated annealing calculations for much larger (NH4X)n systems in order to determine what size nanoparticles would need to be in order to favor the formation of the bulk CsCl or wurtzite solid phase.73 In the case of ammonium fluoride, such calculations would minimally need to consider all possible permutations of (NH3/HF, NH4+/F-) species pairs within each cluster as a function of cluster size.

Acknowledgement GridChem (http://www.gridchem.org)71-74 provided computational resources and services in support of selected results presented in this work. This work used the Extreme Science and Engineering Discovery Environment (XSEDE), which is supported by National Science Foundation grant number OCI-1053575.

16


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Supporting Information The Supporting Information for this article includes a table of all parameters used to form the interaction potential used in the MW-SSA calculations of (NH4Br)n and (NH4Cl)n. The coordinates of the (NH4Br)n clusters (n=1-13) at the M06-2X/6-31G(d,p) level and (NH4F)n clusters (n=1-5) at the RI-MP2/aug-cc-pVTZ level are also provided. Supporting Information is available free of charge via the Internet at http://pubs.acs.org.

17



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TABLES Table 1. Selected experimental and computed distances for (H3N ... HBr)

Method

rNH

Basis Set

Expt. a CCSD

RI-MP2 MP2

rN---H rHBr rN---Br

---

---

---

3.255

aug-cc-pVDZ-2.5 b

1.021

1.865

1.461

NR

aug-cc-pVTZ

1.013

1.857

1.448

3.305

6-311++G(2df,2p) aug-cc-pVDZ c

1.012 NR

1.721 1.706

1.480 1.487

3.202 3.193

aug-cc-pVTZ

1.013

1.718

1.480

3.197

B3LYP

6-31G(d,p) 6-311++G(2df,2p)

1.017 1.014

1.550 1.677

1.555 1.508

3.105 3.185

M06-2X

6-31G(d,p) 6-311++G(2df,2p)

1.016 1.014

1.362 1.332

1.638 1.654

3.000 2.986

All distances given in Angstroms. a. Reference 27. b. Reference 55. c. Reference 56. rNH is the covalent N-H bond distance within the NH3 molecule, and rN...H is the (hydrogen-bonded) distance between N of the NH3 molecule and H of the HBr molecule.

18


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Table 2. Calculated interatomic distances for (NH4Br)2 and (NH4Br)4 (NH4Br)2 Method

Basis Set

% Dev CCSD a

rH...Br rN...Br

CCSD

6-311++G(2df,2p)

2.139

3.186

---

RI-MP2

6-31G(d,p) 6-311++G(2df,2p) aug-cc-pVTZ

2.138 2.114 2.095

3.189 3.166 3.151

0.1% -0.6% -1.1%

B3LYP

6-31G(d,p) 6-311++G(2df,2p)

2.124 2.135

3.190 3.192

0.1% 0.2%

M06-2X

6-31G(d,p) 6-31+G(d) 6-311++G(2df,2p) cc-pVTZ

2.120 2.122 2.105 2.114

3.180 3.181 3.163 3.180

-0.2% -0.2% -0.7% -0.2%

rH...Br rN...Br

% Dev MP2 b

(NH4Br)4

(Å)

(Å)

RI-MP2

6-311++G(2df,2p)

2.253

3.272

----

B3LYP

6-31G(d,p) 6-31+G(d) a 6-311++G(2df,2p) cc-pVTZ aug-cc-pVTZ

2.260 2.282 2.266 2.268 2.273

3.290 3.314 3.293 3.296 3.301

0.6% 1.3% 0.6% 0.7% 0.9%

M06-2X

6-31G(d,p) 6-31+G(d) 6-311++G(2df,2p) cc-pVTZ aug-cc-pVTZ

2.264 2.279 2.271 2.270 2.274

3.281 3.299 3.288 3.288 3.293

0.3% 0.8% 0.5% 0.5% 0.6%

All distances are given in Angstroms. a. Percent deviation of r N...Cl from the value predicted by CCSD/6-311++G(2df,2p) calculations. b. Percent deviation of r N...Br from the value predicted from RI-MP2/6-311++G(2df,2p) calculations. Here r X...Br (X=H or N) is the noncovalent distance between an atom within NH4+ and the nearest Br- within the ring (n=2) or cube (n=4).

19



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Table 3. Selected nearest-neighbor distances for ammonium fluoride clustersa Species NH3

rNH

rN...F

1.012

HF

(NH3-HF) n=1

rHF

Description N-H covalent bond

0.922

H-F covalent bond

1.678 (65.8%)b 1.687 (66.7%)

0.958 (3.9%)c 0.960 (4.1%)

2.647

1.535 (51.7%) 1.020 (0.8%)

0.995 (7.9%) 1.941 (110.5%)

2.527 (-4.1%)e 2.919 (10.7%)

1.462 (44.5%)

1.024 (11.1%)

2.482 (-5.8%)

HF to NH3 hydrogen bonds on edges

1.031 (1.9%)

1.767 (91.6%)

2.767 (5.0%)

NH3 to HF hydrogen bonds on sides

1.139 (12.5%)

1.314 (42.5%)

2.450 (-7.1%)

Interior proton-shared hydrogen bond

(NH4X)4 n=4

1.053 (4.1%)

1.591 (72.6%)

2.612 (-0.9%)

Interior ion-pair hydrogen bonds

1.050 (3.8%)

1.611 (74.7%)

2.630 (-0.2%)

Average ion-pair hydrogen bond lengths inside cube

(NH4X)4 (NH3-HF)

