Helium Nanodroplet Study of the Hydrogen-Bonded OH Vibrations in

Article pubs.acs.org/JPCA

Helium Nanodroplet Study of the Hydrogen-Bonded OH Vibrations in HCl−H2O Clusters Julia Zischang,†,∥ Dmitry Skvortsov,‡,⊥ Myong Yong Choi,‡,§ Ricardo A. Mata,*,† Martin A. Suhm,† and Andrey F. Vilesov*,‡ †

Institute of Physical Chemistry, Georg-August-Universität Göttingen, Tammannstraße 6, 37077 Göttingen, Germany Department of Chemistry, University of Southern California, Los Angeles, California 90089, United States § Department of Chemistry and Research Institute of Natural Sciences, Gyeongsang National University, Jinju 660-701, South Korea ‡

S Supporting Information *

ABSTRACT: Mixed (HCl)N(H2O)M clusters have been assembled in He droplets from the constituting molecules. Spectra of the clusters were obtained in the range of hydrogen-bonded OH vibrations (3100−3700 cm−1) by infrared laser depletion spectroscopy. The observed bands were assigned to cyclic hydrogen-bonded aggregates containing up to two HCl and three H2O molecules. The obtained frequencies are in good agreement with the results of harmonic quantum chemical calculations upon appropriate uniform shifts mimicking anharmonic corrections. Although larger clusters containing up to six water molecules were also produced in the droplets, their spectra were found to contribute to the unresolved signal in the range 3250−3550 cm−1. The fact that no narrow bands could be unambiguously assigned to the mixed clusters containing more than three water molecules may indicate that such clusters exist in many isomeric forms that lead to overlapped and unresolved bands giving rise to broad structureless features. Another possible explanation includes the formation of elusive zwitterionic clusters, whose bands may have considerable breadth due to electrostatic coupling of different vibrational modes and concomitant intramolecular vibrational relaxation. four water molecules6,15 was revised,16,17 and now there is a consensus that the sharp band in question belongs to hydrogenbonded (H2O)2(HCl)2 clusters.16−18 It was recognized that the large width (≈100 cm−1) of the hydronium band,16,17 as previously observed in ionic water clusters,19 makes the unambiguous detection problematic. Most recently, the broad background in the 2500−2800 cm−1 range was assigned to an ionized form of HCl(H2O)M (M ≥ 4) clusters in helium droplets that were aligned in an external electric field.18 However, conclusions based on the constitution of such broad spectral features may be unreliable, because they must contain contributions from other broad bands from clusters of different size or structure, which are virtually impossible to disentangle. Indeed, at least for free jet expansions,12 it was shown convincingly13 by chemical and isotope substitution as well as by comparison to low temperature surface experiments, that the dominant contribution to this broad band is from undissociated HCl adsorbed on water clusters, with only minor contributions from hydronium bands under appropriate conditions. Besides the hydronium bands, the HCl(H2O)M clusters have a number of free OH and bound OH stretching bands in the

1. INTRODUCTION Ionization of acids in water is one of the most fundamental processes in chemistry. Therefore, the ionization mechanism and coordination of the ions by solvent molecules in bulk solution have attracted considerable attention. A bottom up way for the study of ionization includes free clusters containing an acid and a few water molecules from quantum chemical calculations and molecular beam spectroscopic experiments. A large number of works concentrated on clusters with HCl due to its diatomic character and its importance in chemistry. Thus, mixed clusters of water and hydrogen chloride have been considered a valuable model system for the understanding of acidity and the mechanism of acid ionization. Upon addition of H2O, the H−Cl bond of hydrogen chloride becomes successively longer to the point of zwitterion formation. The results of quantum chemical calculations at different levels of theory indicate that the strength of hydrogen bonding increases upon addition of water molecules and that the ionization of HCl takes place upon addition of just four water molecules.1−8 The calculations also predict that the ionized clusters are characterized by strong infrared bands due to absorption of hydronium ions (H3O+) around 2700 cm−1. Several experimental groups have attempted to pinpoint the ionization effect via observation of the predicted hydronium bands,9−14 which, however, remains elusive. A recent assignment of a sharp 2770 cm−1 band in helium droplets to ionized clusters containing © XXXX American Chemical Society

