Photochemistry of Hydrogen Halides on Water Clusters: Simulations of

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Photochemistry of Hydrogen Halides on Water Clusters: Simulations of Electronic Spectra and Photodynamics, and Comparison with Photodissociation Experiments Milan Oncak and Petr Slavícek* Department of Physical Chemistry, Institute of Chemical Technology Prague, Technicka 5, Prague 6 and J. Heyrovsky Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejskova 3, 182 23 Prague 8, Czech Republic

Michal Farník* J. Heyrovsky Institute of Physical Chemistry, v.v.i., Academy of Sciences of the Czech Republic, Dolejskova 3, 182 23 Prague 8, Czech Republic

Udo Buck Max-Planck Institut f€ur Dynamik und Selbstorganisation, Bunsenstr. 10, D-37073 G€ottingen, Germany

bS Supporting Information ABSTRACT: The photochemistry of small HX 3 (H2O)n, n = 4 and 5 and X = F, Cl, and Br, clusters has been modeled by means of ab initio-based molecular simulations. The theoretical results were utilized to support our interpretation of photodissociation experiments with hydrogen halides on ice nanoparticles HX 3 (H2O)n, n ≈ 102-103. We have investigated the HX 3 (H2O)n photochemistry for three structural types: covalently bound structures (CBS) and acidically dissociated structures in a form of contact ion pair (CIP) and solvent separated pair (SSP). For all structures, we have modeled the electronic absorption spectra using the reflection principle combined with a path integral molecular dynamics (PIMD) estimate of the ground state density. In addition, we have investigated the solvent effect of water on the absorption spectra within the nonequilibrium polarizable continuum model (PCM) scheme. The major conclusion from these calculations is that the spectra for ionic structures CIP and SSP are significantly red-shifted with respect to the spectra of CBS structures. We have also studied the photodynamics of HX 3 (H2O)n clusters using the Full Multiple Spawning method. In the CBS structures, the excitation led to almost immediate release of the hydrogen atom with high kinetic energy. The light absorption in ionically dissociated species generates the hydronium radical (H3O) and halogen radical (X) within a chargetransfer-to-solvent (CTTS) excitation process. The hydronium radical ultimately decays into a water molecule and hydrogen atom with a characteristic kinetic energy irrespective of the hydrogen halide. We have also investigated the dynamics of an isolated and water-solvated H3O radical that we view as a central species in water radiation chemistry. The theoretical findings support the following picture of the HX photochemistry on ice nanoparticles investigated in our molecular beam experiments: HX is acidically dissociated in the ground state on ice nanoparticles, generating the CIP structure, which is then excited by the UV laser light into the CTTS states, followed by the H3O radical formation.

I. INTRODUCTION In this work, we focus on two interrelated aspects of water particles doped with hydrogen halides: ground state chemistry (acidic dissociation) and photochemistry. The primary focus is on the latter topic, that is, on light-induced processes in HX 3 (H2O)n systems. The photochemistry is, however, controlled by the corresponding ground state structure. Therefore, both the acidic dissociation in the ground state and the photochemistry in the excited states are investigated in parallel in this paper. The acidic ionization of hydrogen halides in water and on ice surfaces, HX þ H2O f X- þ H3Oþ (X = F, Cl, Br, I), attracts r 2011 American Chemical Society

broad attention of both chemists and physicists for two major reasons. First, the acidic dissociation of hydrogen halides is the simplest prototype of this kind of reaction. It is therefore ideal for the exploration of the dissociation mechanism at the molecular level. Second, hydrogen halides in/on water and ice have gained Special Issue: Victoria Buch Memorial Received: November 26, 2010 Revised: January 3, 2011 Published: January 25, 2011 6155

dx.doi.org/10.1021/jp111264e | J. Phys. Chem. A 2011, 115, 6155–6168

The Journal of Physical Chemistry A widespread interest in the practical context of atmospheric chemistry, namely, the ozone depletion process.1-5 For example, hydrogen chloride serves as a reservoir of atmospheric chlorine due to its photochemical stability even at stratospheric conditions. Once the HCl molecule is adsorbed on the surface of ice particles in polar stratospheric clouds, it can be transformed into molecular chlorine Cl2 via ground state reactions starting with the acidic dissociation. The chlorine molecule can then be readily photolyzed in the stratosphere and ozone destructing chlorine Cl radicals are formed.6 Thus, the research in stratospheric chemistry also ignited interest in the hydrogen halide photochemistry. While there is no doubt that HCl is the most important hydrogen halide from the point of view of atmospheric chemistry, it is important to compare its behavior to the other hydrogen halides. Hydrogen halides are on the one hand similar, but on the other hand they differ significantly both in the ground and in the excited states. One property that changes in the HX series is the acidity. Hydrogen fluoride is a weak acid, with pKa = 3.2. However, it has been recently argued that even HF might under certain conditions still acidically dissociate.7,8 The acidity strength then increases from HCl to HBr, with HI being the strongest acid. The hydrogen iodide is also the easiest hydrogen halide to photodissociate in its covalent state (absorption maximum ∼ 120 nm for HF, 155 nm for HCl, 180 nm for HBr, and 225 nm for HI) and also upon the acidic dissociation (the CTTS transition have their maxima at about 175 nm for Cl-, 200 nm for Br-, and 230 nm for I-).9,10 The acidic dissociation of hydrogen halides on/in water has been addressed by numerous experimental1,11-20 and theoretical8,21-30 studies. The essential question addressed by many studies of small hydrogen halide-water clusters is: How many water molecules are needed to trigger the acidic dissociation? While the general agreement is that for HCl, HBr, and HI the number is quite small (below 5), the precise number is still a matter of some controversy.11,12,31-36 Experiments and calculations most relevant in the context of atmospheric science explore hydrogen halides (mostly HCl) on bulk ice surfaces.13-19 Here, the acidic dissociation represents already quite a complex process. The dissociation depends on many parameters such as temperature, surface coverage, and ice type. Experiments set the minimum temperature for the acidic dissociation somewhere between 80 and 120 K. Another important question is in which form the acidically dissociated structures emerge, contact ions versus solvent separated ions, H3Oþ as Zundel or Eigen structure, and so on. These questions can conveniently be addressed by IR spectroscopy combined with ab initio calculations, as was done for example by Devlin and Buch.37,38 Photoinduced processes in HX/water systems have been studied to a much lesser extent compared to the acidic dissociation. It follows from several studies of Domcke and Sobolewski and others that the light-initiated processes in covalently bound structures are rather different from the photochemical reactions in acidically dissociated species.39-43 In the first case, only local excitations take place, while the processes including states of a charge-transfer-to-solvent (CTTS) character can occur after the acidic dissociation. The CTTS processes have been extensively studied for many decades,44 in part because of their role in the photochemical generation of solvated electrons.44 It is worth mentioning in this context that the H3O radical formed within the CTTS process in the HX/H2O system can actually be viewed as a form of the solvated electron.41,45,46

