Proton Transfer Rates in Ionized Hydrogen Chloride–Water Clusters

Article pubs.acs.org/JPCA

Proton Transfer Rates in Ionized Hydrogen Chloride−Water Clusters: A Direct Ab Initio Molecular Dynamics Study Hiroto Tachikawa* Division of Applied Chemistry, Graduate School of Engineering, Hokkaido University, Sapporo 060-8628, Japan S Supporting Information *

ABSTRACT: Reactions of the microhydrated hydrogen chloride radical cation, [HCl−(H2O)n]+ (n = 1−5), following the ionization of the parent neutral cluster were investigated by the direct ab initio molecular dynamics (AIMD) method to elucidate the cluster size dependence of the proton transfer (PT) rate in the ionized state. The ionization occurred from the HCl moiety of the clusters. The proton of HCl+ was transferred to the neighboring water molecule in the cluster. The time of PT was strongly dependent on the cluster size (n); the time of PT decreased with increasing n and reached a limiting value at n = 4−5 (the time of PT was ca. 7 fs). The acceleration of the PT rate was mainly caused by the shortness of the hydrogen bond between HCl+ and H2O in larger clusters, that is, a short hydrogen bond causes fast PT. The electrostatic effects of the water cluster further accelerated the rate of PT. After the first PT from HCl+ to H2O, the second PT (H3O+ + H2O →H2O + H3O+) was detected for n = 3−5. The times of the first and second PTs were calculated as 7−15 and 30−40 fs, respectively. The reaction mechanism was discussed based on the theoretical results.

1. INTRODUCTION Microhydrated hydrogen chloride, HCl(H2O)n, has been extensively investigated from both experimental1−11 and theoretical points of view.12−20 The HCl(H2O)n cluster is a model system where a strong acid dissolves in water. It is used to determine the number of water molecules required for the ionic dissociation of the HCl molecule in the water environment.21−27 HCl(H2O)n also plays a key role in ozone depletion in polar stratospheric clouds (PSCs) as ozone depletion is initiated by the dissociation of HCl on ice surfaces.28−33 To understand the dissociation of acids into water clusters, Re et al.34 calculated the structures of HCl(H2O)n (n = 1−5) using the density functional theory (DFT) method. The most stable structures for n = 1−3 were the proton nontransferred type (undissociated). At n = 4, the proton nontransferred and proton transferred (dissociated) structures had nearly similar energies. In the case of n = 5, the ionic dissociation form (dissociated) was more stable than the proton nontransferred forms (undissociated). The undissociated and dissociated structures are schematically expressed by HCl(H2O)n and H3O+(H2O)nCl−, respectively. Recently, Odde et al.35 carried out systematic calculations for HX(H2O)n clusters (X = F, Cl, Br, and I) up to n = 6 using the © 2017 American Chemical Society

B3LYP and MP2 levels of theory. The dissociated and undissociated clusters resulted in very different vibrational spectra, suggesting that the measurements of the IR spectrum can be used to monitor the ion dissociation reaction, HCl(H2O)n → H3O+(H2O)nCl−. To understand the dissociation of HCl into water clusters, Gutberlet et al. observed microhydrated HCl in helium droplets below 1 K.36 High-resolution mass-selective infrared laser spectroscopy revealed that the aggregation of HCl with water molecules, HCl(H2O)n, results in the formation of hydronium ion (H3O+). The smallest cluster size was determined to be n = 4. Their ab initio calculations supported the observations. Although the ionic dissociation process of HCl in water clusters has been previously investigated, there is little information on the ionization of HCl(H2O)n. Using static ab initio calculation, Calatayud et al. investigated the ionization of HCl and HF molecules trapped in ice lattice that consisted of replacing one water molecule by the HCl or HF molecule.37 The potential energy curve plotted as a function of H−Cl Received: May 25, 2017 Revised: June 29, 2017 Published: June 30, 2017 5237

