Trapping of Hydrochloric and Hydrofluoric Acid at Vacancies on and

Article pubs.acs.org/JPCA

Trapping of Hydrochloric and Hydrofluoric Acid at Vacancies on and underneath the Ice Ih Basal-Plane Surface Pedro Augusto Franco Pinheiro Moreira*,† and Maurice de Koning*,‡ †

Departamento de Física, UFSCar, Rodovia Washington Luiz, km 235, CP 676, 13565-905 São Carlos, SP, Brazil Instituto de Física “Gleb Wataghin”, Universidade Estadual de Campinas, 13083-859 Campinas, SP, Brazil

‡

ABSTRACT: We investigate the uptake of HCl and HF at lattice vacancies in ice Ih as a function of their distance to the basal-plane surface layer using density-functional theory calculations. The results for HCl display large dispersions in the binding-energy results due to the appearance of distinct dissociation states. The layer-averaged results suggest that the uptake of HCl is most favorable in the two layers just below the surface, which is consistent with available experimental indications. The behavior of HF is found to be manifestly different due to the fact that it is a weaker acid. The dispersion in the binding-energy values is significantly less compared to the case of HCl, and the average values are essentially equal to the bulk value, regardless of layer position. This suggests that, in contrast to the case of HCl, there should not be any tendency for accumulation of HF near the surface.

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INTRODUCTION An understanding of the interaction between hydrogen halides and ice-like surfaces is of essential importance to atmospheric chemistry and climate research.1−4 The uptake of hydrochloric acid (HCl) at the surface of polar stratospheric clouds, for instance, is known to play a key role in the mechanism of ozone destruction.2−5 A significant part of the HCl in nature is dispersed by volcanic eruptions. However, due to its high solubility in water, essentially all the HCl from the troposphere from this source precipitates with rain. On the other hand, the HCl produced indirectly through the industrial release of chlorofluorocarbons (CFCs) is able to reach the stratosphere. CFCs hardly degrade and do not dissolve easily in water, allowing them to arrive at the upper stratosphere before precipitating. The CFCs are then broken down into smaller species by solar radiation, one of them being HCl.3 In spite of the stratospheric concentration levels of HF being as large as those of HCl, including at the Antarctic pole, fluorine has a much smaller impact on the ozone layer. The large HF bond strength restrains the gas reaction with OH, reducing the significance of the fluorine ozone-depletion process.2 Yet, a study of the uptake of HF by ice is useful in that it can shed light on the fundamental mechanisms of acid ionization reactions on ice and ice-like surfaces.6,7 Interactions between gas molecules and ice involve combinations of several processes and continue to be a topic of intensive investigation.8−15 The gas adsorption on the ice surface is often followed by a chemical reaction on the surface. This composite process represents a surface reaction that can be described in terms of reaction probabilities that can be measured experimentally. However, it is very difficult to access information regarding the individual steps that constitute the composite process. In this light, atomistic modeling techniques © XXXX American Chemical Society

provide a useful complementary approach to understanding processes such as those involving the uptake of gas molecules by ice surfaces. Using classical molecular dynamics (MD) simulations, Gertner and Hynes studied HCl molecules adsorbed mainly on the second layer of first bilayer.16 For HF, Gardner et al. also use classical trajectory simulations to study the adsorption and penetration into the (0001) face of ice Ih.17 These simulations, however, are based on classical interaction models that are mostly unable to describe proton and/or electron transfer processes. For this purpose, first-principles modeling approaches in which the electrons are treated explicitly are more reliable. Such approaches have been applied to study interactions between the hydrogen halides and the ice surface. Bussolin et al.18 used Hartree−Fock calculations to compute HCl and HF adsorption energies of different crystalline faces of two proton-ordered structures of ice using very thin slabs. Catalayud and co-workers,19 on the other hand, studied the ionization of HCl and HF in bulk cubic ice using densityfunctional theory (DFT) and very small periodic supercells. Here we use state-of-the-art DFT calculations to investigate the uptake of HCl and HF through the basal-plane surface of ice Ih under conditions where surface premelting is not an issue and the oxygen Wurtzite lattice remains intact up to the surface. In particular, we investigate the energetics of incorporation of these two molecules at vacant lattice sites on and underneath the surface. Watkins et al.20,21 have recently shown that, due to the proton disorder, such defects are characterized by formation energies showing very large variations and that their Received: August 13, 2013 Revised: October 1, 2013