Special Issue: Markku Räsänen Festschrift Received: September 24, 2014 Revised: November 7, 2014

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Figure 1. (A) Depletion spectra of (HCl)N(H2O)M clusters in helium nanodroplets obtained at different average numbers of captured HCl molecules as indicated in each panel. Band assignments to (HCl)N(H2O)M clusters are given in the form of N−M numbers. Spectrum a shows a spectrum for neat water clusters. The spectra were smoothed by the Savitzky−Golay technique38 over 25 points. (B) log−log plots of the intensity ratio (IX/ID) as a function of the average number of HCl molecules.

optical pathways are continuously purged with dry air to prevent absorption from water in the ambient air. The laser beam is aligned antiparallel and coaxial to the helium nanodroplet beam. The absorption of laser photons by encapsulated clusters is followed by rapid energy transfer to the host He droplets and subsequent evaporation of several hundreds of helium atoms. The total flux of the droplet beam is detected by a quadrupole mass spectrometer. The absorption of photons by clusters followed by the evaporation of He atoms leads to a decrease in the mass spectrometer ion signal, which is recorded by a lock-in amplifier. The obtained spectra are corrected for the variation of the laser output energy over the studied spectral range. The abundance of the molecules in clusters can be approximated by a Poisson distribution.21−24 The average number of captured molecules, ZM, is proportional to the pickup pressure, and the proportionality coefficient is obtained by fitting the pickup pressure dependencies of the band intensities of single H2O or HCl molecules as described earlier.25,26 For binary clusters, the abundance is given by the product of the corresponding Poisson distributions.17,27

mid-IR spectral range. However, the free OH range of the clusters is rather congested and could not be used to study clusters containing more than two water molecules.14,20 Remarkably, the bands due to hydrogen bond bridge vibrations remain relatively poorly understood, even though these bonded OH bands may be better resolved due to the larger spectral separation of the bands of different clusters and smaller band breadth. This is linked to the fact that the bonded vibrations are particularly sensitive to changes of hydrogen bond strength and cluster geometry. Exploratory investigations of this spectral region by a free jet FTIR12,14 technique suffered from the high number of close lying bands as well as strong overlap of mixed cluster bands with signals originating from neat water clusters whereas the HCl stretching bands allowed for less ambiguous assignments up to two or even three water molecules.12,14 In this work, we assemble mixed clusters containing different numbers of HCl and water molecules in helium droplets and study the obtained clusters via infrared laser depletion spectroscopy in the range 3100−3700 cm−1. The analysis of cluster structures is facilitated by ab initio quantum chemical calculations. As a result, we are able to identify the bands of mixed clusters containing up to two HCl and three water molecules, which have cyclic structures and demonstrate hydrogen bonding. We also discuss the spectra of larger clusters, which consist of broader features and have considerable overlap.

3. QUANTUM CHEMICAL CALCULATIONS Theoretical calculations have been carried out on selected clusters with different numbers of H2O and HCl molecules, including also the neat water clusters. Depending on the number of molecules included, one or more isomers have been optimized on the basis of previous theoretical/experimental evidence and/or following common patterns in H2O/HCl bonding. The optimizations have been carried out with the density fitted local Møller−Plesset second-order perturbation theory (DF-LMP2) method28 and the aug-cc-pVTZ basis set of Dunning and co-workers.29,30 The density fitting basis used for the Hartree−Fock (DF-HF)31 and the correlation calculations were the corresponding JKFIT and MP2FIT sets.32,33 The orbitals were taken from a Pipek−Mezey localization,34 and the domains were determined according to a NPA criterium (TNPA = 0.03).35 Harmonic frequency calculations were carried out on the obtained minima. In the case of the smaller aggregates, canonical coupled cluster theory with singles, doubles, and