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The Journal of Physical Chemistry A distance of HCl+ shows that the HCl+ dissociates to H+ + Cl without an activation barrier in the ice lattice. In contrast, the HF molecule does not dissociate. The photoreaction of HCl(H2O)n plays a fundamental role in chemistry, physics, life sciences, and environmental sciences.38 In the present study, to elucidate the effects of water clusters on the ionization dynamics of HCl, the reaction of microhydrated HCl clusters, HCl(H2O)n (n = 1−5), following ionization was investigated using the direct ab initio molecular dynamics (AIMD) method.39−41 In particular, we focused on the effects of water clusters on the rate of proton transfer (PT) from HCl+ to water clusters after ionization. In our previous study, we investigated the reaction mechanism of ammonia dimers interacting with water clusters following ionization using a direct AIMD method and compared the results with the gas-phase reaction.41 In the gas phase, the rate of PT was slow, whereas the ammonia dimer cation interacting with water clusters had a higher rate. However, the effects of the water cluster on the reaction mechanism were not clearly understood. In this work, we focus on the role of the water clusters on the ionization dynamics of microhydrated HCl.

2. COMPUTATIONAL DETAILS 2.1. Ab Initio Calculations. First, the geometry of microhydrated hydrogen chloride, HCl(H2O)n (n = 1−5), was fully optimized using the MP2/6-311++G(d,p) method. Single-point energy calculations for n = 1 were carried out by the coupled-cluster single−double and perturbative triple excitations (CCSD(T)) theory with the MP2 geometry. The atomic and molecular charges were calculated using the natural population analysis (NPA). The standard Gaussian 09 program package was used for all static ab initio calculations.42 2.2. Direct AIMD Calculations. The trajectories of [HCl(H2O)n]+ following the ionization of HCl(H2O)n were calculated at the MP2/6-311++G(d,p) level under the assumption of vertical ionization at the neutral state. The trajectory calculations of [HCl(H2O)n]+ were performed using the condition of constant total energy. The velocity Verlet algorithm was used with a time step of 0.05 fs to solve the equation of motion of the system. The drifts of total energies in all trajectory calculations were less than 0.01 kcal/mol. To check the effect of the level of theory on the reaction rate of the PT, two sets of methods were examined as follows:

Figure 1. Optimized structures and geometric parameters of microhydrated hydrogen chloride, HCl−(H2O)n (n = 2−5) calculated at the MP2/6-311++G(d,p) level. Bond lengths are in Å.

bond. At n = 1, the distance of the hydrogen bond is r1 = 1.903 Å, and the H−Cl bond length of HCl is 1.287 Å, slightly longer than that of HCl in vacuo (1.273 Å). The NPA molecular charge of HCl is −0.02, indicating that the HCl molecule acts as a weak electron acceptor in n = 1. The distances of the hydrogen bond for n = 2−5 were calculated as 1.802, 1.677, 1.630, and 1.631 Å, respectively, indicating that the hydrogen bond gradually shortened as a function of the cluster size (n) and reached a limiting value for n = 4−5 (r1 = 1.63 Å). The H−Cl bond lengths were 1.273 (n = 0), 1.287 (n = 1), 1.300 (n = 2), 1.316 (n = 3), 1.324 (n = 4), and 1.323 Å (n = 5). The elongation of the H−Cl bond was saturated at n = 4−5. The NPA molecular charges of HCl were −0.04 (n = 2) and −0.05 (n = 3−5). The atomic and molecular charges of all clusters are given in Table S1 and Figure S1 in the Supporting Information (SI). 3.2. Electronic States of [HCl(H2O)n]+ Clusters at the Vertical Ionization Point. Figure 2 shows the spatial distribution of spin densities on the [HCl(H2O)n+]ver cluster cation at the vertical ionization point from parent neutral clusters. The calculations were carried out at the MP2/6-311+ +G(d,p) level. The hole and spin densities were almost localized on the moiety of HCl in all cluster cations. The electron was removed from the 3p orbital of Cl atom after ionization. NPA molecular charges on HCl+ in [HCl(H2O)n+]ver were +1.00 (n = 0), +0.95 (n = 1), +0.91 (n = 2), +0.88 (n = 3), +0.87 (n = 4), and +0.87 (n = 5). About 13% of the positive