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dx.doi.org/10.1021/jp408098e | J. Phys. Chem. A XXXX, XXX, XXX−XXX

The Journal of Physical Chemistry A

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equilibrium concentration at the surface is expected to be far larger than in the bulk. In this manner, vacancies can act as traps of varying strength for hydrogen halide molecules such as HCl and HF, thus expected to play a role in the processes relevant to atmospheric chemistry. Indeed, Watkins et al.21 investigated these trap strengths for a number of different gases for vacant sites on the surface. Here, we extend these results by analyzing trap strengths and ionization tendencies of HCl and HF as a function of their position with respect to the surface layer, mapping the transition between surface-like and bulk-like behavior. The latter is relevant, for instance, in the context of the question to what extent HCl and HF penetrate from the surface into the bulk, which has been assumed not to occur for HCl in uptake experiments using exposure times ∼1000 s.22−24 The remainder of the paper has been organized as follows. The following section is concerned with the employed methodology, giving technical details of the simulations that have been carried out. Next, we present and discuss the obtained results, followed by a summary and conclusions.

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METHODOLOGY All our calculations were carried out within the framework of DFT as implemented in the VASP package.25,26 The projectoraugmented-wave (PAW) method27 is employed to describe the interactions between ions and electrons, and the exchange− correlation functional is determined within the generalized gradient approximation (GGA) as parametrized by Perdew et al.28 Unless stated otherwise, the plane-wave cutoff in the calculations is 700 eV. Brillouin-zone sampling was limited to the Γ-point, and structure optimizations were conducted until the magnitude of the maximum force on all the ions was smaller than 0.05 eV/Å. All supercells are based on the 360-molecule cell (5 × 3 × 3) of ice Ih prepared by Hayward and Reimers.29 It contains six bilayers along the c-axis. This proton-disordered cell has zero net dipole moment and obeys the Bernal−Fowler ice rules at each site.1 All surface calculations were carried out by adding a vacuum gap of 10 Å along the direction of the c-axis, as shown schematically in Figure 1. This gap is sufficiently wide to render the spurious interactions between the surfaces negligible.21 The energetics of trapping of the gas molecules HX, with X = Cl or X = F, at a vacancy is analyzed in terms of the reaction21 HX(g) + H 2O(ice)N − 1 → H 2O(ice)N − 1 + HX(ice)

Figure 1. Bilayer structure of the ice Ih supercell used in the calculations. It consists of six bilayers along the c axis containing a total of twelve planes. These planes are indexed (1) through (6) according to their position relative to the closest surface plane. Also shown is an HCl molecule adsorbed at a vacancy in the topmost surface layer, with its proton pointing outward.

slab calculation, such that the X− ion is positioned at the unoccupied Wurtzite lattice site. Using the total-energy results of these three runs, ΔEs is computed as ΔEs = (Evac + E HX(g)) − E HX(ice) f = [Evac + E HX(g) + (N − 1)E H2O(ice)] − E HX(ice)

(3)

where EHX(ice) is the total energy of the slab configuration in which the HX molecule is inserted at a vacant lattice site, Evac is the total energy of the ice slab with a single vacancy, EHX(g) is the total energy of an isolated HX molecule placed in the otherwise empty slab supercell, Efvac is the vacancy formation energy, and EH2O(ice) is the average energy of a water molecule in bulkf ice. For reference, we also compute ΔEs for solvation at a vacancy in bulk ice. For this purpose, we use the bulk 96-atom ice Ih cell labeled 3 × 2 × 2 by Hayward and Reimers.29 For the gas-phase HX reference energy we use the total energy of a single HX molecule in a supercell of the same dimensions of the 96-molecule bulk cell. To sample the effects of the proton disorder, both for the surface slab and for the bulk reference, the HX molecules are inserted at a number of different vacancy sites for each layer. In addition, at each vacancy, the HX molecule is inserted in the two orientations that coincide with the two proton-donor directions of the water molecule that was removed to create the vacancy. This is shown schematically in Figure 2, which displays views of the molecule that is removed to create the vacant lattice site, both in the bulk and at the surface, and the two orientations in which the HX molecule can be inserted. Figure 2a displays a molecule that is removed to create a bulk vacant lattice site and the two orientations in which the HX molecule

