The protonated HCl dimer and trimer complexes were prepared by pulsed discharges in supersonic expansions of helium or argon doped with HCl and hydrogen. The ions were mass selected in a reflectron time-of-flight spectrometer and investigated with photodissociation spectroscopy in the IR and near-IR regions. Anharmonic vibrational frequencies were computed with VPT2 at the MP2/cc-pVTZ level of theory. The Cl–H stretching fundamentals and overtones were measured in addition to stretch–torsion combinations. VPT2 theory at this level confirms the proton-bound structure of the dimer complex and provides a reasonably good description of the anharmonic vibrations in this system. The trimer has a HCl–HClH+–ClH structure in which a central chloronium ion is solvated by two HCl molecules via hydrogen bonding. VPT2 reproduces anharmonic frequencies for this system, including several combinations involving core ion Cl–H stretches, but fails to describe the relative band intensities.

Protonated HCl, known as the chloronium cation HClH+, has been known for many years in mass spectrometry,1,2 and its structure was derived by high resolution infrared3,4 and microwave5 spectroscopy. HClH+ has been proposed as an important intermediate in interstellar halogen chemistry6 and was detected in the interstellar medium by the Herschel satellite.7–9 Recent infrared spectroscopy studies have examined this ion via rare gas tagging methods.10,11 Neutral HCl dimers and trimers have been well studied in the van der Waals spectroscopy community.12–17 HCl–water mixed clusters have been studied to explore the possible dissociation of HCl induced by water solvation.18–23 Protonated clusters of HCl/water mixtures have been studied in mass spectrometry,24 but there are limited studies of pure ionized HCl clusters. In the present work, we describe infrared spectroscopy and theory on the protonated HCl dimer and trimer.

Proton-bound dimers have been studied widely in the past with mass spectrometry25–29 and more recently by infrared photodissociation spectroscopy.30–58 The vibrational frequencies associated with the shared proton vary widely with the difference in proton affinity of the two molecular subunits that bind the proton.37 These systems can display severe vibrational anharmonicity and thus provide challenging tests for theory. Previous experimental studies explored these systems in the region of the fundamentals, with only a few cases in which the spectral range was expanded into the near-infrared.55,59 The overtones and combination vibrations of these systems can yield valuable information about the interaction potential at higher energies. Therefore, in this study of the protonated dimer and trimer of HCl, we investigate the infrared region of the fundamentals and we also set out to measure vibrational transitions in the near-infrared to compare the results with second order vibrational perturbation theory.59 

Although there are several investigations of neutral or cationic clusters of HCl–water mixtures,18–24 and much work on the “monomer” HClH+ chloronium cation,3–11 there is virtually no previous work on pure protonated HCl clusters. An early computational study by Del Bene and Shavitt explored the structures and energetics of the dimer and trimer species14 but did not investigate their spectroscopy. To our knowledge, there has been no experimental study of ion energetics, fragmentation, or spectroscopy on these systems. Our work provides an updated computational study and the first spectroscopic data on these systems.

The HCl–H+–ClH–Ar cations were generated in a pulsed discharge/supersonic expansion of argon doped with 1% H2 and 3% HCl gases using methods described previously.60 The H+(HCl)3 ions were generated in a helium discharge with similar added gas concentrations. The desired ion complexes were mass selected in a reflectron time-of-flight spectrometer61,62 and probed for photodissociation in the mid- and near-infrared employing a Nd:YAG-pumped optical parametric oscillator (OPO)/optical parametric amplifier (OPA) laser system (LaserVision). The infrared spectrum was recorded as the photodissociation yield with respect to the energy of the laser in the regions of 1000–4550 and 4850–7350 cm−1. Above 3500 cm−1, a 20 cm quartz lens was used to increase the overlap of the laser beam with the ion packet in the turning point of the reflectron and thus increase the photofragmentation yield.