A: [CAM‐B3LYP/6‐311++G(d,p):MP2/6‐311++G(d,p)] B: [MP2/6‐311++G(d,p):CAM‐B3LYP/6‐311++G(d,p)]

where [X:Y] means that the AIMD calculation was carried out at the X level from the optimized structure obtained at the Y level. Note that all levels of theory gave similar results (see section 3.6). In addition to the AIMD calculations from the optimized geometries of HCl(H2O)n, the direct AIMD calculations with zero-point energy (ZPE) were performed. The details of direct AIMD calculations including ZPE are described in our recent work.43

3. RESULTS 3.1. Structures of Neutral HCl(H2O)n Clusters. The optimized structures of HCl(H2O)n (n = 1−5) are illustrated in Figure 1. The calculations were carried out at the MP2/6-311+ +G(d,p) level of theory. In all clusters, the proton of HCl moves toward the oxygen atom of H2O(W1) with a hydrogen 5238

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35.7 fs. However, the complex was gradually dissociated into H3O+ + Cl owing to the excess energy generated by the PT. Potential Energy. The time evolution of the potential energy of (HCl−H2O)+ is shown in Figure 3B. The zero level of the energy corresponds to that of [(HCl−H2O)+]ver at a vertical ionized point of the neutral complex. The potential energy decreased rapidly to −5.0 (9.4 fs) and −26.0 kcal/mol (14.2 fs) following the ionization of HCl−H2O. This reduction in energy was caused by PT from HCl+ to H2O. After PT, the energy increased suddenly (−10.0 kcal/mol) due to the collision of the proton with the oxygen atom of H2O. The energy was once minimized at 35.7 fs (−25.0 kcal/mol), which correspond to the ion−radical complex (H3O+−Cl). This complex was gradually dissociated to H3O+ + Cl. Distances. The time evolution of the distances (r1 and r2) is presented in Figure 3C. At time zero, the distances (r1, r2) were 1.903 and 1.287 Å. After ionization, the distance r1 decreased with time, whereas r2 increased. These distances crossed each other at 8.0 fs. Immediately, r1 reached the lowest point, corresponding to the collision of H+ to H2O. The time dependence of r1 and r2 indicates that PT takes place at 5−20 fs and is completed within ∼20 fs of ionization. The intermolecular distance (R1) was almost constant during PT (R1 = 3.10−3.20 Å), and the proton was transferred from Cl to H2O under the fixed intermolecular distance. 3.4. Reaction of [HCl(H2O)4]+ Following Ionization. Snapshots of the [HCl(H2O)4]+ cluster after vertical ionization of the parent neutral cluster are displayed in Figure 4. The positive charge and the cation hole were mainly localized on a part of HCl in the [HCl(H2O)4]+ cluster (the spin density on HCl was 1.021). The proton distances (r 1 , r 2 ) and intermolecular distance (R1 = r(Cl−O)) at time zero were 1.630, 1.324, and 2.954 Å, respectively. After ionization, the proton of HCl+ moved suddenly to the direction of the oxygen atom of W1. The distance of the proton from Cl and H2O was r1 = 1.363 Å and r2 = 1.584 Å at 4.2 fs, respectively, indicating that the proton was located at the central position between Cl and W1. At 6.7 fs, the distance of the proton was r1 = 0.964 Å and r2 = 1.971 Å, indicating that the PT occurred in very short time (∼7 fs). The time of PT was calculated as 6.7 fs at n = 4. After PT, the second water molecule (W2) gradually approached H3O+(W1) (10−20 fs). The second PT occurred from H3O+(W1) to W2 at 30.2 fs. After the second PT, H3O+(W2) was solvated by two water molecules (W1 and W3), and the hydrated complex composed of H3O+ was formed (30−60 fs). Finally, the Zundel-type complex (H2O−H−OH2)+ was formed at 61.3 fs. The interatomic distances of [HCl(H2O)4]+ after ionization are plotted as a function of time in Figure 5A. At 0 fs (before ionization), the bond lengths were r1 = 1.630 Å, r2 = 1.324 Å, and R1 = 2.954 Å (R1 is the distance between Cl and the oxygen atom of W1). The distance of the proton from H2O (r1) decreased with time, whereas the distance of the proton from Cl (r2) oscillatory increased after ionization. These distances crossed each other at 3.0 fs when the proton was located in the center of Cl−OH2. The time evolution of the distances of the proton indicates that PT occurred from HCl+ to H2O and was completed at 6.7 fs. At 8.5 fs, the distance r1 was minimized where the collision of the proton with H2O occurred. The intermolecular distance between HCl and H2O (R1) was almost constant during PT, indicating that PT from HCl+ to H2O took place at a constant intermolecular distance, Cl−OH2.