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In our laboratory, we have recently investigated the photochemistry of large water particles doped with different hydrogen halides (HCl, HBr, and HI)42,47-49 in a cluster beam experiment. These studies followed our previous exploration of hydrogen halides adsorbed on rare gas atoms.48-56 The rare gas clusters can conveniently serve as a reference point. They do not initiate chemical changes in the HX molecule, nevertheless, they can still play the role of solvent with just mechanical effects on the photodissociation. We will discuss our recent experiments with HX molecules on ice nanoparticles in more detail in section IV. At this point, let us just briefly summarize the major findings from these experiments. We came to a tentative conclusion that for all HCl, HBr, and HI hydrogen halides the following scenario takes place: (1) hydrogen halides acidically dissociate on the surface of ice nanoparticles; and (2) charge-transfer-to-solvent states are excited upon the photon absorption and subsequently the neutral hydronium H3O and X radicals are formed. Both these products are of great interest. The halogen atom radicals initiate further reactions, such as the ozone destruction cycle, as discussed above. The H3O radical is maybe an even more exciting species; this radical probably plays an important role in the photochemistry of water and water solutions in general.42,57,58 The hydronium radical was also studied in the gas phase.59-63 As mentioned above, the hydronium radical has been proposed as a model for the solvated electron. Its electronic structure in a solvated state is somewhat unclear: Is the electron localized within the molecule or is there some sort of H3Oþ 3 3 3 eion pair formed, similarly as, for example, in the case of the hydrated sodium?64 In which electronic state is the H3O radical formed? How stable are various hydronium structures? In this paper, we complement our previous mostly experimental studies by an extended theoretical investigation of the HX 3 (H2O)n system. Our goal is 2-fold: First, to rationalize and confirm the experimental observations, and second, to provide molecular details which are not directly accessible to the current experimental measurements. We employ a whole plethora of theoretical methods, including ab initio-based path integral simulations to explore the ground state structure and methods of nonadiabatic dynamics for tracking the events initiated by the light absorption. Dynamic calculations are important not only because they offer time scales of the processes under study, but they also enable us to distinguish the relative importance of different reaction channels. Our calculations are based on various electronic structure methods, ranging from single-reference (TD)DFT, MP2, and EOM-CCSD to multireference CASSCF, CASPT2, and MRCI approaches. We use a small cluster model with four or five water molecules solvating HX. We then calculate (1) the ground state structure considering the nuclear quantum effects; (2) the absorption spectra; and (3) the nonadiabatic dynamics following the photon absorption. (4) We also investigate the photochemistry of the hydronium radical as a central structure in aqueous photochemistry. We compare photochemical mechanisms and measurable quantities between covalently bound hydrogen halides and ion pairs, either contact ones or solvent separated. We also discuss the transition from our limited model systems with several water molecules to the bulk limit. The results are then critically compared with our photodissociation experiments and a unified view on the photochemistry of hydrogen halides on water or ice particles is provided. The paper is organized as follows: In section II we describe the theoretical methods used, results of our simulations are then presented in section III. Section IV briefly summarizes the 6156

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The Journal of Physical Chemistry A

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Figure 1. Solvated hydrogen halide clusters used as model systems in the present study. Structures are optimized at the MP2/aug-cc-pVDZ level of theory.

previous photodissociation experiments on HX on ice nanoparticles and these experiments are discussed together with the current calculations to provide a unified view on the photochemistry of hydrogen halides adsorbed on water or ice. Finally, section V concludes the paper.

II. SIMULATION METHODS Our simulation protocol includes three major steps. In the first one, we have sampled structure distributions in the ground state, in the second step, we have calculated electronic absorption spectra for the different investigated structural types, and in the third step, we have investigated the nonadiabatic dynamics of HX 3 (H2O)n clusters in the first excited state S1 and H3O 3 (H2O)n clusters in the ground electronic state D0. The electronic structure of the clusters in the ground state is described at the DFT/BHandHLYP and MP2 levels of theory. Electronically excited states of the HX 3 (H2O)n clusters were described both at the single-reference level (TDDFT/CAMB3LYP and EOM-CCSD methods) and using multireference approaches to account for static correlation (CASSCF and CASPT2 methods). The functional used (CAM-B3LYP65) was chosen as it does not suffer from the spurious charge transfer problem. For the majority of the calculations we have used the 6-31þþg** basis set for H, O, F, and Cl atoms and Stuttgart RLC effective core potential (ECP28MWB) for Br.66 The bromine basis set was further augmented by s, p, and d functions with exponents of 0.074, 0.018, and 0.601, respectively. We have tested the basis set effect on excitation energies of HX 3 (H2O)5 clusters in Figure 1. When passing from 6-31þþg** to aug-cc-pVTZ basis set, the mean unsigned error of first excitation energies was calculated to be 0.03 eV. We thus conclude that the excitation energies are described satisfactorily with the 6-31þþg** basis set.

The nuclear ground state density was sampled either using ground state wave functions within the harmonic approximation or, alternatively, using path integral molecular dynamics (PIMD). When sampling with the harmonic approximation at the temperature of 0 K, we completely neglect all thermal and anharmonic effects. Both effects are covered within the PIMD approach. For floppy systems (such as solvated chromophores), the anharmonicity effects can potentially be of some importance. The calculated ground state densities were first used to calculate electronic absorption spectrum using the reflection principle approximation. This allows us to estimate positions, widths, and intensities of the absorption spectra for the simulated species. Details of the method are described in our previous work.67 The ground state vibrational harmonic wave function was calculated with the MP2/6-31þþg** method. Excitation energies were calculated at 1000 points according to their transition probability. Frequencies below 500 cm-1 were neglected as the harmonic approximation is inadequate for such low modes. In the case of PIMD, we have run one trajectory for each cluster on the BHandHLYP/6-31þþg** potential energy surface, with a time step of 30 au, total length of 22000 frames, and 10 random walkers. The system was thermalized at 250 K using a NoseHoover thermostat of four chains, with the Nose-Hoover mass of 0.2 au; 1000 geometries sampled from the PIMD runs (after subtracting initial 2000 frames accounting for system thermalization) were then used for the spectra modeling. The first 15 electronically excited states were utilized in the spectra simulation. To account for bulk solvation, we have employed the dielectric model, in particular, the polarizable continuum model (PCM).68 Note that only the optical part of the solvation response has to be taken into account for vertical processes, that is, we have used the nonequilibrium solvation scheme.69 6157



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Table 1. Relative Energies (in kcal/mol) of Model Clusters Used in This Study (See Figure 1)a isomer HF 3 (H2O)4

HCl 3 (H2O)4

HBr 3 (H2O)4

HF 3 (H2O)5

HCl 3 (H2O)5

HBr 3 (H2O)5

DFT/BHandHLYP/6-31þþg**

MP2/6-31þþg**

MP2/aug-cc-pVDZ

MP2/aug-cc-pVTZ

CBS

0.00 (0.00)

0.00 (0.00)

0.00 (0.00)

0.00 (0.00)

CIP

4.23 (3.81)

3.81 (3.22)

2.73 (2.25)

2.91 (2.43)

SSP

12.51 (13.16)

11.60 (11.97)

9.44 (10.06)

10.21 (10.83)

CBS

2.76 (0.00)

0.00 (0.00)

3.27 (0.76)

4.00 (1.50)

CIP

2.56 (2.03)

2.21 (3.76)

2.45 (1.74)

2.66 (1.96)

SSP

0.00 (0.38)

0.52 (3.30)

0.00 (0.00)

0.00 (0.00)

CBS

6.70 (3.30)

3.09 (0.00)

6.77 (3.97)

8.04 (5.24)

CIP SSP

2.02 (1.68) 0.00 (0.00)

1.93 (1.35) 0.00 (0.11)

1.92 (1.71) 0.00 (0.00)

2.13 (1.93) 0.00 (0.00)

CBS

0.16 (1.69)

0.00 (0.70)

0.00 (0.64)

0.00 (1.37)

CIP

0.00 (0.00)

0.40 (0.00)

0.73 (0.00)

0.41 (0.00)

SSP

6.18 (7.15)

6.02 (6.45)

5.66 (5.99)

6.10 (7.15)

CBS

5.09 (3.68)

1.35 (0.00)

3.59 (2.51)

4.47 (3.39)

CIP

0.16 (0.00)

0.00 (0.09)

0.00 (0.00)

0.02 (0.00)

SSP

0.00 (0.02)

0.35 (0.69)

0.10 (0.29)

0.00 (0.20)

CBS CIP

8.91 (7.13) 0.74 (0.60)

4.39 (2.26) 0.25 (0.14)

7.32 (5.63) 0.42 (0.30)

9.32 (7.62) 0.46 (0.33)

SSP

0.00 (0.00)

0.00 (0.00)

0.00 (0.00)

0.00 (0.00)

a

ZPE-corrected values are given in parentheses. Energies of clusters with aug-cc-pVTZ basis set are calculated for clusters optimized with the aug-ccpVDZ basis set, using the corresponding zero-point correction.