(1)

which describes the process in which a hydrogen halide molecule in the gas phase is transferred to a vacant lattice site within the ice crystal. The energetics of this vacancy-solvation process is described by the binding energy ΔEs ≡ E HX(g) − E HX(ice)

(2)

where EHX(g) is the total energy of a system composed of an ice crystal containing N − 1 molecules, a vacant lattice site, and an HX molecule in the gas phase, and EHX(ice) is the total energy of the system in which the gas-phase molecule has been moved to the vacancy. ΔEs is computed using the results of three separate DFT calculations. First, we relax a supercell containing the ice Ih surface slab with a single vacancy, followed by another simulation in which a single HX molecule is placed in a periodic supercell of the same dimensions as those used in the slab calculations. Finally, we execute a third simulation in which an HX molecule is inserted at the site of the vacancy of the first B



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terized by a 1000 eV kinetic-energy cutoff. No significant discrepancies with respect to a 700 eV plane-wave cutoff was found. Next, we consider the energetics of the uptake of gas-phase HCl molecules at the vacancies considered in Figure 3. Following the protocol described in the previous section, we compute the binding energies ΔEs using eq 3. The results are shown in Figure 4, which displays the data for 34 different

Figure 2. Schematic representation of two distinct orientations in which the HX molecule can be inserted at vacant lattice site in the bulk and at the surface. (a) The bulk central water molecule is removed to produce the vacancy. (b) and (c) display the two possible orientations of the HX molecule at the bulk vacancy. (d) The surface water molecule with dangling proton indicated by an arrow is removed to produce surface vacancy. (e) and (f) display the two possible orientations of the HX molecule at the surface vacancy.

can then be inserted are shown in Figure 2b,c, respectively. Parts d−f of Figure 2 show the same for a surface vacancy and the two corresponding HX orientations, respectively.

Figure 4. Distribution of HCl binding energies in ice Ih slab for the first five layers. Circles represent individual data points. Squares and error bars describe average values and standard deviations of the data, respectively, for each layer. The full line is to guide the eye in the trend of average values as a function of layer position. The dashed line represents the average binding energy at a bulk ice vacancy. The descriptions “2 hops” and “3 hops” denote cases in which the acid proton has moved away from the anion by 2 and 3 molecular hops, respectively.

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RESULTS AND DISCUSSION First, we computed the vacancy-formation energies in the ice slab as a function of its position with respect to the closest of the two surface layers. To sample the influence of proton disorder, we analyzed 10 different vacancy positions for the outermost surface layers and 6 for the layers underneath it. The results, shown in Figure 3, are coherent with those published by

vacancy sites distributed over all layers in the slab. The fact that all binding energies are positive implies that incorporation of the HCl molecule into the ice matrix is energetically favorable in all cases. It is evident that the fluctuations in ΔEs vary strongly with the layer position of the considered vacancy. The fluctuations in the surface layer are very large, spanning almost an order of magnitude between largest and smallest values. The spread in values for ΔEs then decreases as the layer position of the vacancy is further separated from the surface. In the fifth layer the variation of ΔEs is already quite small, with its average value being essentially equal to the bulk value. The large fluctuations are directly correlated to the degree of dissociation of the HCl molecule. In the outermost surface layer the group of smallest binding energies is associated with HCl molecules inserted at surface vacancy sites with their protons pointing outward from the surface, as shown in Figure 1. In this case, the HCl molecule essentially retains its gas-phase structure, with a H−Cl distance of ∼1.29 Å. At the other extreme, the cases associated with the largest values are those in which the HCl molecule has fully dissociated, with the hydronium cation and chlorine anion being separated by at least one water molecule. The group of intermediate values is characterized by the formation of a contact ion pair in which the hydronium and chlorine ions remain next to each other. In the second layer we observe similar behavior, with the main group being associated with the formation of contact ion pairs and ΔEs values with relatively small dispersion. The single outlier with the largest binding-energy value corresponds to a fully dissociated ion pair with the hydronium and chlorine ions being separated by two water molecules. For the deeper layers

Figure 3. Distribution of vacancy formation energies for the first five bilayers on a (0001) ice Ih slab. Squares represent results using a 700 eV plane-wave cutoff. Circles denote results obtained for 1000 eV. The dashed line represents the average formation energy at a bulk ice vacancy.