Figure 2. Spatial distributions of spin density on HCl+−(H2O)n (n = 0−4) at the vertical ionization point from the parent neutral clusters, calculated at the MP2/6-311++G(d,p) level.

charge was transferred from HCl+ to the water clusters (n = 4 and 5). The electronic states of HCl+ were affected by the water clusters. The spin densities on HCl in [HCl(H2O)n+]ver were +1.021 (n = 4). The hole and spin densities were mainly localized on the HCl moiety of [HCl(H2O)n+]ver. 3.3. Reaction of 1:1 Complex (HCl−H2O)+ Following Ionization. Snapshots. Snapshots of the (HCl−H2O) + complex after the vertical ionization of the parent neutral complex are illustrated in Figure 3A. The optimized structure obtained by the MP2/6-311++G(d,p) level was used for the initial structure of (HCl−H2O)+ at time zero. The hydrogen bond distance and the H−Cl bond length were r1 = 1.903 Å and r2 = 1.287 Å at time zero, respectively. The intermolecular distance was R1 = r(Cl−O) = 3.190 Å. The spin densities of HCl and H2O were 1.000 and 0.000 at time zero, respectively. The positive charge and the cation hole were localized on a part of HCl in the (HCl−H2O)+ complex, which is schematically expressed as (HCl)+−H2O. Immediately, the proton of HCl+ moved to the direction of H2O. At 9.4 fs, the distances of the proton (r1, r2) and intermolecular distance (R1) were 1.473, 1.683, and 3.155 Å, respectively, indicating that the proton was located in the middle of Cl and H2O. At 14.3 fs, the proton reached the oxygen atom of H2O (r1 = 0.968 Å) and the O−H bond was newly formed. The ion− radical complex, H3O+−Cl, was formed as the intermediate. This complex was once stabilized by structural relaxation at 5239

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Figure 3. (A) Snapshots of HCl+−H2O (1:1 complex) after vertical ionization from the neutral state calculated as a function of time. Bond distances are in Å. Time evolutions of (B) the potential energy and (C) bond distances of the system after vertical ionization from the neutral state.

Figure 4. Snapshots of HCl+−(H2O)4 after vertical ionization from the neutral state calculated as a function of time. Bond distances are in Å.

The second PT was slower than the first PT because the first PT is an exothermic reaction (HCl+ + H2O → H3O+ + Cl) and the second PT is an isothermic reaction (H3O+(W1) + H2O(W2) → H2O(W1) + H3O+(W2)). These results suggest that the total reaction is composed of the following three steps (the approximate time for each is given in parentheses): (1) Ionization takes place on the moiety of HCl in the HCl(H2O)4 clusters. The rapid PT occurs from HCl+ to H2O(W1) after ionization (7 fs), and the ion−radical Cl(H3O+) complex is formed as the intermediate.

Figure 5B shows the time evolution of the interatomic distances (r3 and r4) in [HCl(H2O)4]+. Both distances crossed each other at 26.0 fs when the second proton was located in the center of W1 and W2. The second PT was completed at 30.2 fs. The time dependence of the intermolecular distance between the oxygen atoms of W1 and W2 (R2) is displayed in Figure 5B. The distance (R2) was constant during the first PT at 0−10 fs (R2 = ∼2.70 Å). In contrast, the distance (R2) decreased after H3O+ ion formation. At the second PT, the distance (R2) decreased to 2.30 Å, indicating the approach of W2 to H3O+(W1) in the second PT. 5240

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Figure 6. Time of PT in HCl+−(H2O)n (n = 1−5).