2. EXPERIMENTAL SECTION Helium nanodroplets are formed in a supersonic cryogenic expansion of helium as described in detail elsewhere.21−24 In this work, droplets having an average size of about 6000 atoms are obtained at a nozzle temperature of T0 = 15 K and at a stagnation pressure of P0 = 20 bar. The droplets capture HCl molecules in a separate differentially pumped chamber, followed by H2O molecules in a pickup cell further downstream. Upon sequential pickup, the molecules combine rapidly to form clusters. The infrared spectra of the clusters are obtained using a pulsed optical parametric oscillator (OPO) amplifier (spectral resolution: 1 cm−1, pulse duration 7 ns, pulse energy ≈1 mJ, repetition rate 20 Hz). The laser cabinet and the B

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Figure 2. (A) Depletion spectra of (HCl)N(H2O)M clusters in helium nanodroplets obtained at different average numbers of captured H2O molecules ((a), (c), (e)) as indicated in each panel in comparison with the spectra of neat water clusters ((b), (d), (f)). Band assignments to (HCl)N(H2O)M clusters are given in the form of N−M numbers. The spectra were smoothed by the Savitzky−Golay technique38 over 25 points. (B) log−log plots of the intensity ratios (IX/IB) as a function of the average number of H2O molecules.

Table 1. Assignment of the Mixed HCl−H2O Cluster Bands in the Bonded O−H Stretching Regiona wavenumber/cm−1 aggregate

band

exp

(HCl)2(H2O)1 (HCl)2(H2O)2

A C I B F D G E H

(H2O)2 (H2O)3

3622.6 3594.7 3406.7 3614.9 3509.5 3560.1 3476.2 3546.8 3438.5 3597.0 3529.6

(H2O)4

3393

(HCl)1(H2O)2 (HCl)1(H2O)3

DF-LMP2 3621.4 3592.3 3406.6 3619.7 3504.7 3563.1 3467.3

(1.2) (2.4) (0.1) (−4.8) (4.8) (−3.0) (8.9)

3597 (0.0) 3540.6 (−11.0) 3531.7 (−2.1) 3397.7 (−4.7) 3397 (−4.0)

splitting/cm−1

CCSD(T) 3616.5 (6.1)

3612.5 3501.7 3561.9 3465.9

(2.4) (7.8) (−1.8) (10.3)

matrix (12)

exp

DF-LMP2

CCSD(T)

188

186

105

111

115

84

96

96

3607

3605 3485 3554 (3430)

3597.0 (0.0) 3534.5 (−4.9) 3526.4 (3.2)

Calculated wavenumbers were obtained at the DF-LMP2/aug-cc-pVTZ and CCSD(T)/aug-cc-pVTZ levels of theory and shifted by −130 cm−1 (DF-LMP2)/−138 cm−1 (CCSD(T)) for O−H···O vibrations and −150 cm−1 (DF-LMP2)/−153 cm−1 (CCSD(T)) for O−H···Cl vibrations (italicized in the Table). Numbers in parentheses mark deviations between experimental and calculated numbers. Splittings denote the wavenumber difference between two bands of the same aggregate. The assignments for the bands of neat water clusters are from refs 25 and 40. a

2, respectively. Spectra a, c, and e of Figure 2A show the spectra measured at a constant average number of captured HCl molecules ⟨HCl⟩ ≈ 1 and different ⟨H2O⟩ ≈ 1, 2 and 3, respectively. The number of captured HCl and H2O molecules per droplet can be approximated by a Poisson distribution.17 Therefore, if ⟨HCl⟩ is kept constant, the ratio of the integrated intensity of some band, IX, with unknown number of water molecules (M) to the reference band intensity, Iref, with a known number of water molecules (Mref) (IX/Iref), is given by eq 1.

perturbative triple excitations (CCSD(T)) was also used in combination with the same orbital basis set. All calculations were carried out with the Molpro2012.1 software package.36,37