Watkins et al.21 as shown in their Figure 2. The fact that these results are also consistent with values obtained using smaller 96-molecule cells30 indicates that the 360-molecule cells are sufficiently large for finite-size effects to be negligible. In addition, to verify basis-set convergence, we repeated some formation-energy calculations using a plane-wave set characC



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this trend continues, showing relatively narrow groups associated with contact-ion pairs and occasional outliers related to fully dissociated hydronium and chlorine ion pairs. Indeed, when all binding energies are plotted as a function of the distance between the hydronium and chlorine ions of the fully relaxed pair (measured as the distance between the chlorine ion and the nearest proton of the hydronium ion), as shown in Figure 5, the strength of the HCl binding increases with the amount of separation between the ions.

Figure 6. Distribution of HF binding energies in ice Ih slab for the first five layers. Circles represent individual data points. Squares and error bars describe average values and standard deviations of the data, respectively, for each layer. The full line is to guide the eye in the trend of average value as a function of layer position. The dashed line represents average binding energy at a bulk ice vacancy.

HCl, it is clear that the fluctuations for HF are significantly smaller than those for HCl. This difference is associated with the fact that HF is a weaker acid than HCl, leading to a smaller dissociation tendency. In only four cases, all of them on the surface layer, did the HF molecule dissociate to some degree, forming a contact ion pair. In all other situations, the HF molecule does not dissociate at all, maintaining essentially its gas-phase structure. This is consistent with the behavior of the average values, which show that the binding energies are essentially equal to the bulk value, regardless of layer position. In other words, because HF is a weaker acid than HCl, the energetics of its uptake at ice vacancies becomes significantly less sensitive to the structural surroundings of the vacant lattice site at which it is trapped. This also suggests that, in contrast to the case of HCl, there should not be any tendency for accumulation of HF near the surface. Figure 7 displays this difference in another way. It plots the binding energy of both molecule types as a function of the vacancy-formation energy of the site at which they were inserted. For the HF results, denoted by the squares, there is a distinct correlation between the binding energy and the formation energy of the vacancy at which it was inserted, for both cases in which the HF molecule remains intact (open squares) and forms a contact ion (full squares). Indeed, the fact that straight lines with a slope of 1, as shown by the red lines, provide good fits demonstrates that the total energy of a system in which HF molecule has been inserted at a vacancy is effectively insensitive to variations in the structural surroundings of that vacancy. This can be understood by considering eq 3, in which the binding energy is expressed in terms of the vacancy-formation energy Efvac is linear in Efvac with coefficient 1 and only the term EHX(ice) incorporates a possible influence of the vacancy structure. The fact that straight lines provide good descriptions of ΔEs as a function of Efvac then implies that EHX(ice) is effectively constant for a given dissociation state (i.e., intact gas molecule or contact-ion pair), independent of the variations in the vacancy structure. The situation is somewhat different for HCl. For the main group of data (open circles), representing the cases that lead to the formation of contact-ion pairs, there is no correlation between binding energy and vacancy-formation energy. Following the reasoning of the preceding paragraph, this

Figure 5. HCl binding energies as a function of the relaxed hydronium−chlorine distance. The full line is proportional to the inverse distance between the chlorine and hydronium ions and serves as a guide to the eye.