Figure 5. Time evolutions of bond distances of HCl+−(H2O)4 after vertical ionization from the neutral state. (A) Bond distances in HCl+− H2O(W1) and (B) bond distances in W1−W2.

(2) The second PT takes place from H3O+(W1) to W2 (30 fs) after the approach of the second water molecule (W2) to H3O+(W1). (3) After the second PT, H3O+(W2) is gradually solvated by two water molecules (W1 and W3), and the Zundel-type complex (H2O−H−OH2)+(W2, W3) is stabilized by two water molecules (W1, W4) after solvation. 3.5. Time of PT in [HCl(H2O)n]+ (n = 1−5). The direct AIMD calculations were carried out for the other clusters (n = 2, 3, and 5). Snapshots of [HCl(H2O)n]+ (n = 2, 3, and 5) are illustrated in Figures S2−S5 in the Supporting Information. Similar dynamics features were obtained in all cases (n = 1−5). The reaction time of PT for n = 1−5 is plotted in Figure 6. The times of the PT were calculated as 14.3 (n = 1), 9.8 (n = 2), 7.1 (n = 3), 6.7 (n = 4), and 6.8 fs (n = 5), indicating that the time of PT decreases with increasing n, until it reaches a limiting value (∼7 fs). To elucidate the origin of the cluster size dependency of the PT time, the intermolecular distance of each water cluster was analyzed in detail. The distances in HCl(H2O)n for n = 1−5 were calculated as R1 = r(Cl−O) = 3.190 (n = 1), 3.068 (n = 2), 2.987 (n = 3), 2.954 (n = 4), and 2.954 Å (n = 5) at the MP2/ 6-311++G(d,p) level. The reaction time of PT is plotted as a function of R1 in Figure 7. The time of PT increased with the intermolecular distance (R1). Thus, the long hydrogen bond caused a slow PT. To determine the distance dependency in more detail, a model calculation was performed using the HCl−H2O 1:1 complex. First, the distance of R1 = r(Cl−O) in the complex with the optimized geometry was changed from 2.90 to 3.20 Å

Figure 7. Time of PT of HCl+−(H2O)n (n = 1−5) plotted as a function of intermolecular distance between HCl and H2O(W1). The dashed line indicates the time of PT obtained from the model calculations from the 1:1 HCl−H2O complex.

at intervals of 0.05 Å. Next, the direct AIMD calculations were conducted using these geometries. The results are plotted in Figure 7 (dashed line). The tendency of the time of PT obtained by the model calculation (dashed line) was similar to that in the clusters (circle). This result indicates that the acceleration of the PT rate is mainly caused by the intermolecular distance between HCl and H2O in the clusters (hydrogen bond): a long hydrogen bond leads to slow PT. For n = 2−5, the results of the model calculation were slightly different from those in clusters (arrow in Figure 7), meaning that the rate of PT is somewhat accelerated under the water cluster. To elucidate this effect, the bond populations of [HCl+(H2O)4]ver (R1 = r(Cl−O) = 2.954 Å, Cl−O bond distance in the optimized structure) were compared to those of the 1:1 complex at the vertical ionization point with a fixed bond distance (R1 = r(Cl−O) = 2.954 Å). The Cl−H and H− O bond populations of the 1:1 complex cation were calculated as P(Cl−H) = 0.176 and P(H−O) = 0.019, respectively. In contrast, these values were P(Cl−H) = 0.007 and P(H−O) = 5241

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The Journal of Physical Chemistry A 0.044 in the water cluster (n = 4). The results imply that the Cl−H bond of HCl+ becomes weaker in water clusters, whereas the hydrogen bond of H−O becomes stronger. The molecular charges on the HCl moiety were +0.93 in the 1:1 complex and +0.87 in HCl+(H2O)4. The hole was more widely delocalized over the water cluster in the latter case. Thus, the water cluster slightly affects the electronic states of HCl+. The electrostatic effects of the water clusters accelerate the time of PT in HCl+(H2O)n. 3.6. Effects of Zero-Point Energy (ZPE) on the Reaction Mechanism. The importance of ZPE on the reaction mechanism was pointed out in previous studies.44−51 In this section, the effects of ZPE on PT time in HCl(H2O)n+ are examined. First, ZPE simulations of neutral systems, HCl(H2O)n, were carried out at the MP2/6-311++G(d,p) level. Second, the geometries and velocities of atoms were selected from the ZPE simulations. Next, direct AIMD calculations were carried out for cation systems. The results are presented in Table 1 (ZPE). The kinetic energy, intermolecular distance, and angle of sample simulation (n = 4) are given in the Supporting Information.