We have modeled the nonadiabatic dynamics on the excited state with the Full Multiple Spawning (FMS) method.70,71 For HX 3 (H2O)4 clusters, we used the active space of four electrons in five orbitals (4,5). CASSCF calculation with this active space was found to provide excitation energies close to the EOMCCSD and CASPT2 values (see Supporting Information). A total of 30 dynamical trajectories were calculated for each isomer, with a time step of 30 au. During the runs, the new nuclear basis was spawned on the lower electronic state whenever nonadiabatic coupling exceeded 5 au (the independent first generation approximation was used). Initial conditions were sampled from the Wigner distribution as retrieved from the vibrational wave function calculated at the MP2/6-31þþg** level of theory. Clusters were simulated for 0.5 ps or until the dissociation event took place (dynamics was stopped when the respective O-H or H-X distance exceeded 7 Å). We have also simulated the structure and dynamics of the H3O radical using multireference CASSCF, CASPT2, and MRCI methods in various active spaces. In the case of the bare H3O radical, various active spaces up to the full valence space of 9 electrons in 7 orbitals (9,7) were used. For larger clusters, either the (1,1) or (5,5) active space was employed. In these active spaces, CASSCF or CASPT2 molecular dynamics was performed for 1.5 ps (0.75 ps for the H3O 3 (H2O)8 cluster) or until the dissociation event had taken place (O-H distance of 7 Å was chosen as a threshold of dissociation). A total of 40 runs were performed for each isomer and each method, with a time step of 30 au and with initial conditions sampled from the Wigner distribution of MP2/6-31þþg** (H3O, H3O 3 (H2O)3) and DFT/B3LYP/6-31þg* (H3O 3 (H2O)8) vibrational wave function. In the case of excited state calculations, active spaces of (9,7) for the H3O radical and (3,4) for solvated H3O 3 (H2O)n, n = 2, 4, and 6, clusters were used, with a state average of two doublet states, corresponding to one 3s and one 3p electronic states (see below). Conical intersections were searched by internal algorithms, as implemented in the Molpro quantum chemistry code.72

For calculations, Molpro72 and Gaussian73 quantum chemical packages were used. For nonadiabatic molecular dynamics, FMSMolpro code was employed.74

III. RESULTS A. Ground State Structure of HX 3 H2On. One of the principal goals of this study is to explore differences in excited state properties of HX 3 (H2O)n clusters. We will consider three structural types (Figure 1): covalently bound structures (CBS), in which the hydrogen halide stays intact, contact ion pairs (CIP), where the HX acidically dissociates and the anion formed stays in direct contact with the hydronium cation, and finally, solvent separated pairs (SSP), where the two ions formed are separated by at least one water solvent molecule. To avoid unnecessary computational expenses, we have performed our simulations on the smallest possible system, where all isomers already represent stable local minima. As was discussed in the Introduction, the acidic dissociation of heavier hydrogen halides starts at about 3 or 4 water molecules, even though the dissociated structure is not necessarily a global minimum. In our study, we have therefore concentrated on small clusters with 4 or 5 water molecules (see Figure 1). For these species, all possible structural motifs are present, that is, HX 3 (H2O)n can form a covalently bound structure and both contact and solvent separated ion pairs. The calculated relative stability of different HX 3 (H2O)n, n = 4 and 5, clusters is summarized in Table 1. Two general trends are observed: With increasing proton number of halide atoms, ion pair structures are stabilized with respect to the CBS isomers; stabilization of ion pair structures is also observed when switching from four to five solvating water molecules. Thus, the most stable isomer of the HF 3 (H2O)5 cluster is still CBS (with CIP closer than 1 kcal/mol), while for both HCl 3 (H2O)5 and HBr 3 (H2O)5 clusters, the CIP and SSP structures are the minima. Zeropoint energy may invert the stability when the energy differences 6158



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Figure 2. Absorption spectra of HBr 3 (H2O)5 clusters calculated at the CAM-B3LYP/6-31þþg** level of theory, with a different sampling of the ground state, harmonic approximation at zero temperature (full line), and PIMD (dashed line).

are under 1 kcal/mol. Otherwise, the structure is defined by energy minima. From the methodological point of view, the BHandHLYP/6-31þþg** approach can be seen to be in quite good agreement with the MP2/aug-cc-pVXZ method, at least as far as cluster energetics is concerned (see Table 1). The conclusions drawn are fully consistent with other ab initio studies on small solvated hydrogen halides clusters.8,21-29 A special comment should be given on the CIP structure of HF 3 (H2O)n clusters. While, for example, the CIP structure of HF 3 (H2O)5 has a relatively short H-F bond of 1.05 Å (as compared to 0.93 Å in bare the HF molecule), only 3.3 kcal/mol are needed to increase this distance to 1.4 Å and to form an O-H bond of 1.06 Å (all values given at the MP2/6-31þþg** level of theory). These clusters may be thus viewed as semidissociated. For small clusters, the most stable isomer can be either the contact or solvent separated pair. Because we attempt to mimic the structure of adsorbed hydrogen halide, we assume that the CIP structural type is more probable: the formation of SSP would require ice structure perturbations that bring another energetic expense. The contact ion pair, on the other hand, can be formed within the quasi-liquid layer, even for solid clusters.14,16,37,75 B. Excited Electronic States and Electronic Absorption Spectra. Absorption spectra represent a key quantity for modeling both the atmospheric photochemistry of adsorbed hydrogen halides and the photodissociation experiment. In our previous work,42 we have already provided an estimate how the absorption spectra of hydrogen halides shift upon acidic dissociation. Here, we explore this issue in more detail. The character of the excitation depends on both the hydrogen halide and the type of cluster. In the case of CBS structures, the first excitation is localized on the water molecules for clusters with solvated HF and on the hydrogen halide for HCl and HBr. All these excitations lead to the dissociation of the respective O-H, Cl-H, and Br-H bonds. On the other hand, when the hydrogen halide is acidically dissociated and the H3Oþ moiety is formed, the charge transfer to solvent state emerges. The excitation can then be described as a transition from the p orbital on the halide anion (in the case of F- combined with water oxygen p orbitals) to the H3O moiety. In the current study, we calculate the absorption spectra within the reflection principle. The density in the ground state is calculated using the PIMD approach. In this way, both the quantum and thermal fluctuations are properly taken into account (providing that the simulation is converged). We first

Figure 3. Absorption spectra of HX 3 (H2O)5 (X = F, Cl, and Br) clusters calculated at the CAM-B3LYP/6-31þþg** level of theory; the ground state is sampled with the PIMD method. Calculated absorption spectra of bare HX molecules are shown for comparison.

address the question whether the effects of anharmonicity and finite temperature influence the calculated spectrum. In Figure 2, we compare the absorption spectrum of HBr 3 (H2O)5 in three different forms (CBS, CIP, SSP) calculated within the harmonic approximation and using the PIMD technique. The basic shape of the spectrum is identical, yet there is a slight red shift for the PIMD-based spectrum, of about 0.2 eV. Similar phenomena, even though less pronounced, can also be observed for the other members of the hydrogen halide family (the spectra are shown in SI). The conclusion is that, while the simulated absorption spectrum based on a harmonic wave function provides a surprisingly good estimate for such a floppy system as HX 3 (H2O)n, for a quantitative modeling, more advanced approaches are needed. This is especially true for atmospheric simulations where the red tail of the spectrum plays a central role. The absorption spectra calculated within the PIMD protocol for HF 3 (H2O)5, HCl 3 (H2O)5, and HBr 3 (H2O)5 species in the three different structures considered (CBS, SSP, and CIP) are shown in Figure 3. The absorption energies shift to lower values as we move from HF to HBr. The difference is much more pronounced for the acidically dissociated structures than for the covalently bound ones. In the case of HF 3 (H2O)5, the spectrum does not significantly change upon the acidic dissociation of the initial cluster, as the hydrogen fluoride molecule is readily regenerated during dynamics due to its pronounced stability (see Table 1). The first absorption band at lower wavelength can, in all cases, be attributed to water. Therefore, water photodissociation will take place upon excitation. Water and HCl photodissociation compete at the onset of the HCl 3 (H2O)5 absorption. This is consistent with the overlapping absorption spectra of HCl and H2O molecules. A significant red shift occurs upon the acidic dissociation. The absorption spectrum then extends up to 225 nm for CIP and 235 nm for SSP. In this way, absorption can take 6159