Geometry optimizations of the ions of interest and their argon complexes were carried out at the MP2 level of theory using the cc-pVTZ basis set. Vibrational frequencies were computed with second order vibrational perturbation theory (VPT2) employing finite differences as implemented in the Gaussian 16 program package.63 

To model the splitting of the stretch–torsion combination band, a torsional potential curve was computed for ArH+(HCl)2 with the coupled-cluster single, double, and pertubative triple excitations [CCSD(T)] method at MP2 optimized geometries, also using Gaussian 16. Hydrogen, chlorine, and argon were described with the aug-cc-pVTZ, aug-cc-pV(T + d)Z, and aug-cc-pVTZ basis sets, respectively.63–67 Torsional eigenstates were determined by expanding the potential and kinetic energy in a Fourier series and solving the 1D Schrödinger equation variationally in a basis of free rotor functions.68,69 The kinetic energy terms were determined numerically from the optimized coordinates, and pseudopotential contributions were neglected.

The pulsed-discharge supersonic expansion source produces a variety of ions of the form H+(HCl)n and H+(HCl)nArm. Mass spectra under different conditions are shown in Figs. S1 and S2 in the supplementary material. Mass selection and infrared excitation of the H+(HCl)2 dimer do not produce measurable photodissociation signal, but the H+(HCl)3 trimer dissociates efficiently by the elimination of HCl. The argon-tagged dimer H+(HCl)2Ar dissociates efficiently by the loss of argon. These observations indicate that the binding energy of H+(HCl)2 is greater than that of the photon energy in the 2800 cm−1 energy range (∼8 kcal/mol) and that the binding energies of H+(HCl)3 and H+(HCl)2Ar are less than this.

The wavelength dependence of the photodissociation for the H+(HCl)2Ar and H+(HCl)3 ions, referred to hereafter as the “tagged dimer” and “trimer,” are shown in Fig. 1. Both ions have resonances in the 2800 cm−1 region, with the tagged dimer having two main sharp features (2590 and 2761 cm−1) and the trimer having one sharp band (2798 cm−1) and several broad, weaker features. The sharp bands for both ions occur just slightly to lower frequency than the H–Cl stretch in the non-protonated HCl monomer, which occurs at 2886 cm−1, as indicated by the red dashed vertical line. These resonances can also be compared to the symmetric and antisymmetric stretches of the H2Cl+ chloronium ion, which occur at 2630 and 2643 cm−1 for the H235Cl+ isotopomer.3,4 We can anticipate that the H+(HCl)2 ion has a proton-bound dimer structure and that H+(HCl)2Ar has argon attached to one of the terminal ClH positions. The 2590 cm−1 band is then likely the Cl–H stretch perturbed by a weak hydrogen bond to argon, and the higher frequency 2761 cm−1 band is from the terminal “free” Cl–H stretch. The trimer should have a central chloronium ion solvated by two HCl molecules, and the 2798 cm−1 band is also likely from a similar terminal “free” Cl–H stretch. The trend in these Cl–H stretches from chloronium to the dimer and trimer is a shift to higher frequency approaching that of isolated HCl as the vibrational chromophore is more remote from the proton. From another point of view, protonation causes a red shift of the nearby hydrogen stretches. This kind of behavior has been seen for proton-bound dimers of other small hydrogen-containing molecules, such as water,30–34,47 ammonia,39,40 or acetylene,44 and is attributed to electron charge redistribution from the molecules in the cluster toward the proton.

FIG. 1.

Experimentally measured photodissociation spectrum of the H+(HCl)2Ar “dimer” cation compared to that of the H+(HCl)3 “trimer” ion. The dimer spectrum is measured in the mass channel corresponding to the loss of argon, whereas the trimer spectrum is measured in the channel corresponding to the loss of HCl.

FIG. 1.

Experimentally measured photodissociation spectrum of the H+(HCl)2Ar “dimer” cation compared to that of the H+(HCl)3 “trimer” ion. The dimer spectrum is measured in the mass channel corresponding to the loss of argon, whereas the trimer spectrum is measured in the channel corresponding to the loss of HCl.