4. RESULTS Figure 1A traces a−e and Figure 2A traces a−f show infrared depletion spectra of mixed (HCl)N(H2O)M as well as neat (H2O)M clusters in the bonded O−H stretching region for different average numbers of captured HCl (⟨HCl⟩) and H2O (⟨H2O⟩) molecules. The bands of neat water clusters are marked by dashed lines, and the nine peaks originating from mixed HCl−H2O aggregates are indicated by solid lines and labeled with characters A−I (see also Table 1 for the wavenumbers). Two series of spectra are shown: In Figure 1A spectra a−e, the average number of embedded H2O molecules was fixed to ⟨H2O⟩ ≈ 1 and the average number of captured HCl molecules was set to ⟨HCl⟩ ≈ 0, 0.35, 0.5, 1, and

log

IX = (M − M ref ) ·log(⟨H 2O⟩) + const Iref

(1)

where ⟨H2O⟩ is proportional to the water pickup pressure. A similar relation holds if the HCl pressure is varied at constant H2O pickup pressure. According to eq 1, the slopes equal to (M C

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− Mref) or (N − Nref) give the stoichiometry of clusters for each band if Mref and Nref are known. However, because using eq 1 requires accurate band intensities, it can only be reliably applied to sharp, well separated, rather intense bands devoid of any overlap with other signals. Inspection of the spectra in Figure 1A renders bands C, E, and I, which have significant overlap with bands of neat water clusters, as well as broad weak bands F and G inappropriate for this technique. So, eq 1 was applied to identify the origin of the bands labeled by A, B, D, and H in Figures 1A and 2A. At low HCl pickup pressure (⟨HCl⟩ < 1), strong bands of mixed clusters must originate from aggregates containing one or two HCl molecules. Figure 1B shows the values of log10 (IX/ ID), with band D serving as a reference band, as a function of log10(⟨HCl⟩). It becomes clear that only two groups of slopes (and thus clusters with two different N numbers) appear: whereas the slope for bands B, D, and H is close to zero, the slope for band A has a value of 1.1. We conclude that bands B, D, and H correspond to clusters containing N = 1 HCl molecule, whereas band A originates from clusters having N = 2 HCl molecules. However, results for band H should be regarded with reservations because its low intensity in Figure 1A and the broad spectral features underneath the band for higher numbers of ⟨HCl⟩ might lead to substantial deviations of the integrated intensities. We tentatively assign this broad unresolved offset extending from 3650 to about 3300 cm−1 in panel e, to clusters containing more than two HCl molecules. The assignment of the bands labeled by C, E, F, G, and I was facilitated by a visual examination of the intensity evolutions in the spectra. Upon an increase of ⟨HCl⟩ from 0.5 to 1 in Figure 1A spectra c and d, respectively, bands A and I demonstrate a strong increase in intensity. In comparison, the relative intensity of other bands changes insignificantly except for band C, which has strong overlap with the neat water dimer band close to 3600 cm−1. However, comparison of the spectra obtained at ⟨1⟩:⟨1⟩ (Figure 1A spectrum d) and at ⟨2⟩:⟨1⟩ (Figure 1A spectrum e) shows a strong intensity increase of band C upon increase of ⟨HCl⟩, which is comparable with that of band A. The similar band I has a strong overlap with the neat water tetramer band close to 3400 cm−1. Summarizing, spectra measured at different ⟨HCl⟩ reveal two groups of bands: B, D, E, F, G, and H showing weak ⟨HCl⟩ dependence are assigned to clusters with a single HCl molecule. The second group constitutes bands A, C, and I, which are assigned to clusters containing two HCl molecules each. Traces a, c, and e of Figure 2A show the spectra obtained at constant ⟨HCl⟩ ≈ 1 with different ⟨H2O⟩, as indicated in each panel. Corresponding spectra for neat water clusters are shown in panels b, d, and f. The assignment of the bands to clusters with particular numbers of water molecules was executed on the basis of their ⟨HCl⟩ dependencies, similar to that described previously for HCl. Accordingly, band B was taken as reference for the double logarithmic plot in Figure 2B, correlating the integral ratio (IX/IB) to the average number of water molecules in the droplet, ⟨HCl⟩. As in the case of the ⟨HCl⟩ dependence, the four clean bands A, B, D, and H were used for the log−log analysis. It is seen that the bands show different slopes: negative slope close to −0.5 (A), slope ≈0 (B), and slopes 0.5 and 0.7 (H and D). We conclude that bands A, B, and D/H belong to clusters containing three successive numbers of water molecules. Assuming that band A belongs to clusters having a single water molecule, band B was assigned to clusters with two water molecules and bands D and H to aggregates with three