The Journal of Physical Chemistry A place even in atmospherically relevant spectral regions. The main absorption peak for the covalently bound HBr 3 (H2O)5 structure starts at about 205 nm. There is, however, a pronounced read tail in the absorption spectrum that originates from the temporary formation of the Br 3 3 3 H 3 3 3 O motif in the PIMD run. The first peak can clearly be assigned to the nσ* excitation of HBr. Compared to HCl, the bromine system starts to absorb at much lower energies upon the acidic dissociation. For CIP, the spectrum extends up to 250 nm and for SSP up to 265 nm. Hydrogen iodide is not included in our study because the absorption spectrum is complicated by a strong spin-orbit coupling in iodine. However, our recent calculations show that HI follows the general trend outlined above.49 The absolute value of the absorption cross section for acidically dissociated structures is significantly larger than this quantity for the bare molecules. This is not surprising because the character of the excitation is completely different after the acidic dissociation than for isolated hydrogen halide. Interestingly, the absorption intensity is also elevated for solvated HBr in its covalent state upon the hydration and the energy is shifted to higher excitation energies. The experiments that we aim to rationalize here were performed on clusters much larger than five water molecules. The same is true for atmospheric particles, which are in the size region from nanometers to micrometers. Absorption modeling for such large particles is not technically feasible. We can, however, take advantage of the localized nature of the excitation. It is certainly localized for the covalently bound structure. The situation is less clear for dissociated structures in which the electron is removed from the anionic precursor to the solvent (charge transfer to solvent process). The electron will presumably stay close to the hydronium cation, forming a H3O radical or more generally a H3Oþ 3 3 3 e- ion pair. Thus, only a limited number of water molecules are involved in the process and the remaining ones can be considered as spectator molecules. As such, they can be modeled as dielectric continuum, for example, utilizing the polarizable continuum model. Within this model, we can further distinguish optical and orientational effects of the solvent. For the absorption process, only the optical part of the solvation response is taken into account because the solvent atoms do not have enough time to reorient within the time span of the absorption process. Note also that embedding the HX 3 (H2O)n clusters in the polarizable continuum corresponds to the internally solvated HX rather than HX adsorbed on the surface. Jungwirth and Bradforth have, however, shown that for the CTTS process the difference in absorption spectra between bulk and surface solvated precursors is rather limited.76 Figure 4 shows the absorption spectra of HX 3 (H2O)n clusters (in CBS, CIP, and SSP forms) immersed in the polarizable continuum. Predictably, the further solvation leads to a relatively large blue shift of the absorption spectra. The shift is not very much pronounced for the covalently bound structures since the electron distribution does not change too much upon the excitation. However, the effect on the CTTS states is dramatic. This can be rationalized purely in terms of electrostatics. In the ground state, the large dipole moment of the H3Oþ 3 3 3 X- pair is supported by the polarization of the solvent. Upon the photon absorption, the H3O and X radicals are formed. The H3O 3 (H2O)nX structure still bears some dipole moment because the extra electron in the H3O radical can be rather detached from the H3Oþ “core”, yet the system will have a much smaller dipole moment after the excitation. Consequently, the splitting between

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Figure 4. Absorption spectra of HX 3 (H2O)5 (X = F, Cl, and Br) clusters calculated at the CAM-B3LYP/6-31þþg** level of theory with PIMD sampling of the ground state. Water solvation effects were included using the nonequilibrium PCM scheme.

Figure 5. Evolution of excited state energies of the HCl 3 (H2O)n clusters, optimized at the BHandHLYP/6-31þg* level of theory in the gas phase. Excitations were calculated at the CAM-B3LYP/6-31þþg** level of theory both in the gas phase and for clusters embedded in the dielectric continuum (PCM scheme).

the ground and excited states will increase and the spectrum will move to the blue part. This effect cannot be seen for the HF 3 (H2O)5 system, as the excitations are localized on water molecules. A significant shift is, however, observed for CIP and SSP structures of HCl 3 (H2O)5 and HBr 3 (H2O)5. In both cases, the onset of the absorption spectra shifts by about 0.2 eV for CBS (and all isomers of HF 3 (H2O)5) and 0.6 eV for CIP and SSP to higher excitation energies. The absorption of the acidically dissociated hydrogen halides can be compared to the CTTS spectra of halide anions in water. The CTTS spectrum peaks at 200 nm for bromine and at 180 nm for chlorine.9,10 The corresponding hydrogen halide peaks are shifted to higher wavelengths only by several nanometers. This suggests that the hydronium counterion does not play a decisive role in the CTTS process. 6160



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Table 2. Calculated Lifetimes of the Hydronium Radical and Kinetic Energies of the Dissociated Hydrogen Atomsa method

time/fs

Ekin/eV

H3O

CASSCF(1,1)

64.1 ( 51.7

1.53 ( 0.13

H3O H3O

CASSCF(5,5) CASPT2(1,1)

52.9 ( 43.1 53.7 ( 14.6

1.60 ( 0.20 1.09 ( 0.18

system

Figure 6. Dissociation of H3O radical along O-H coordinate, using constrained optimization with a fixed O-H distance, calculated with 6-31þþg** basis set, (9,7) active space, and one electronic state. Energy of the first excited state D1 calculated with two-state average is also supplied. For clarity, excited state is plotted only for lower O-H distances, as higher states come in along dissociation coordinate. Note that CASPT2 and MRCI curves almost coincide.

We can also ask whether the results are converged with respect to the quantum mechanical “buffer zone”, that is, whether the absorption spectra would be further shifted if n is increased for the HX 3 (H2O)n clusters in the dielectric continuum. Figure 5 shows that the further shift would be already rather small, for clusters embedded in the dielectric continuum the first excitation energy stays essentially constant. The excitation energies for gas phase clusters also seem to converge to the bulk limit in the range of 6.8-7.0 eV. Note also that the actual spectra would be finally shifted upward by a few hundredths of eV due to the insufficient basis used in our study (see section II). C. Dynamics of Hydronium Radical. The hydronium radical is the central species in the photochemistry of the hydrogen halides42 and of the water photochemistry.58 This radical, either in its ground or excited state, is formed within the charge transfer to solvent process during the photon absorption by CIP and SSP structures of HX 3 (H2O)n clusters (vide infra). We will therefore start with a brief discussion of the electronic structure and dynamics of this radical. The hydronium radical has a structure which is rather similar to that of the hydronium cation H3Oþ. This is related to the 3s Rydberg character of this species, that is, the extra electron is only loosely bound.61 This remains true also for the solvated H3O 3 (H2O)n cluster; the structure here can then be best described as the H3Oþ 3 3 3 e- ion pair. As an isolated radical, hydronium is a metastable species. As already pointed out by Sobolewski and Domcke,45 the radical is stabilized only by a small barrier. This barrier amounts according to our calculations to 0.08 eV at the CASSCF(9,7) and 0.16 eV at both CASPT2(9,7) and MRCI(9,7) levels, see Figure 6. Hydronium in the ground electronic state decays to the H2O þ H products. In this asymptote, the products are 1.28, 0.81, and 0.82 eV lower in energy (at the CASSCF(9,7), CASPT2(9,7), and MRCI(9,7) levels of theory, respectively) than the hydronium radical. The radical thus has only a very short lifetime in the ground state. Our dynamical calculations at the CASPT2 level provide an estimate of the lifetime of the H3O radical amounting to 40 fs, with the kinetic energy of the released hydrogen of about 1.1 eV (see Table 2). The CASSCF dynamics (which we use for HX 3 (H2O)n clusters) is in qualitative agreement with the CASPT2 results; the kinetic energy of dissociating hydrogens is, however, higher by about 0.5 eV. It should be noted that there are also present other reaction channels (e.g., formation of H2 molecule and OH radical); they, however, require much higher activation energy.61

a

H3O

CASPT2(5,5)