Close modal

To further investigate the structures of these complexes, we performed computations on the protonated monomer, dimer, and trimer ions as well as on the tagged protonated dimer. The results of these computations are shown as their structures in Fig. 2 and their energetics in Table I. The full details on these computations are given in the supplementary material. The protonated dimer ion has a proton-bound structure with C2 symmetry and a dihedral angle between the two hydrogens of 101.4°. The terminal H–Cl bond distances are almost the same as those in the chloronium monomer (1.29 Å), and the H+–Cl distance is longer (1.56 Å). Argon tagging is predicted to lengthen the adjacent H–Cl distance and shorten the nearest Cl–H+ distance, breaking the symmetry of the complex. The protonated trimer has a central chloronium ion solvated symmetrically by two HCl molecules, with C2 and Cs isomers differing only in their torsional rotation. This structure is reminiscent of that for the protonated water trimer, which has a central hydronium and terminal water molecules.47,52,55 As shown in Table I, the binding energy of HCl to the protonated dimer is much greater than the photon energy in the IR, whereas the binding energy of argon to this ion is much less, consistent with the dissociation behavior observed experimentally. The binding energy of HCl to the trimer ion is computed to be 10.1–10.2 kcal/mol, but reasonably efficient photodissociation is detected down to about 2200 cm−1 (6.3 kcal/mol). This suggests that the dissociation energy is significantly overestimated by MP2 theory or that the ions detected are not cooled completely and have some residual internal energy.

FIG. 2.

Structures of protonated HCl ions relevant for this study obtained at the MP2/cc-pVTZ level of theory. Bond lengths are in Angstroms and angles are in degrees.

FIG. 2.

Structures of protonated HCl ions relevant for this study obtained at the MP2/cc-pVTZ level of theory. Bond lengths are in Angstroms and angles are in degrees.

Close modal
TABLE I.

Energetics for protonated HCl complexes from computations at the uMP2/cc-pVTZ level, including correction for zero-point energy.

ComplexComputed energy HartreesBinding energy (kcal/mol; X–HCl or X–Ar)
H2Cl+ −460.513 672 ⋯ 
H+(HCl)2 −920.846 168 18.83 
H+(HCl)2Ar −1447.868 532 2.08 
H+(HCl)3 (C2−1380.164 883 10.18 
H+(HCl)3 (Cs−1380.164 792 10.12 
ComplexComputed energy HartreesBinding energy (kcal/mol; X–HCl or X–Ar)
H2Cl+ −460.513 672 ⋯ 
H+(HCl)2 −920.846 168 18.83 
H+(HCl)2Ar −1447.868 532 2.08 
H+(HCl)3 (C2−1380.164 883 10.18 
H+(HCl)3 (Cs−1380.164 792 10.12 

Figure 3 shows an extended view of the spectrum of the argon-tagged protonated dimer including the near-IR region of about 5000–7200 cm−1, where an additional band is detected at 5490 cm−1. A vibration here can only occur from an overtone or combination band. We also show the comparison of the experimental spectrum to that predicted by theory for both the tagged and tag-free complexes. To be able to describe the anharmonicity in this system and to include such overtone and combination bands, we have done anharmonic theory using the VPT2 method. Although this method does not include all possible anharmonic interactions, and it has some limitations, it is a workable approach for non-specialists in theory. As shown, the VPT2 approach captures the essence of the main bands in the fundamental region and also explains the band at 5490 cm−1. The two Cl–H stretches in the tagged complex become nearly a single band in the tag-free complex (doublet spaced by ∼3 cm−1), as expected for its higher symmetry. The argon-bound Cl–H frequency is roughly 80 cm−1 lower than the frequency in the tag-free complex, whereas the free Cl–H frequency in the tagged complex is about 20 cm−1 higher. The experimental band positions and the most intense bands predicted by theory are presented in Table II. A full list of all the bands predicted by theory is included in the supplementary material.

FIG. 3.

Experimentally measured photodissociation spectrum of the H+(HCl)2Ar ion compared to that predicted by VPT2 theory for the tagged (middle trace, blue) and tag-free ions (lower trace, red).

FIG. 3.

Experimentally measured photodissociation spectrum of the H+(HCl)2Ar ion compared to that predicted by VPT2 theory for the tagged (middle trace, blue) and tag-free ions (lower trace, red).

Close modal
TABLE II.

Experimentally observed infrared transitions of the H3Cl2+Ar ion compared with computed harmonic and anharmonic vibrations from VPT2 theory.