The presence of distinct groups in our results is consistent with experimental data. McNeill and coauthors31 studied the interaction of HCl with ice using a coated-wall flow tube and chemical ionization mass spectrometry. They suggested the existence of two possible binding sites for HCl adsorption, one nondissociative and reversible and the other dissociative and irreversible, with the former characterized by a weaker binding energy. They were able to provide an estimate for the binding enthalpy of the reversible site, giving 0.16 ± 0.02 eV. This result is consistent with our binding energy of ∼0.17−0.22 eV for the HCl adsorbed at a surface vacancy with its proton pointing outward from the surface. In this light, the picture of two sites with distinct features, one nondissociative with dangling bonds and the other dissociative with the formation of a H3O+−Cl− pair may explain the adsorption features observed by McNeill and coauthors.31 Considering the overall statistics of binding energies as a function of layer position in terms of the average binding energy, as depicted by the squares in Figure 4, our results indicate that the uptake of HCl is most favorable in the two layers just below the surface. This suggests that, in equilibrium, the concentration of the Cl1− anion is expected to be larger close to the surface compared to that in the bulk. This is consistent with the experimental findings of Park et al.,32 who concluded that hydroniums and chlorides tend to accumulate near the ice surface. Finally, comparing the slab results to bulk properties, it is evident that the binding energies display a quick approach to bulk behavior, with the fifth-layer binding energies already being essentially indistinguishable from the bulk value. Using the same methodology, we also investigated the uptake of hydrofluoric acid molecules at ice Ih vacancies near the basalplane surface. Figure 6 depicts the HF binding energy as a function of layer position. Comparing the results to those of D



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that in the bulk, which is consistent with experimental data of Park et al.32 The situation for HF is rather different because it is a weaker acid and displays a lesser tendency toward dissociation. Indeed, in virtually all cases, the HF molecule was found to remain intact within the ice crystal. Only in very few cases was the formation of a contact-ion pair observed. As a result, the dispersion in the binding-energy values is significantly less compared to the case of HCl and the average values are essentially equal to the bulk value, regardless of layer position. This indicates that, in contrast to the case of HCl, there should not be any tendency for accumulation of HF near the surface.

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AUTHOR INFORMATION

Corresponding Authors

Figure 7. HCl (circles) and HF (squares) binding energies as a function of the vacancy-formation energy of the site at which they were inserted. All straight lines are characterized by a slope 1 and serve as guides to the eye. Open squares are results for the case in which the HF molecule remains intact. Solid squares represent data for the cases in which the HF molecule dissociates into a contact-ion pair. Open circles are results for cases in which HCl dissociates into contact-ion pair. Solid black circles represent eight cases in which the HCl molecule dissociates into a hydronium−chlorine ion pair separated by one water molecule. Gray circles represent cases in which HCl molecule dissociates into a hydronium−chlorine ion pair separated by two water molecules.

*P. A. F. Pinheiro Moreira: e-mail, [email protected]. *M. de Koning: e-mail, dekoning@ifi.unicamp.br. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS P.A.F.P.M. and M.K. acknowledge financial support from the Brazilian agencies Fapesp, Capes, and CNPq. All calculations were performed at CCJDR, IFGW, Unicamp.

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REFERENCES

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implies that the total energy of a system in which an HCl molecule has been inserted at a vacancy and dissociated into a contact-ion pair, is sensitive to variations in the structural surroundings of that vacancy. For the two groups of data points indicated by the full circles, however, the linear trend is once again observed. These correspond to cases in which the HCl molecule has dissociated into a hydronium−chlorine ion pair separated by a water molecule. The two black dashed lines have different intercepts due to the fact that the two groups belong to the first and third layers, respectively, as can be seen in Figure 4.

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CONCLUSIONS We have conducted DFT-based first-principles calculations on the uptake of HCl and HF by vacant lattice sites in ice Ih at the basal-plane surface and layers underneath it under conditions in which the formation of a quasi-liquid layer does not occur. For HCl, the dispersion in the binding-energy values is significant due to the different dissociation states, ranging from undissociated HCl molecules at the outermost surface layer to fully dissociated ion pairs separated by two water molecules. At the outermost surface layer, the existence of undissociated and dissociated states of the HCl molecule is coherent with experimental data of McNeill and coauthors31 that suggest the existence of two adsorption site types, one reversible and the other irreversible. The dispersion in the binding-energy values rapidly decreases with the distance of the vacant lattice to the outermost surface layer. Effectively, bulk behavior is attained at the fifth layer below the surface. When the average binding energies are considered as a function of layer position, our results indicate that the uptake of HCl is most favorable in the two layers just below the surface. This suggests that, in equilibrium, the concentration of the Cl− anion is expected to be larger close to the surface compared to E



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Trapping of Hydrochloric and Hydrofluoric Acid at Vacancies on and

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