61.6 ( 42.2

1.07 ( 0.14

H3O 3 (H2O)3

CASSCF(1,1)

312 ( 290

1.25 ( 0.17

H3O 3 (H2O)3

CASSCF(5,5)

286 ( 179

1.22 ( 0.16

H3O 3 (H2O)3

CASPT2(1,1)

194 ( 174

0.66 ( 0.15

H3O 3 (H2O)8

CASSCF(1,1)

g390 ( 158

1.15 ( 0.20

Data calculated from molecular dynamics of the H3O 3 (H2O)n clusters. O-H distance of 7 Å was chosen as a threshold criterion for a completed hydrogen dissociation event. For H3O 3 (H2O)8 cluster, only 42% of trajectories dissociated in time of simulation (750 fs), and time of dissociation given is thus only a lower bound.

Figure 7. Structure of H3O 3 (H2O)n clusters used in this study. Shown are also spin densities calculated at the MP2/6-31þþg** level of theory with spin isovalues of 0.01 (n = 0) and 0.002 (n = 3 and 8).

The radical is further stabilized by solvation of other water molecules. We picked the solvated clusters of H3O 3 (H2O)n as those with one (n = 3) and two solvation layers (n = 8), see Figure 7. In these clusters, the kinetic energy of the dissociated hydrogen atoms is lowered. H3O is also more stable with respect to the dissociation, i.e. the radical will start to dissociate later. The first solvation layer shifts the time of hydrogen dissociation from about 60 to 300 fs and causes a decrease in the kinetic energy of the dissociated hydrogen atoms by 0.4 eV. The second solvation layer has a much smaller impact, shifting the time of dissociation up by at least another 100 fs (note that dissociation time given in Table 2 is only a lower bound due to a limited number of successful dissociation events) and slowing dissociating hydrogen atoms by another 0.1 eV. The kinetic energy of dissociating hydrogen atoms is lowered, as the H3O radical is effectively stabilized by surrounding water molecules. Longer time scales of the dissociation can be rationalized by the fact that hydrogen atoms need to move along the water wire to dissociate (or wait until the cluster slowly disintegrates). Also, the solvated H3O radical tends to delocalize the electron, as can be seen from the spin densities shown in Figure 7; this further stabilizes the H3O moiety with respect to the dissociation. We can thus expect that the hydronium radical in large clusters will have enough time to thermalize. If, however, the hydrogen atom is released, it would happen via an activated process, with a minimum excess energy. The hydrogen atom formed in this way will not be able to react again with water due to the larger activation energy for the H þ H2O f H3O reaction. Such hydrogen atom can then leave the cluster, with an energy that further decreases by the cage effect within the water cluster. We were also concerned about excited states of the H3O radical, as they can also be populated during the photodissociation 6161



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Figure 8. Points with low D1/D0 energy splitting of H3O, H3O 3 (H2O)4, and H3O 3 (H2O)6 clusters, optimized at the CASSCF(9,7)/ 6-31þþg** (H3O radical) and CASSCF(3,4)/6-31þþg** (other clusters) level of theory. Energies are given with respect to the corresponding D0 minimum. Energy with respect to the D1 energy in the D1 minimum geometry is given in parentheses.

experiment. Figure 6 shows that the hydronium radical does not dissociate in its first electronically excited state (D1, corresponding to the 3p Rydberg state). Such a conclusion was already drawn by Chulkov et al.77 in their study on the electronic structure of hydrated hydronium and the same stabilization was also found in our calculations for O-H dissociation in the H3O 3 (H2O)2 cluster. What are the reaction routes for the excited state hydronium? The radical could transfer its population via a conical intersection into the ground state and later dissociate in this state. Geometry and energetic accessibility of the conical intersection (CI) in fact depends substantially on the degree of solvation (see Figure 8). For the H3O radical itself, D0/D1 CI corresponds to the geometry with two dissociated O-H bonds, see Figure 8. While low in energy (0.16 eV compared to the D1 state energy in the D1 minimum at the CASSCF(9,7)/6-31þþg** level of theory), this CI can be accessed only by suppling a few eV of energy.63 The structure of this conical intersection explains why molecular hydrogen is often formed in the ring storage experiments upon collision of electrons with H3Oþ ions.59 On the other hand, when 3 or 5 water molecules are added, mimicking thus the minimal model of solvated H3O and solvated Zundellike structures with two potential H3O moieties (Figure 8), the region with low D0/D1 energy splitting comes geometrically much closer to the ground state structure while preserving its low energy with respect to the excitation energy. When the solvated hydronium radical is formed in the ring storage experiment, the almost exclusive product is the hydrogen atom.60 This is again rationalized by the structure of the conical intersection in this case. D. Photodynamics of Covalently Bound Structures. We will start by discussing the photochemistry of covalently bound structures of HX 3 (H2O)n clusters. The basic photochemical pathways are sketched in Figure 9. We will always concentrate on the events following the excitation into the first absorption band. For covalently bound structures, we can excite either hydrogen halides or water molecules. In the latter case, the primary event will be the O-H bond dissociation into free space. If, on the other hand, the hydrogen halide is excited, then its dissociation leads to a formation of transient H3O structure. The lifetime of this newly formed hydronium radical can be extremely short, it might last for just one O-H vibration, that is, the dissociated hydrogen is immediately reflected from the water molecule. Alternatively, another hydrogen from the H3O moiety can be released. For our model HX 3 (H2O)4 clusters, all reaction channels described above are actually observed, see Table 3. For HF 3 (H2O)4 in the CBS structure, only the water O-H dissociation takes place, within ∼40 fs and with the kinetic energy of

Figure 9. Possible reaction pathways of the covalently bound HX 3 (H2O)n clusters in the excited state. UV photons can excite the HX molecule to an A state, where the H-atom is transferred to the neighboring H2O molecule generating a short-lived H3O moiety from which either the transferred H0 -atom is dissociated (I) or another one (II). Alternatively, a water molecule is excited into an A state and can decay releasing an H-atom from water molecule (III).

Table 3. Reaction Channels (in %) for Processes Following the Excitation of HX 3 (H2O)4 Clusters into the First Excited State, as Obtained from the FMS Molecular Dynamics (see Figures 9 and 10)a (IV) isomer HF 3 (H2O)4

HCl 3 (H2O)4

HBr 3 (H2O)4

(I)

(II)

(III)

direct

after H-transfer

CBS

0

0

100

0

0

CIP

0

0

100

0

0

SSP

0

0

0

57

43

CBS

60

40

0

0

0

CIP

0

0

0

77

23

SSP

0

0

0

73

27

CBS

67

33

0

0

0

CIP SSP

0 0

0 0

0 0

60 63

40 37

a

Direct H-X dissociation (I), dissociation of O-H bond after collision with H-X hydrogen (II), direct H2O dissociation (III), and H3O dissociation, direct and after hydrogen transfer (IV).