ExperimentωharmωanharmIanharm (km/mol)Assignment
⋯ 950.5 600.7 5407.7 ν5 (ǁ proton stretch) 
⋯ 985.6 910.5 4.8 ν4 (⊥ proton bend) 
⋯ 1142.7 1058.0 347.6 ν3 (⊥ proton bend) 
⋯ 1936.0 1354.2 510.9 ν4 + ν5 
2590 2724.0 2630.3 633.7 ν2 (Ar-bonded Cl–H stretch) 
2692 2825.1 2730.5 37.6 ν2 + ν10 (H–Ar stretch) 
2761 2927.2 2802.1 151.3 ν1; free Cl–H 
2798     
2820, 2833 3015.7 2871.0 15.5 ν1 + ν11 (H+–ClH torsion) 
2868     
3146 3222.4 3121.9 1.1 ν2 + ν6 (H+–Cl–H rock) 
 3333.7 3205.9 2.4 ν1 + ν7 (Cl–H in-plane bend) 
3500–3800 3709.5 3437.1 0.3 ν2 + ν4 
 3912.8 3534.3 1.0 ν1 + ν4 
 3866.6 3676.1 0.7 ν2 + ν3 
5412 5447.9 5081.4 0.20 2 
5490 5854.4 5499.3 0.9 1 
ExperimentωharmωanharmIanharm (km/mol)Assignment
⋯ 950.5 600.7 5407.7 ν5 (ǁ proton stretch) 
⋯ 985.6 910.5 4.8 ν4 (⊥ proton bend) 
⋯ 1142.7 1058.0 347.6 ν3 (⊥ proton bend) 
⋯ 1936.0 1354.2 510.9 ν4 + ν5 
2590 2724.0 2630.3 633.7 ν2 (Ar-bonded Cl–H stretch) 
2692 2825.1 2730.5 37.6 ν2 + ν10 (H–Ar stretch) 
2761 2927.2 2802.1 151.3 ν1; free Cl–H 
2798     
2820, 2833 3015.7 2871.0 15.5 ν1 + ν11 (H+–ClH torsion) 
2868     
3146 3222.4 3121.9 1.1 ν2 + ν6 (H+–Cl–H rock) 
 3333.7 3205.9 2.4 ν1 + ν7 (Cl–H in-plane bend) 
3500–3800 3709.5 3437.1 0.3 ν2 + ν4 
 3912.8 3534.3 1.0 ν1 + ν4 
 3866.6 3676.1 0.7 ν2 + ν3 
5412 5447.9 5081.4 0.20 2 
5490 5854.4 5499.3 0.9 1 

The anharmonic computations reproduce the main experimental bands in the fundamental region reasonably well for the tagged dimer. The frequencies predicted are each about 40 cm−1 higher than the experimental band positions, and the relative intensity of the more intense band at the higher frequency is lower than in the experiment, but otherwise the pattern matches pretty well. This confirms our initial guesses for the assignment of the 2590 cm−1 band to the Cl–H stretch where argon is attached (ν2) and the 2761 cm−1 band to the free Cl–H stretch (ν1). The weaker band between these at 2692 cm−1 can be assigned to the combination of the ν2 Cl–H stretch and ν10, where ν10 is the H–Ar stretch. The doublet at 2820/2833 cm−1 can be assigned to the ν1 + ν11 combination, where ν11 is the torsional bend of the ClH remote from the argon. Two bands are observed because of the splitting in the torsional potential induced by tunneling (see below). The weak band at 3146 cm−1 is explained by a band predicted at 3205.9 cm−1 assigned to the ν7 + ν1 combination, where ν7 is the H–Cl in-plane bend remote from argon. Like the other main features, this is also predicted higher in frequency than the experimental band.