water molecules. Noninteger slopes were previously assigned to deviations of the experimental cluster abundance distribution from Poissonian, due to evaporative cooling of the clusters upon capture of molecules, droplet size distribution in the beam, and beam scattering upon pickup.17 The assignment of band A to clusters with single water molecules is in agreement with the spectra a and c in Figure 2A obtained for ⟨HCl⟩:⟨H2O⟩ ≈ ⟨1⟩:⟨1⟩ and ⟨1⟩:⟨2⟩, respectively, which show the intensity decrease of band A upon an increase of ⟨H2O⟩. Thus, band A was assigned to (HCl)2(H2O)1 clusters. In the binary clusters (HCl)1(H2O)1 the hydrogen chloride acts as the donor, thus the O−H stretching bands have wavenumbers larger than 3700 cm−1 20 and are beyond the spectral range studied in this work. Consequently, band B is attributed to a cluster with two water molecules and bands D and H to clusters containing three water molecules. The visual assignment of the bands containing three water molecules in Figure 2A spectra a, c, and e is complicated due to the overlap with bands of neat water dimers and trimers. For comparison, the spectra of the neat water clusters are included in Figure 2A traces b, d, and f. It is seen that upon addition of HCl, the intensity of neat water bands decreases and new bands due to mixed HCl−water clusters appear. Upon an increase of ⟨H2O⟩ from 1 to 2 in Figure 2A spectra b and d, respectively, the intensity ratio of the water trimer and dimer bands increases by a factor of about 2. It is seen that the intensities of bands B, C, F, and I in Figure 2A spectra a and c remain approximately unchanged with ⟨H2O⟩ just as the water dimer band, consistent with their assignment to mixed clusters containing two water molecules. In comparison, bands D, E, G, and H show a strong increase in relative intensity with ⟨H2O⟩, indicating they belong to clusters having at least three water molecules. These assignments are also in agreement with the log−log plot of the intensities of bands D and H in Figure 2B. A comparison of the intensity evolution of band F with the intensities of a group of bands “D−E−water trimer” in Figure 2A spectra a, c, and e vividly illustrates their different identities with respect to the number of water molecules. Similar arguments could be applied for the F−G−H band group. In summary, the depletion spectra obtained at different average numbers of captured HCl and H2O molecules show distinct bands from aggregates containing one or two HCl and one to three water molecules. As expected, the (presumably cyclic) (HCl)2(H2O)1 cluster yields a single band in the bound O−H stretching region labeled A in the spectra. Clusters (HCl)2(H2O)2 contribute the two bands C and I. The large wavenumber difference of these two bands is consistent with a cluster with adjoining water molecules and excludes the alternating form. This structure of the (HCl)2(H2O)2 cluster is further supported by previous measurements in the H−Cl stretching region.16,17 Concerning clusters with single HCl molecules, the smallest mixed aggregate (HCl)1(H2O)1 does not contain a hydrogen-bonded O−H and thus does not show any spectral activity in the studied range. For the (HCl)1(H2O)2 clusters, two bands (B and F) have been identified, as expected for the cyclic structure and two bonded O−H entities. In the case of cyclic (HCl)1(H2O)3 clusters, three bands within the bonded O−H stretching region are expected. However, four bands (D, E, G, H) have been assigned to the clusters having 1:3 stoichiometry. This is reminiscent of the water trimer case, where an extra IR active band is observed, which is sensitive to the environment and to D