dissociated hydrogen atoms of about 2 eV (see Tables 3 and 4). For both HCl 3 (H2O)4 and HBr 3 (H2O)4 clusters, direct hydrogen halide dissociation is observed in our dynamical simulations. The dissociated hydrogen atom then collides with water molecules and is reflected in about 60% of the trajectories, while the water hydrogen atom is dissociated in the other cases. For both hydrogen halides, the dissociation was calculated to occur in about 40 fs, with the kinetic energy of hydrogen atoms of 2.5 eV (see Table 4). Low difference of kinetic energies for both molecules (2.36 eV for HCl and 2.71 eV for HBr) reflects the fact that the higher vertical excitation energy for HCl is compensated by its higher bond dissociation energy. The kinetic energy is significantly larger than that observed in the current experiments on the hydrated HX. The kinetic energy above 2 eV, on the other hand, agrees well with the KED distribution measured for HBr 3 Arn clusters at 193 nm (wavelength close to the HBr absorption maximum).56,78 Note also that photodissociation for HCl 3 Arn at the same wavelength leads to slower products.55 E. Photodynamics of the Acidically Dissociated Structures. Quite different is the photodynamics following the charge 6162



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Table 4. Average Time before the Hydrogen Atom Dissociate upon HX 3 (H2O)4 Excitation and Kinetic Energy of the Dissociated Hydrogen Atomsa isomer HF 3 (H2O)4

HCl 3 (H2O)4

HBr 3 (H2O)4

a

time/fs

Ekin/eV

CBS

36.3 ( 9.4

2.10 ( 0.53

CIP

36.1 ( 8.7

2.14 ( 0.33

SSP

113.2 ( 45.4

1.66 ( 0.31

CBS

45.9 ( 7.4

2.36 ( 0.88

CIP SSP

69.5 ( 34.6 106.4 ( 32.3

1.72 ( 0.37 1.56 ( 0.27

CBS

43.9 ( 7.6

2.71 ( 0.87

CIP

102.4 ( 55.2

1.42 ( 0.54

SSP

143.2 ( 66.8

1.32 ( 0.48

Calculated from the FMS molecular dynamics starting in the S1 electronic state. Hydrogen is considered to be dissociated when X-H distance exceeds the threshold of 7 Å.

Figure 10. Possible reaction pathways of the acidically dissociated X- 3 H3Oþ 3 (H2O)n-1 clusters in the excited state. UV photons can transfer the species to a ground state of hydronium radical H3O(X), where the decay yielding the released H-fragment can proceed. Alternatively, the excited H3O(A) state can be populated, which is essentially bound but can relax via a conical intersection (CI) to the ground state, where the dissociation occurs.

transfer to solvent processes in the acidically dissociated structures (i.e., CIP and SSP), see Figure 10. The excitation leads to a transfer of the electron from the halogen anion into the water solvent. Halide and H3O radicals are created during the absorption. Depending on the excitation wavelength, either the ground or the excited state of the hydronium radical can be formed. The excitation immediately triggers the departure of the halogen radical from the cluster. At the same time, the hydronium radical will start to evolve. The hydrogen atom can move relatively freely along the water wire. Ultimately, the hydronium radical dissociates via a low lying transition state. When the excited state of the hydronium radical is formed, the system stays in the excited state for some time before the population is transferred into a state corresponding to the hydronium radical ground state. This is achieved via a conical intersection lying relatively high in energy (see section IIIC). Results of the photodynamics are quantified in the Tables 3 and 4. In all CIP and SSP clusters, the H3O radical is formed; the only exception is the CIP of the HF 3 (H2O)4 cluster where the direct O-H dissociation takes place (with energy and time characteristics analogous to that of the respective CBS structure). When the H3O radical is formed, it has a lifetime of about 100 fs

and produces hydrogen atoms of 1.3-1.7 eV kinetic energy. These energies are too high because of the CASSCF method used in our dynamical calculations. It has been shown in section IIIC that balanced inclusion of both static and dynamic correlation leads to the decrease of the hydrogen kinetic energy by about 0.6 eV. During the dynamic simulations, hydrogen transfer to neighboring molecules is observed in the minor part of the simulations. The dominating reaction channel is therefore a direct dissociation of the hydronium radical. While the process is ultrafast for small clusters, in the fully solvated system, the lifetime of the hydronium will probably be substantionally longer (compare with lifetime data in Table 2).

IV. DISCUSSION: UNIFIED VIEW OF HX 3 (H2)ON CHEMISTRY AND PHOTOCHEMISTRY FROM EXPERIMENT AND THEORY In this section, we discuss the theoretical results from this work in the context of our experiments to provide the overall picture of how the hydrogen halides behave on small water clusters and ice nanoparticles. Most of the experimental results discussed here have been published previously;42,47-49 therefore, only a very brief account of the experimental methods and the major findings will be given below first, before discussing them in the view of the new calculations. The large water clusters ∼ 102-103 (ice nanoparticles) were produced in a molecular beam experiment and doped by hydrogen halide molecules in a pickup cell filled with HX gas. The HX 3 (H2O)n clusters were interrogated by nanosecond UV laser pulses, and the arising H-fragments were detected by a time-offlight spectrometer. The H-fragment kinetic energy distribution (KED) is the main observable in our experiments. The UV wavelength of 193 nm was used to excite the molecules in clusters. In addition, overlapped 243 nm pulses were employed for resonance enhanced multiphoton ionization of H-atoms. In some cases (HI) the H-fragments were produced by the 243 nm laser alone. Further experimental details can be found in the corresponding publications.42,47-56 The question targeted by our experiments originally was whether the hydrogen halide was covalently bound or ionically dissociated on the ice nanoparticles. First evidence for the acidic dissociation was provided by the comparison between the photodissociation of hydrogen halides on Arn and on (H2O)n clusters, which pointed to a different photodissociation mechanism. The HX 3 Arn clusters were investigated in detail previously with the present experiment for HCl,55 HBr,50-53,56 and HI.54 The left column of Figure 11 shows representative H-fragment KED spectra of HX 3 Arn. The vertical arrows indicate the kinetic energies corresponding to the H-fragments from the direct photodissociation of HX molecules at 243 and 193 nm.79 The arrows labeled by X and X* correspond to the formation of the dissociation product in the ground X(2P3/2) and spin-orbit excited X(2P1/2) states, respectively. In all cases, a narrow peak at zero kinetic energy corresponding to the caged fragments is observed, and some contribution of relatively fast H-atoms from the direct exit of the fragments after the HX photodissociation. The relative ratio of the caged fragments and direct exit depends on the species and experimental conditions such as clusters size, and the detailed discussion can be found in refs 50-56. However, the general features of the KEDs are represented in Figure 11, and here we focus on the comparison with the photodissociation of HX on (H2O)n. 6163



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Figure 11. Kinetic energy distributions from HX molecules on Arn (left), X = I (top), Br (middle), and Cl (bottom). The dashed spectra show the KEDs from HX on (H2O)n clusters from the right column for comparison. Analogically, the right column shows the low energy part of the KEDs from HX 3 (H2O)n and the dashed lines show the HX 3 Arn spectra for comparison.