The anharmonic theory for H+(HCl)2Ar can also explain the higher frequency features in the spectrum. The most prominent is a sharp band at 5490 cm−1, which is assigned as the overtone of the ν1 free Cl–H stretch predicted at 5499.0 cm−1. This can be compared to a similar overtone of the Cl–H stretch seen for chloronium at 5225 cm−1.11 The overtone of the ν2 Cl–HAr stretch is predicted at 5081 cm−1 and to be about three times weaker in the theory, but there is no obvious band here in the experiment except a much weaker band at 5412 cm−1. The only reasonable assignment for the 5412 cm−1 band is the ν2 overtone, but this implies negative anharmonicity for this vibration and a significant deviation from the prediction of theory. A weak but reproducible area of the broad signal occurs in the 3500–3800 cm−1 region. The theory assigns several combination bands here, all with weak intensity. These include the ν4 perpendicular proton stretch in combination with each of the ν1 and ν2 Cl–H stretches, as well as the ν3 H+–Cl–H bend in combination with the ν2 stretch. The activity of the proton stretch in combination with other hydrogen stretches makes sense mechanically, but this kind of combination band was not seen for protonated water clusters, which are the only other species like this studied in the near-IR.55 

The doublet band at 2820/2833 cm−1 is particularly interesting. A single band is predicted with considerable intensity here, which is assigned to the ν1 + ν11 combination band, i.e., the free Cl–H stretch and its torsion. The behavior of torsional vibrations is well known in vibrational spectroscopy, and methods have been developed to describe the multiplet structure that can arise from such a motion, which depends on the height of the torsional barrier.12–17 To model the splitting of the combination band, a torsional potential curve was computed for H+(HCl)2Ar with the CCSD(T) method at the MP2 optimized geometries. The barrier heights were determined to be 134 cm−1 for the C2h-like structure (ignoring the effect of argon on the symmetry) and 288 cm−1 for the C2v-like structure. Figure 4 shows the level pattern resulting for the v = 0 and 1 torsional levels with their expected splittings, together with the allowed transitions (parity must change) that would produce the doublet. Figure 4 also shows an expanded view of the doublet feature. Its experimental spacing of 12.5 cm−1 can be compared to that predicted by theory of 10.5 cm−1. Considering that the computations were for the isolated torsion, and the experiment measures a combination band, the agreement is reasonable, confirming the nature of this combination band and its splitting.

FIG. 4.

Expanded view of the combination band at 2820/2833 cm−1 and the level diagram showing the source of the splitting from the torsional vibration.

FIG. 4.

Expanded view of the combination band at 2820/2833 cm−1 and the level diagram showing the source of the splitting from the torsional vibration.

Close modal

According to the anharmonic theory, the parallel proton stretch in the tagged dimer has a frequency of 600.7 cm−1, with an extremely large intensity of 5407.6 km/mol. This mode is predicted to have a much higher frequency of 1004.5 cm−1 in the tag-free complex, with a likewise high intensity (5657.5 km/mol) (see Table S1 of the supplementary material). The perpendicular proton bending mode would be doubly degenerate in a complex with a center of symmetry but produces two close frequencies in these complexes. In the tagged complex, these frequencies are 910.5 (I = 4.8 km/mol) and 1058.0 cm−1 (I = 347.6 km/mol). The tag-free dimer has predicted frequencies (intensities) for these vibrations of 870.7 (6.5 km/mol) and 999.4 cm−1 (223.4 km/mol). In both kinds of proton vibrations, the presence of argon has a significant effect, even though it is bound remotely from the shared proton on a terminal Cl–H. The parallel proton stretch of these complexes has a remarkably high infrared intensity. If this ion were present in interstellar space, this vibration would be the best target for its detection. However, the tag-free molecule would be the species present, and our knowledge of its frequency comes only from theory. On the basis of previous work,31–34 the VPT2 prediction for this frequency is not likely to be highly reliable.