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with the appearance of the peaks at 3225 and 3335 cm−1 due to neat water hexamers (0−6).25,40,41 Comparison of (c) and (d) as well as (e) and (f) of Figure 2A shows that these bands are hardly detectable in the spectra of the mixed clusters. This is somehow in disconcert with the expectation based on the Poisson distribution, that at ⟨HCl⟩ = 1 about e−1 = 37% of the droplets should be free of HCl molecules. The weakness of the (H2O)6 signals in the mixed spectra possibly indicates that larger clusters are preferentially obtained in the larger He droplets. It is known that He droplets in the beam have lognormal distribution over the number of He atoms, NHe,43 with the half-width equal to the average size. Larger droplets have correspondingly larger capture cross sections, which approximately scale as NHe2/3, and accordingly, larger abundances of HCl molecules. Due to these effects, the spectral subtraction is not an exact operation. However, it could be used to minimize the contribution of the neat water clusters in the spectra. Figure 3 shows the appearance of a broad and structureless feature in the spectra of the mixed clusters, which extends from about 3250 to 3550 cm−1 and should be assigned to mixed clusters. The fact that no narrow bands could be assigned to mixed clusters containing more than 3 water molecules may indicate that such clusters exist in many isomeric forms that give rise to overlapped and unresolved bands. This does not exclude that some of these clusters may be due to dissociated forms of the (HCl)N(H2O)M clusters, which are expected to have broader bands. Unfortunately, the bound OH spectral range encounters problems similar to those of the HCl region.16,17 The spectra of the large clusters become broad and unresolved and could not be used for identification of the structure and charge separation. Figure 4 and Table 1 show the comparison of the band positions in the experimental ⟨1⟩:⟨2⟩ depletion spectrum with the adapted wavenumbers and intensities calculated at the DFLMP2/aug-cc-pVTZ (upward) and CCSD(T)/aug-cc-pVTZ (downward) levels of theory. Calculated harmonic wavenumbers were shifted by −130 cm−1 (DF-LMP2)/−138 cm−1 (CCSD(T)) to obtain consistent values for the well-known bound OH stretching band of neat water dimer, thus accounting to first order for anharmonic effects. The resulting theoretical wavenumbers reproduce known hydrogen-bonded OH stretching transitions in water trimer and tetramer within less than 0.5% (Table 1), which is better than one could expect due to the varying amount of anharmonicity for different cluster sizes and the He droplet shift. To take into account the different acceptor character of HCl, calculated bands originating from O−H···Cl stretching vibrations were empirically but uniformly shifted by another −20 cm−1 (DF-LMP2)/−15 cm−1 (CCSD(T)). In Figure 4, these shifts are marked by arrows and gray symbols. It is seen that the experimental band assignments for (HCl)1(H2O)2, (HCl)2(H2O)1, and (HCl)2(H2O)2 agree well (with a maximum deviation of 10 cm−1) with both theoretical approaches after scaling. For the cyclic global minimum structure of (HCl)1(H2O)3 bands D and G appear to be the most likely contributors, whereas the third, most red-shifted band is not identified. Most probably this missing band is broad because of fast IVR and falls in the shaded low frequency spectral range where no distinct sharp bands can be identified. After all, the photon energy should be sufficient to drive the cluster into a zwitterionic state, if the excitation mode is coupled sufficiently to the reaction coordinate by moving the relevant acidic protons in phase. The origin of bands E and H remains ambiguous. Pickup pressure dependence indicates they

deuteration.39 This effect could be related to the tunneling motion of the dangling OH groups between the two sides of the cluster plane. Furthermore, the expected most strongly redshifted bands for the 1−3 cluster may well have a substantial width that often correlates with the hydrogen bond strength and could therefore be hidden underneath the baseline or have strong overlap with bands of neat water clusters. A similar effect was also observed in an early Ar matrix isolation study.11 In line with their intensity, we tentatively attribute two of the four observed bands (D and G or H) and an elusive broader band to the main 1−3 contributions and the remaining bands (E and H or G) to a minor component that has to await firm assignment like in the water trimer case. Bands B and D have previously been identified in free jet expansion experiments (labeled S13 and S14, blue-shifted by only 3 cm−1 due to the absence of the He droplet environment) and ascribed to aggregates containing one HCl molecule.12 Both bands were tentatively assigned to (HCl)1(H2O)2. However, (HCl)1(H2O)3 could not be excluded. The present reassignment of band D to a 1−3 complex is consistent with an earlier Ar matrix isolation assignment further red-shifted by 6 cm−1 11 and its appearance in the spectra lends additional support to the tentative assignment of the very broad (Δν ≈ 150 cm−1) HCl stretching band at 2180 cm−1 to the (HCl)1(H2O)3 complex in the free jet study.12 The latter shows how broad vibrational modes with synchronous hydrogen stretching motion can become due to protontransfer-related IVR, though this might be less pronounced for the bound OH stretching vibrations. The spectra with the largest average numbers of water molecules ⟨H2O⟩ ≈ 3 in Figure 2A spectra e and f indicate the appearance of additional unresolved bands in the range between 3550 and 3250 cm−1. In the spectrum of neat water clusters, the bands in this frequency range have been assigned to clusters having four and more water molecules.25,39−42 In the mixed clusters, these broad features also remain for ⟨H2O⟩ ≥ 2 after reduction of the contributions from neat water clusters by scaled subtraction of the respective ⟨0⟩:⟨M⟩ water spectrum. The scaling was chosen to minimize the rather sharp band due to the water pentamer around 3350 cm−1 (Figure 3). The chosen scaling also minimizes the contribution of the 0−3 band without producing artificial negative peaks in the difference spectrum. On the other hand, there is a noticeable anomaly