Table 5. Ratios of H-Fragment Signals from HX 3 (H2O)n Clusters to H Signals from the Deuterated Species HX 3 (D2O)n and DX 3 (H2O)n X= exciting

Cl

Br

wavelength λ

193 nm

193 nm

193 nm

243 nm

value

HX 3 (D2O)n DX 3 (H2O)n

2.7 ( 0.4

3.0 ( 0.3

3.1 ( 0.5

3.9 ( 1.0

3.0

1.1 ( 0.4

1.4 ( 0.2

1.6 ( 0.4

2.5 ( 1.0

1.5

I expected

The KED spectra from HX 3 (H2O)n clusters shown by the dashed lines in left column of Figure 11, on the other hand, contain only the slow fragments with energies below ≈0.5 eV. In the right column of Figure 11 this low energy part of the KEDs is shown in detail by solid lines (here the dashed lines show the corresponding HX 3 Arn spectra). The differences between the HX 3 Arn and HX 3 (H2O)n spectra could be explained by postulating the formation of the H3O radical in HX 3 (H2O)n clusters.80 The suggested mechanism starts with the acidic dissociation of the HX molecule in the ground state followed by the laser excitation to a CTTS state and then the transition into the biradical state occurs. The H3O radical can ultimately decay, yielding an H2O molecule and the H atom, which is detected. Several experimental findings supported this mechanism. (1). Double Isotope Substitution. The measurements with isotopic variants of HX and H2O provided a strong experimental evidence for the hypothesis that the detected H-atom originated from the H3O species. Assuming the hydronium radical generation from HX and H2O molecule (and no H/D scrambling) the H3O, H2DO, and HD2O would be produced in HX 3 (H2O)n, DX 3 (H2O)n, and HX 3 (D2O)n clusters, respectively. Therefore, the expected ratio of H-signals from these species would correspond to the number of H-atoms in these radicals, that is, 3:2:1. Table 5 summarizes the measured ratios of the H-fragment

signals from HX 3 (H2O)n clusters to H signals from the deuterated species HX 3 (D2O)n and DX 3 (H2O)n, which are generally in good agreement with the expected values.81 These ratios also suggest that the statistical H/D scrambling does not occur in the clusters, at least on the time scale of the present experiment ∼0.65 ms.82 Thus, the proposed model assumes the generation of a contact ion pair of rather local nature. (2). KED Spectra. It has been already mentioned above that the differences between HX 3 Arn and HX 3 (H2O)n spectra point to a completely different mechanism of the H-fragment formation in HX 3 (H2O)n rather than the direct HX molecule photodissociation. In addition, the spectra in Figure 11 for all three HX molecules are the same within the experimental error bars. The agreement between these spectra suggests that the H-fragments originate from the same species in all three systems, namely, from the H3O radical, rather than from the three different molecules. At this point, we shall discuss whether the simulations presented in this paper are consistent with the above observations and their interpretation. We have to be aware that size of particles in the experiment is much larger than the minimal model used for the calculations. This has several consequences. First, the cage effect can not be observed in our model because not enough solvent molecules are present to hinder the motion of fragments and to dissipate the energy. Second, the large water clusters are very likely solid and their structure is primarily defined by the interaction between water molecules rather than by the interaction with hydrogen halides. Finally, in the experiment we can not completely rule out the possible formation of hydrogen halide oligomers, yet the experimental results were rather insensitive to the average number of HX molecules picked up by the clusters. We will now discuss several aspects of our calculations in the view of the experiment: (1) The ground state structures have been calculated for HX 3 (H2O)n, n = 4 and 5. In this size range, the acidically dissociated structures (CIP, SSP) represent the stationary points on PES (i.e., stable energetic minima) for HCl and HBr at all implemented levels of theory. The calculations also show that the stability of the ionic structures increases with increasing n. The small clusters studied here theoretically are different from the bulk ice surfaces in many respects.14,16,37,75 Furthermore, the precise structure of adsorbed HX (at least for HCl) is to a large extent controlled by temperature, ice type or surface coverage. The calculations nevertheless show that the stability of the acidically dissociated ion pairs increases in order of the increasing strengths of the corresponding acid. For example, calculations for HI 3 (H2O)n49 show that acidic dissociation occurs already for n = 3. It is therefore very likely that the strongest acid in the series HI can be safely assumed to be acidically dissociated. Because the results of the photodissociation experiment are independent of the adsorbed hydrogen halide (HCl, HBr, and HI), we may assume that there are the same intermediate species, which is consistent with the acidically dissociated structural type. Typically, solvent separated structures represent the global minima for the small clusters. In the large clusters, however, formation of solvent separated structures would require diffusion of the hydronium defect into the ice lattice structure. In this view, the calculations are not in a contradiction with the double isotope experiment, which require CIP rather than SSP structures being present at the system. (2) The electronic absorption spectra have been calculated quantitatively for HX 3 (H2O)n, n = 5. The remarkable feature of 6164


The Journal of Physical Chemistry A these spectra for HCl and HBr is their significant red shift for both ionically dissociated structures CIP and SSP with respect to the spectra of CBS. This is again in qualitative agreement with the experimental findings. First, the measured H-signal is proportional to the absorption cross section. This signal increases by more than an order of magnitude when HX is deposited on (H2O)n rather than on Arn clusters of approximately the same size. It is not straightforward to compare these signals quantitatively due to the different expansion conditions for (H2O)n and Arn, which may result in different cluster densities in the beams. Yet, under the assumption that the densities would not be significantly different, the corresponding cross sections for HX 3 (H2O)n clusters would be more than an order of magnitude larger than for HX 3 Arn. This is quite in agreement with the calculated red shift of the spectra upon the ionic dissociation, which occurs for HX 3 (H2O)n, see Figure 3. The ratio of cross sections between gas phase and acidically dissociated structures at 193 nm exceeds a factor of 10 for both HCl and HBr. Note that for HBr the 193 nm cross section increases significantly even for the CBS structure. The electronic absorption spectrum for the CBS structure is, however, steeply falling in this spectra range. The absorption cross section for the acidically dissociated structures further increases once the structures immerse in dielectric continuum, mimicking thus the longrange solvation effects, see Figure 4. The experimentally observed increase in intensity can therefore be rationalized by the shift of the first absorption band caused by the acidic dissociation. One should keep in mind that the situation might still be different on the large ice nanoparticles yet the qualitative trend of cross section increase upon acidic dissociation will be preserved as the CTTS transition is of rather localized nature. We have also compared quantitatively the experimental signals at 193 nm from HBr 3 (H2O)n and HCl 3 (H2O)n clusters in our previous publication.42 Their ratio was about 7.4 ( 1.0, which is much smaller than the cross section ratio for HBr and HCl molecules, which is ≈25. Our previous calculations42 have shown that the significant decrease in this ratio can be a result of the spectral shift due to the acidic dissociation. The present calculations also qualitatively support this conclusion. The cross section ratios between HBr and HCl at 193 nm are around 1 for both CIP and SSP in Figure 3. The same holds true for SSP structure when long-range water solvation effects are included in Figure 4. The intensity ratio is increased for the CIP structure. This is due to the fact that we are already in the region of steep increase in the intensity, and the ratio is thus a strongly varying function of the excitation wavelength. The ratio for covalently bound structure would be extremely high according to our calculations. The clusters in the experiment should stay somewhere in between the gas phase and fully solvated result. Here, the hydrogen production rate for acidically dissociated structures for HBr and HCl are roughly comparable, while the much higher intensity of HBr should be observed for covalently bound structures. The assumption of the acidically dissociated state is therefore in the agreement with the hydrogen intensity measurements. It would also be highly desirable to measure the shape of the absorption cross section experimentally, which cannot be performed with our lasers. Nevertheless, we have recently obtained at least rough information about this shape for HI 3 (H2O)n, where the H-fragment signals were measured at 243 and 193 nm.49 These measurements were also in a good agreement with our calculations of the absorption cross section for HI 3 (H2O)n and confirmed the acidic dissociation structure.

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(3) Finally, new insight into the dissociation mechanism is provided by our dynamical calculations outlined in sections IIIC, IIID, and IIIE. These calculations show that the kinetic energy of the hydrogen fragments from covalently bound structures have much higher kinetic energies than observed in the experiment. The excitation of the acidically dissociated structures CIP and SSP yield the H3O radicals. These radicals dissociate on the ground state, independently of the electronic state (and therefore wavelength) in which they were created. Ultimately this will result in H-fragments with the same kinetic energy, independent of the fact that hydrogen halide is photodisociated. Photodissociation of acidically dissociated hydrogen halides therefore produces hydrogen atoms with characteristic universal kinetic energy. This characteristic kinetic energy was calculated to be 0.6 eV at the CASPT2 level for all acidically dissociated structures. The dissociation is an activated process, therefore the dissociated hydrogen atoms will mostly have energy close to its minimal possible value. In large water clusters, the characteristic energy of 0.6 eV represents an upper bound for the energy observed, because in large clusters, the hydrogen atom quickly dissipates its energy before it leaves the cluster. At the same time, the hydronium radical most likely will not be formed again because the hydrogen atom does not already have enough energy to overcome the reaction barrier. The above scenario is fully consistent with the experimentally observed data: slow fragments with KED essentially identical for HCl, HBr, and HI. Also, for HI, where the KEDs were measured at the two wavelengths of 243 and 193 nm, both KEDs had the same shape. It also follows from Table 3 that the majority of the dissociated hydrogen atoms leaves the hydronium radical directly, that is, the role of hydrogen exchange in the excited state is rather limited (although noticeable). This is an important finding in connection with the double isotope experiment. If there would be an extensive exchange along hydrogen bond wire, it would be difficult to explain the hydrogen production ratio between experiments with deuterated HX and deuterated water.