Figure 5 shows the spectrum for the H+(HCl)3 trimer compared to the spectra predicted for this ion by anharmonic theory for the two isomeric structures. Table III shows a selected list of the most intense vibrations predicted by anharmonic theory compared to the bands measured experimentally. Because the vibrational frequencies are essentially the same for the C2 and Cs isomers, we present only the predictions for the C2 species. A full list of predicted bands and intensities is presented in the supplementary material. As indicated in Table III, several bands are predicted with significant intensity in the region of 1100–1900 cm−1, where there is only a weak broad signal. These bands arise mainly from the symmetric (ν2) and antisymmetric (ν10) stretches of the core HClH+ chloronium ion and their combinations with various low-frequency bends. It makes sense that the bands here are not detected efficiently because of the binding energy of HCl to the complex. The binding energy is predicted to be about 10 kcal/mol, which corresponds to 3500 cm−1. The observation of resonant signals extends down to at least 2200 cm−1 (6.3 kcal/mol), but not much below this. Hence, the bands predicted in the 1100–1900 cm−1 range are most likely not detected because the binding energy of HCl to the H+(HCl)3 complex is greater than the photon energy in this region. The small amount of broad signal likely comes from ions with some residual internal energy or from a small amount of multiphoton absorption. Another consideration is that these chloronium-based vibrations involve hydrogen bonds to the terminal HCl molecules. Such hydrogen bonding is well-known to cause shifting and band broadening from effects such as spectral diffusion.31,37,38,40,47,48 These effects are not described by VPT2 theory, and the broadening would generate effective intensities that are lower than predicted, making these spectra even more difficult to detect. Tagging experiments on the protonated trimer would presumably make it possible to detect these bands at lower energy, but we were unable to produce the required H+(HCl)3Ar complexes with sufficient intensities for these experiments. Photodissociation is detected more efficiently at higher energies, but fewer intense bands are predicted there.

FIG. 5.

Experimentally measured photodissociation spectrum of the H+(HCl)3 ion compared to that predicted by VPT2 theory for the Cs isomer (middle trace, blue) and the C2 isomer (lower trace, red).

FIG. 5.

Experimentally measured photodissociation spectrum of the H+(HCl)3 ion compared to that predicted by VPT2 theory for the Cs isomer (middle trace, blue) and the C2 isomer (lower trace, red).

Close modal
TABLE III.

Experimentally observed infrared transitions of the H+(HCl)3 ion compared with computed harmonic and anharmonic vibrations from VPT2 theory. Because the vibrations computed for the C2 and Cs conformers are essentially the same, we present only the frequencies computed for the C2 species. ip = in-plane; oop = out-of-plane.