1.510 (49.2%) 2.812 (177.9%) 1.021 (0.9%)

1.005 (9.0%) 1.806 (95.9%) 1.893 (105.3%)

2.513 (-4.7%) 2.812 (6.7%) 2.811 (6.6%)

NH3 to HF edge-attached hydrogen bond

(NH3-HF)2 n=2

(NH3-HF)2 (H3N…Hd+…Fd-) n=3

Hydrogen bond between NH3 and HF 2.636 Experimentd

HF to NH3 hydrogen bond NH3 to HF hydrogen bond

n=5

NH3 attachment to cube HF attachment to cube

All distances are given in Angstroms. a. Unless otherwise indicated, all distances were calculated at the RI-MP2/aug-cc-pVTZ level of theory. b. Percent deviation of rNH from the value calculated for isolated NH3. c. Percent deviation of rHF from the value calculated for isolated HF. d. From Ref. 31. e. Percent deviation of rN...F from the value calculated for the (NH3-HF) cluster. 20


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Table 4: Interaction energies per ion pair for (NH4Br)n and (NH4Cl)n.a n

Vn0/n (NH4Br)n

Vn0/n (NH4Cl)n

1 2 3 4 5 6 7 8 9 10 11 12 13

-508.6 -579.3 -591.6 -623.3 -621.3 -631.7 -631.4 -637.5 -638.7 -640.7 -640.4 -644.4 -642.2

-558.2 -611.8 -624.3 -655.4 -651.8 -663.8 -660.0 -669.5 -670.3 -672.4 -670.6 -676.1 -674.2

a

Energies in kJ/mol; calculated at M06-2X/6-31G(d,p)//M06-2X/6-311++G(2df,2p) level of theory (see text).

21



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Table 5. Enthalpies, entropies and Gibbs energies for cluster nucleation reactions R2 and R3 a (NH4Br)n n

∆H2

∆S2

∆G2

∆H3

∆S3

∆G3

2 3 4 5 6 7 8

-150.4 -126.7 -222.4 -114.7 -197.7 -109.2 -216.6

-284.1 -304.5 -315.8 -315.8 -311.1 -310.9 -323.3

-65.8 -36.0 -128.2 -20.6 -105.0 -16.5 -120.2

-183.3 -310.1 -532.5 -647.2 -845.0 -954.1 -1170.7

-396.4 -700.9 -1016.8 -1332.5 -1643.6 -1954.4 -2277.8

-65.2 -101.1 -229.4 -250.0 -354.9 -371.4 -491.6

-403.1 -692.3 -1000.9 -1307.8 -1616.1 -1920.5 -2241.5

-32.2 -59.5 -169.5 -177.5 -262.6 -278.6 -368.1

(NH4Cl)n 2 3 4 5 6 7 8

-120.9 -113.5 -202.0 -99.6 -177.0 -106.8 -185.1

-295.5 -289.2 -308.6 -306.9 -308.3 -304.5 -320.9

-32.8 -27.3 -110.0 -8.1 -85.1 -16.0 -89.5

-152.4 -265.9 -467.9 -567.5 -744.5 -851.2 -1036.4

a. Enthalpies and free energies of reaction are given in kJ/mol; entropies of reaction are given in J / (mol K). All values calculated at (298.15K, 1 atm). See text for description of calculation methods.

22


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Figure 1. Computed structures of (NH4Br)n clusters (n=2-13) located via MW-SSA Monte Carlo calculations. 165x218mm (96 x 96 DPI)


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Figure 2. Structures of the n=2 (NH4Br)2 (left) and (NH3…HF)2 (right) clusters at the RI-MP2/aug-cc-pVTZ level of theory. 338x190mm (96 x 96 DPI)



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Figure 3. Computed RI-MP2/aug-cc-pVTZ structures of selected (NH4F)n clusters with n = 3, 4 and 5 (left to right). 338x190mm (96 x 96 DPI)


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Figure 4. Highest occupied molecular orbital (HOMO) for ammonium fluoride clusters with n=1 (upper left), n=2 (upper right) and n=3 (center), computed at the RI-MP2/aug-cc-pVTZ level of theory. In cases where the HOMO is degenerate, the orbital with sigma character is displayed. 338x190mm (96 x 96 DPI)



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Figure 5. HOMO for ammonium fluoride clusters with n=4 (left) and n=5 (right). See Figure 4. 338x190mm (96 x 96 DPI)


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Figure 6. Difference in ionic interaction energy Vn0 (Hartree) per n between (NH4Br)n and (NH4Cl)n, calculated at the M06-2X/6-31G(d,p)//M06-2X/6-311++G(2df,2p) level of theory (circles). The difference in experimental lattice energies for NH4Br(s) and NH4Cl(s) is also shown (dashed line). 338x190mm (96 x 96 DPI)



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Figure 7. Changes in ionic interaction energies ∆Vn0 (Hartree) as a function of n for (NH4Br)n (diamonds) and (NH4Cl)n (squares), calculated at the M06-2X/6-31G(d,p)//M06-2X/6-311++G(2df,2p) level of theory. 338x190mm (96 x 96 DPI)


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Figure 8. Computed Gibbs free energy of reaction for sequential growth reaction R2 for (NH4Br)n (diamonds) and (NH4Cl)n (squares). 338x190mm (96 x 96 DPI)



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Figure 9. Computed Gibbs free energy of reaction for “total” growth reaction R3 for (NH4Br)n (diamonds) and (NH4Cl)n (squares). 338x190mm (96 x 96 DPI)


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Table of Contents Image 78x44mm (200 x 200 DPI)


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