Figure 8. Energy diagram for the HCl−H2O 1:1 reaction system. IP means the ionization potential (in eV) of HCl−H2O. The values indicate the relative energies (in kcal/mol).

decreases with increased size of the cluster cations until it reaches a limiting value at n = 4−5. To elucidate the origin of the cluster size dependency of the PT time, the intermolecular distance of each water cluster was analyzed (section 3.5). The reaction time of PT was strongly dependent on the intermolecular distance between HCl and H2O. The difference in the time of PT is caused by the difference of the hydrogen bond in n = 1−5; short hydrogen bonds lead to fast PT. In addition, the electrostatic effects of the water cluster slightly accelerate the time of PT.

Table 1. Time of PT (in fs) in HCl+(H2O)n Obtained from Direct AIMD Calculations at the MP2/6-311++G(d,p) Levela n

non-ZPE

ZPE

A

B

1 2 3 4 5

14.3 9.8 7.1 6.7 6.8

13.1 10.1 7.4 5.8 5.9

13.8 9.5 6.7 5.7 5.6

12.0 10.5 7.4 5.8 5.9

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.7b05112. Complementary data including NPA charges, snapshots of [HCl(H2O)n]+ (n = 2, 3, and 5), and results of zeropoint energy simulation of HCl(H2O)n (n = 4) (PDF)

a

ZPE and non-ZPE mean the results of direct AIMD calculations including zero-point energies or not included, respectively. Notations of A and B are given in the Computational Details section.

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The time of PT including ZPE was significantly close to that of non-ZPE because the PT reaction in HCl+(H2O)n has no activation barrier and the potential energy surface is composed of a purely steep slope. The time of PT calculated at the levels of A and B (see the Computational Details section) was also close to the results of ZPE and non-ZPE, indicating that the effects of the calculation level are negligible in the present system. 3.7. Energy Diagram of the Reaction. The direct AIMD calculations were carried out at the MP2/6-311++G(d,p) level. To determine the level of theory, the energy diagram of the reaction system was calculated using the CCSD(T) method and compared with the result of the MP2 method. The results are presented in Figure 8. The hydration energies of HCl were calculated as ΔEhyd = 6.5 (MP2) and 5.8 kcal/mol (CCSD(T)). Ionization potentials of the HCl−H2O complex calculated by MP2 and CCSD(T) were IP = 11.5 and 11.4 eV, respectively, and available energies of the Cl−(H3O+) complex were ΔEavail = 27.7 (MP2) and 27.5 kcal/mol (CCSD(T)). The dissociation energy of Cl from the complex for MP2 and CCSD(T) were ΔEdiss = 10.6 and 10.2 kcal/mol, respectively. Thus, the potential energy surface obtained by MP2 was in excellent agreement with that of CCSD(T).

AUTHOR INFORMATION

ORCID

Hiroto Tachikawa: 0000-0002-7883-2865 Notes

The author declares no competing financial interest.

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ACKNOWLEDGMENTS The author acknowledges partial support from JSPS KAKENHI Grant Number 15K05371 and MEXT KAKENHI Grant Number 25108004.

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REFERENCES

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4. CONCLUSIONS The results show that the reaction time of PT is strongly dependent on the cluster size (n = 1−5). The time of PT 5242

DOI: 10.1021/acs.jpca.7b05112 J. Phys. Chem. A 2017, 121, 5237−5244

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DOI: 10.1021/acs.jpca.7b05112 J. Phys. Chem. A 2017, 121, 5237−5244