ExperimentωharmωanharmIanharm (km/mol)Assignment
1100–1900 1592.2 1063.6 2771.3 ν10 (H–Cl–H+ antisym. stretch) 
 1170.6 1129.1 5.7 ν3 (H–Cl–H+ scissors bend) 
 1764.4 1212.8 304.2 ν10 + ν14 (HCl–HClH+–ClH ip bend) 
 1367.3 1265.4 488.2 ν4 (HClH+ oop twist) + ν12 (HClH+ ip rock) 
 1551.3 1271.1 312.3 4 
 1805.2 1389.8 295.7 ν6 (ip HCl–HClH+–ClH intermol. st. + ν10 
 1573.5 1433.7 544.8 ν4 + ν11 (H–Cl–H+ oop wag) 
 1526.9 1454.8 572.3 ν3 + ν13 (H–Cl–H+ oop twist) 
 1595.8 1473.2 67.6 11 
 1948.5 1525.3 19.2 ν10 + ν13 
 1959.7 1540.4 25.6 ν5 (H–Cl–H+ twist/torsion) + ν10 
 1960.1 1686.6 102.2 ν2 + ν8 (HCl–HClH+–ClH ip bend) 
 1922.0 1708.5 1235.4 ν2 (H–Cl–H+ sym. stretch) 
 1762.3 1727.2 147.5 ν3 + ν12 
 1946.3 1825.0 29.7 ν3 + ν4 
 1968.5 1852.2 118.3 ν3 + ν11 
 2094.1 1867.8 357.2 ν2 + ν14 
 2135.0 1877.3 31.4 ν2 + ν6 
 3184.5 2094.6 67.4 10 
 3514.2 2213.7 92.1 ν2 + ν10 
2280     
2715 3092.6 2720.2 1.5 ν2 + ν3 
2798 2962.3 2850.7.2 233.2 ν9 (antisym. Cl–H stretch) 
 2962.8 2851.2 5.2 ν1 (sym. Cl–H stretch) 
2834 3036.7 2916.0 7.6 ν7 (HCl–HClH+–ClH torsion) + ν9 
3164 3843.9 3162.6 15.2 2 
3400–3900 3738.4 3546.7 0.15 ν1 + ν4 
 3738.0 3546.0 0.24 ν4 + ν9 
 3760.7 3592.3 0.32 ν1 + ν11 
 3760.2 3591.8 0.13 ν9 + ν11 
ExperimentωharmωanharmIanharm (km/mol)Assignment
1100–1900 1592.2 1063.6 2771.3 ν10 (H–Cl–H+ antisym. stretch) 
 1170.6 1129.1 5.7 ν3 (H–Cl–H+ scissors bend) 
 1764.4 1212.8 304.2 ν10 + ν14 (HCl–HClH+–ClH ip bend) 
 1367.3 1265.4 488.2 ν4 (HClH+ oop twist) + ν12 (HClH+ ip rock) 
 1551.3 1271.1 312.3 4 
 1805.2 1389.8 295.7 ν6 (ip HCl–HClH+–ClH intermol. st. + ν10 
 1573.5 1433.7 544.8 ν4 + ν11 (H–Cl–H+ oop wag) 
 1526.9 1454.8 572.3 ν3 + ν13 (H–Cl–H+ oop twist) 
 1595.8 1473.2 67.6 11 
 1948.5 1525.3 19.2 ν10 + ν13 
 1959.7 1540.4 25.6 ν5 (H–Cl–H+ twist/torsion) + ν10 
 1960.1 1686.6 102.2 ν2 + ν8 (HCl–HClH+–ClH ip bend) 
 1922.0 1708.5 1235.4 ν2 (H–Cl–H+ sym. stretch) 
 1762.3 1727.2 147.5 ν3 + ν12 
 1946.3 1825.0 29.7 ν3 + ν4 
 1968.5 1852.2 118.3 ν3 + ν11 
 2094.1 1867.8 357.2 ν2 + ν14 
 2135.0 1877.3 31.4 ν2 + ν6 
 3184.5 2094.6 67.4 10 
 3514.2 2213.7 92.1 ν2 + ν10 
2280     
2715 3092.6 2720.2 1.5 ν2 + ν3 
2798 2962.3 2850.7.2 233.2 ν9 (antisym. Cl–H stretch) 
 2962.8 2851.2 5.2 ν1 (sym. Cl–H stretch) 
2834 3036.7 2916.0 7.6 ν7 (HCl–HClH+–ClH torsion) + ν9 
3164 3843.9 3162.6 15.2 2 
3400–3900 3738.4 3546.7 0.15 ν1 + ν4 
 3738.0 3546.0 0.24 ν4 + ν9 
 3760.7 3592.3 0.32 ν1 + ν11 
 3760.2 3591.8 0.13 ν9 + ν11 

The most intense experimental band at 2798 cm−1 is explained by overlapping transitions from the symmetric and antisymmetric Cl–H stretches of the terminal HCl molecules. The ν1 (symmetric) and ν9 (antisymmetric) stretches overlap in frequency by less than 1 cm−1, but the antisymmetric stretch is predicted to be far more intense. A combination of the ν2 symmetric H–Cl–H+ stretch and the ν3 scissors bend of the HClH+ may explain the weak shoulder observed at 2715 cm−1, and the ν7 torsion + ν9 antisymmetric stretch combination may explain the shoulder peak at 2834 cm−1. The only higher frequency band with any significant intensity is the ν2 symmetric H–Cl–H+ stretch overtone predicted at 3163 cm−1, which matches almost perfectly with the broad band at 3164 cm−1. The broad appearance of this band is presumably caused by hydrogen bonding interactions, as no other potentially overlapping bands are predicted in this region. A series of weak combination bands is predicted in the 3540–3593 cm−1 range, which may explain the broad signal detected experimentally in this region.