V. CONCLUSIONS We have investigated HX 3 (H2O)n, n = 4 and 5, X = F, Cl, and Br, clusters in their different structures (covalently bound structure, contact ion pair, and solvent separated pair) and critically compared our findings with experiments performed previously in our laboratory on hydrogen halides adsorbed on ice nanoparticles. The ground state structures of these species and their corresponding absorption spectra have been calculated. Our calculations covered both thermal and quantum effects, including anharmonicities, within an approach combining path integral simulations to sample ground state density with the reflection principle method to obtain absorption spectra. We have calculated absorption spectra for different structural types (CBS, CIP, SSP) and discussed the transition from the finite size cluster to bulk. For all the structures, nonadiabatic dynamics within the Full Multiple Spawning method was performed. Reaction paths upon the photoexcitation and distribution of the reaction products have been analyzed. We have also investigated separately the dynamics of the H3O radical, which seems to emerge as a structure central to the water photochemistry. The main findings of our study can be summarized as follows: • For all the studied systems, HX 3 (H2O)n, n = 5, the energetically lowest structure is always the acidically dissociated one either in the CIP or SSP configuration. 6165



•

•

•

•

•

For small clusters, this can be true even for HF, which is a very weak acid. A strong red shift of the absorption spectra has been calculated for both ionic structures CIP and SSP. These spectra are qualitatively comparable with the experimentally measured H-fragment signals from the large HX 3 (H2O)n, ≈ 102-103, clusters leading to the conclusion that the HX molecules are ionically dissociated in the ground state on the ice nanoparticles. The long-range solvent effects introduce a blue shift of the spectra of the ionic species. This can be understood by the fact that the polarizable solvent stabilizes more the ground state of the ion-pair structure than the excited CTTS state, which has essentially neutral character. Yet the spectra of CIP and SSP structures remain red-shifted with respect to the CBS spectra. For covalently bound hydrogen halides on water clusters, the HX dissociation leads to a generation of transient H3O species. In most cases, the dissociated hydrogen is immediately reflected from the water molecule and a less frequent event is the release of another hydrogen from the water molecule. The excitation of the ionic structures leads to CTTS states from which H3O radicals are generated. Hydrogen atoms with characteristic kinetic energy are finally formed via the dissociation of these hydronium radicals. Higher excitations lead to the formation of excited H3O radicals. The above scenario is in qualitative agreement with the experimental hydrogen kinetic energy distributions. The dynamics of the H3O radical was also studied as a bare species and in a microsolvated arrangement. The isolated H3O is stabilized only by a small barrier, and therefore, it has a very short lifetime of about 40 fs in its ground state. It is stabilized by solvation, extending the lifetimes by a factor of almost 10 when solvated with three water molecules. Also, the kinetic energies of the released hydrogen atoms are decreased upon solvation. The hydronium radical is stable in its excited state and it can decay via a conical intersection to the ground state where it dissociates. These conical intersections have been found approximately 0.5 eV above the excited state minimum.

A combination of the experimental measurements42,47-49 and our calculations leads us to a coherent picture of the HX 3 (H2O)n photochemistry: Hydrogen halides first acidically dissociate and the H and X radicals are formed once the CTTS transition takes place. Here, as for the other systems with water,58 the H3O radical seems to play a major role. The characteristic spectrum of the solvated H3O radical can be used for identification of this species. We have focused mostly on discussing the applicability of the photodissociation experiment for probing ground state chemistry (here the dissociation state of acids). The processes studied here have, however, wider relevance. Because the chemistry in the Earth’s atmosphere is controlled by light,83 light-induced processes of hydrogen halides (especially hydrogen chloride) are of potential practical importance. Hydrogen chloride is considered to be a reservoir species for stratospheric chlorine because of its photochemical stability. Atomic chlorine is formed only after HCl is transformed into molecular chlorine Cl2 via ground state heterogeneous reactions, for example, on polar stratospheric clouds formed in the Antarctic region. Can this paradigm be complemented with a second possible reaction channel involving

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the photochemical activation of acidically dissociated HCl? We have shown in our previous paper42 that the photolysis rate increases substantionally under stratospheric conditions upon acidic dissociation. There are, however, two problems to be further considered. First, if this reaction channel should take place, then we would need ice particles and light to be present at the same time. Thus, the mechanism could operate only in a limited time of the year. Second, our previous calculations of rate constants used the absorption cross sections for very small water clusters. The absorption spectrum in the bulk is shifted by a large amount to lower wavelengths and the photolysis rate under the solar influence will thus be much smaller. The absorption profile of hydrogen halides adsorbed on the surface of large finite water particles will be somewhere between the two limits treated in this study. To approach particles of atmospheric relevance directly, it will be necessary to apply more approximate techniques such as the QM/MM division. Only then the question of atmospheric relevance of the hydrogen halide photochemistry can be fully answered.

’ ASSOCIATED CONTENT

bS

Supporting Information. Additional supporting data and figures. This material is available free of charge via the Internet at http://pubs.acs.org.

’ AUTHOR INFORMATION Corresponding Author

*E-mail: [email protected]; [email protected]

’ ACKNOWLEDGMENT This work is dedicated to our longstanding colleague and friend Victoria Buch. We enjoyed the creativity of her research and her admirable personality in humanitarian affairs. Support by the special program “Nanotechnology for Society” of the Czech Academy of Sciences via Grant No. KAN400400651 and Grant No. 203/09/0422 of the Grant Agency of the Czech Republic are acknowledged. P.S. also thanks to the Grant Agency of the Czech Republic, Grant No. P208/10/1724 and to Ministry of Education, Youth and Sport of the Czech Republic, Research Project No. 6046137307. M.O. is a student of International Max Planck Research School “Dynamical Processes in Atoms, Molecules and Solids”. ’ REFERENCES (1) Molina, M. J.; Tso, T. L.; Molina, L. T.; Wang, F. C. Y. Science 1987, 238, 1253. (2) Tolbert, M. A.; Rossi, M. J.; Malhotra, R.; Golden, D. M. Science 1987, 238, 1258. (3) Peter, T. Annu. Rev. Phys. Chem. 1997, 48, 785. (4) Huthwelker, T.; Ammann, M.; Peter, T. Chem. Rev. 2006, 106, 1375. (5) Bianco, R.; Hynes, J. T. Chem. Rev. 2006, 39, 159. (6) Solomon, S.; Garcia, R. R.; Rowland, F. S.; Wuebbles, D. J. Nature 1986, 321, 755. (7) Ayotte, P.; Hebert, M.; Marchand, P. J. Chem. Phys. 2005, 123, 184501. (8) Kuo, J. L.; Klein, M. L. J. Chem. Phys. 2004, 120, 4690. (9) Rabinowitch, E. Rev. Mod. Phys. 1942, 14, 112. (10) Blandamer, M. J.; Fox, M. F. Chem. Rev. 1970, 70, 59. (11) Hurley, S. M.; Dermota, T. E.; Hydutsky, D. P.; Castleman, A. W. Science 2002, 298, 202. 6166


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