Figure 3. Depletion spectra of (HCl)N(H2O)M clusters in helium nanodroplets upon scaled subtraction of the corresponding spectra for neat water clusters. The clusters contain on average one HCl molecule and 1, 2, or 3 water molecules in panels (a), (b), and (c), respectively. Band assignments to (HCl)N(H2O)M clusters are given in the form of N−M numbers. Dashed lines mark positions of neat water clusters. E

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structures. Comparison of the results of these anharmonic calculations for bound OH stretching vibrations shows typical deviations of up to ±40 cm−1, depending on the particular theoretical method applied. A juxtaposition of the experimental data with different theoretical wavenumbers can be found in the Figure S1 and Table S1 of the Supporting Information. Recently, the IR spectra of mixed water−HCl clusters containing different isotopes of oxygen 16 and 18 have been reported.18 It was found that the band due to H−Cl stretch in (HCl)2(H2O)2 clusters shows a 0.5 cm−1 shift toward low energy in clusters with H218O as compared with the case for the H216O clusters. Harmonic frequency calculations show no shift in the wavenumbers. Because an anharmonic calculation for the 2−2 cluster would be extremely demanding, we have opted to qualitatively investigate the effect on the simpler 1−1 binary cluster. The unscaled harmonic H−Cl stretch frequency in both (HCl)1(H216O)1 and (HCl)1(H218O)1 at the DF-LMP2/augcc-pVTZ level of theory is computed as 2812.73 cm−1. To obtain the anharmonic frequencies, calculations were carried out with the vibrational MP2 (VMP2) method 44 as implemented in Molpro2012.1. The potential surface was calculated up to three-body contributions and the underlying electronic structure method was again DF-LMP2/aug-ccpVTZ. The HCl frequency for (HCl)1(H216O)1 was found to be 2699.33 cm−1, whereas (HCl)1(H218O)1 gave a value of 2697.02 cm−1. The shift is overestimated but is qualitatively in line with the experimentally measured spectra. The anomalous isotope effect is therefore consistent with anharmonic couplings of the H−Cl stretch to some other vibrations.

Figure 4. Measured spectrum of HCl−H2O clusters (⟨1⟩:⟨2⟩) and calculated harmonic band wavenumbers at the DF-LMP2/aug-ccpVTZ (upward) and CCSD(T)/aug-cc-pVTZ (downward) levels of theory. The calculated wavenumbers are shifted by −130 cm−1 (DFLMP2) and −138 cm−1 (CCSD(T)) to match the neat water dimer band. Arrows and gray symbols indicate additional empirical shifts of −20 cm−1 (DF-LMP2)/−15 cm−1 (CCSD(T)) for O−H···Cl vibrations. The brackets, aggregate structures, and N−M numbers at the top show the band assignment. Dashed brackets indicate bands that have not been identified explicitly in the spectrum, their positions are based on the predicted spacings from the nearest observed bands of the same aggregate. The band at 3350 cm−1 is (at least partially) due to water pentamer and larger neat water clusters. The gray background for wavenumbers