Considering the spectra for the tagged protonated dimer and that for the protonated trimer, we can see that the VPT2 anharmonic theory performs reasonably well for some band positions but is lacking significantly in its description of band intensities. In the fundamental region of the spectrum for the tagged protonated dimer, the positions of the two main Cl–H stretching bands are predicted to be about 40 cm−1 higher than observed, but the spacing of about 170 cm−1 is reproduced. However, the higher frequency band at 2761 cm−1 is predicted to be five times weaker than the lower frequency band at 2690 cm−1, whereas these bands are observed to have more equal intensities, with the 2761 cm−1 band about 20% more intense than that at 2590 cm−1. The experimental sensitivity here (determined by the laser power) is roughly equivalent for these bands, so their measured relative intensities should be reasonably accurate. It is conceivable that the intramolecular vibrational redistribution (IVR) and predissociation rates are affecting the relative intensities of these bands. Higher excitation energy with a greater density of vibrational states could enhance both the IVR and the dissociation rates, making the higher energy 2761 cm−1 band appear to be more intense, as observed. The 5490 cm−1 band assigned to the Cl–H stretch overtone is in close agreement with the predicted frequency, but the intensity here cannot be evaluated because of issues with different laser pulse energies and focusing used in the high vs low frequency regions. In the case of the protonated trimer, the signals near 2280, 3164, and 3580 cm−1 are all observed to be within factors of 4–5 of the intensity of that of the main Cl–H stretch at 2798 cm−1, but the transitions in these regions are predicted to be weaker by factors of 10–20 or more. It is clear from these spectra that the tagged protonated dimer has a more rigid structure, with much less activity in its spectrum for bands other than the Cl–H stretch fundamentals, whereas the protonated trimer is more floppy, with weakly bonded external HCl molecules and more extensive anharmonic vibrational activity. Many of the linewidths for the trimer are quite broad, which is difficult to explain. The widths could arise from hydrogen bonding for those modes involving the intermolecular connections between the central chloronium and the terminal HCl molecules. However, they could also come from overlapping vibrational transitions, predissociation lifetimes, or unresolved torsional structure like that seen for the dimer.

This initial study of protonated HCl clusters provides an intriguing picture of the structures and dynamics of vibrational motion in this system. Further studies with more inert tag atoms, or even for tag-free ions, could potentially address the lower frequency regions where the proton stretch fundamentals for the dimer and the solvated chloronium framework of the trimer occur. Anharmonic theory employing other methods could also improve the present VPT2 results. These fascinating ions clearly warrant further study by experiments and theory.

Pulsed-discharge supersonic expansions produce the protonated dimer and trimer ions of HCl, which are studied here with infrared photodissociation spectroscopy. The H+(HCl)2 dimer ion is predicted to have a proton-bound structure, but with bond energies too high for study with infrared photodissociation. Argon tagging makes it possible to obtain spectra in the higher frequency region above 2000 cm−1 where Cl–H stretches and their combinations with low-frequency vibrations are detected. Different vibrational frequencies are detected for the Cl–H with argon attached vs the free Cl–H; a distinct signal is also detected for the overtone of the free Cl–H stretch. A Cl–H stretch/ClH torsion combination produces a doublet resulting from tunneling, whose splitting agrees well with that predicted by theory. A very weak structure resulting from combination bands involving the proton stretching motion is also detected. The protonated trimer ion has a structure with a central chloronium ion solvated by two HCl molecules. A sharp vibrational band results from the nearly degenerate symmetric and antisymmetric Cl–H stretches of these solvating molecules. Weaker and broader bands occur throughout the spectrum assigned to combinations and overtones of the symmetric and antisymmetric stretches of the core H–Cl–H+ chloronium ion. The source of the broadening of these bands is not completely clear, but it may be the hydrogen bonding interactions, predissociation widths, or unresolved torsional vibrational structure. Further studies of these protonated HCl clusters should focus on spectra at lower energies, perhaps with more inert tag atoms, and improved treatments of the significant anharmonic interactions.

See the supplementary material for optimized geometries and both harmonic and anharmonic frequencies of all computed isomers. Additional figures present infrared spectra of other argon-tagged isomers.

We acknowledge support for this work by the National Science Foundation (Grant No. CHE-1764111). J.P.W. acknowledges the Alexander von Humboldt-Foundation for a Feodor Lynen Postdoctoral Fellowship.

The data that support the findings of this study are available within the article and its supplementary material.

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