Electronic and mechanical anharmonicities in the vibrational spectra of the H-bonded, cryogenically cooled X⁻ · HOCl (X=Cl, Br, I) complexes: Characterization of the strong anionic H-bond to an acidic OH group

The molecular-level mechanics of the “anionic H-bond” to the OH group have been extensively explored in the binary complexes between water, methanol, and formic acid with the halide ions.^1–5 A major conclusion from these efforts is that the observed spectra above 1000 cm⁻¹ are typically more complex than the simple three-band pattern (e.g., two OH stretches and the HOH intramolecular bend for X⁻ · H₂O) predicted to occur at the harmonic level. Specifically, “extra bands” appear scattered across the spectrum that are traced to surprisingly strong mechanical (potential) and electronic (electric dipole) anharmonicities.^3,6 These effects are well documented in the analysis of neutral van der Waals complexes^7,8 but are amplified in the more strongly bound ionic systems. In the latter case, the extra bands are due to the excitation of soft mode vibrational levels whose displacements break the directional hydrogen bonds. As such, linear vibrational spectroscopy provides a window into the topologies of the potential and dipole surfaces away from the equilibrium geometry. In this paper, we expand this survey to include the hydrogen bonds between halide ions and the more acidic HOCl molecule (pK_a values of 7.54⁹ and 14¹⁰ for HOCl and H₂O, respectively), a choice that is motivated, in part, because of HOCl’s importance in interfacial atmospheric chemistry.^11–17 Both the H₂O and HOCl complexes with halides are observed to adopt the asymmetric, “single ionic H-bonded” geometries indicated in Fig. 1, in which an OH group is bound to the ion, while either the Cl or H atoms are non-bonded. The band assignments are aided by comparison with the behaviors of the X⁻ · HOD isotopomers with the OH group bound to the ion and taking into account the stronger H-bonds between the halide ions and HOCl.

The X⁻ · HOCl (X = Cl, Br, and I) complexes were formed in the gas phase using the so-called “ligand switching” approach that involves displacement of one (or more) water molecule(s) in the reaction

The X⁻ · (H₂O)_n clusters were formed in an electrospray ionization source and injected into a series of radio frequency (RF) ion guides as described in detail in Sec. S1 of the supplementary material. Reaction (1) was carried out in a quadrupole guide filled with HOCl gas (preparation described in Sec. S2) at a pressure of ∼10⁻² mbar. The product ions were then transferred to a three-dimensional quadrupole trap (Jordan) cooled by a closed-cycle He cryostat to about ∼20 K, where H₂ molecules were condensed onto the X⁻ · HOCl binary complexes by pulsing a buffer gas mixture containing ∼20% H₂ in a balance of He. Mass spectra displaying the products of collisions between HOCl and X⁻ · (H₂O)_n are presented in Fig. S1. The dominant species that are generated correspond to the uptake of HOCl onto the parent X⁻ · (H₂O)_n clusters to yield X⁻ · (HOCl) ^· (H₂O)_n. While the presence of multiple chlorine and bromine isotopes results in a number of mass degeneracies between the products and the parent cluster series, the X⁻ · (HOCl) ^· (H₂O)_n species containing the most naturally abundant ³⁵Cl and ⁷⁹Br isotopes (i.e., the major products) are unique and, thus, easily distinguished. The vibrational spectra were recorded over the range of 1000–4000 cm⁻¹ by IR photodissociation of weakly bound H₂ molecules,

in a linear action regime in a triple-focusing photofragmentation mass spectrometer.^18–20 The resulting band patterns are analyzed using an anharmonic treatment of the nuclear motions on extended surfaces of the potential energy and electric dipole moments.

Second-order vibrational perturbation theory calculations were performed using the PyVibPTn package,^21,22 which is based on the formulation of perturbation theory described by Sakurai.²³ These calculations utilized the quartic expansions of the potential energy surface evaluated within the Gaussian16²⁴ software package. Our implementation of VPT2 allows us to evaluate transitions to states with more than two quanta of excitation and provides greater flexibility in the choice of the resonances considered than does the standard implementations of VPT2 in Gaussian. These calculations were augmented by one-dimensional calculations of the vibrational levels of the OH stretch and out-of-plane bend based on cuts through the full-dimensional surface, with all of the coordinates, except the OH bond length constrained to their equilibrium values and the three O–H⋯X⁻ atoms constrained to be collinear. Additional details about the VPT2 and the one-dimensional calculations are provided in Sec. S3 of the supplementary material. Natural bond orbital²⁵ calculations were performed to obtain the partial charges of the atoms as the hydrogen atom is displaced either along the OH bond or perpendicular to the plane containing the other three atoms. All electronic structure calculations were performed at the MP2/aug-cc-pVTZ level of theory/basis using Gaussian 16. The corresponding aug-cc-pVTZ-pp basis set and effective core potential were used as given in Refs. 26 and 27 for I⁻.^26,27

The H₂-tagged vibrational predissociation spectra of the three X⁻ · HOCl ions are compared with those reported earlier¹ for the X⁻ · HOD · Ar series in Fig. 2. The band highest in energy in the X⁻ · HOCl series is due to the activation of the nominally forbidden H₂ stretch (⁠$vH2$⁠) when bound to an ion.²⁸ The calculated structures of the H₂ ternary complexes are shown in Fig. S2, where the H₂ molecule is found to preferentially bind onto the halide, as described in Sec. S4. Note that the asymmetrical X⁻ · HOD clusters occur in two isomeric forms (isotopomers) according to whether the H or D atom is bound to the halide. Bands assigned to the D-bound isotopomer are colored gray in Figs. 2(d)–2(f) to minimize the spectral clutter.

The bands due to the X⁻ · HOD isotopomer with the OH group bound to the ion that occur above 2500 cm⁻¹ are dominated by the strong bound OH stretch fundamentals [denoted $vOHb$ and highlighted in red in Figs. 2(d)–2(f)], which are observed to evolve to higher energy from Cl to I. These generally occur along with weaker multiplet structures that arise from anharmonic interactions, as discussed in detail in Refs. 1–2 (band labels are elaborated in Tables I and II). As is the case with X⁻ · HOD, there are several stable isomers of X⁻ · HOCl: the hydrogen bonded form displayed in Fig. 1(b), the halogen-bound X⁻ · ClOH^29–32 or Cl⁻ · XOH, and possibly the binary complex in which XCl is bound to OH⁻. The spectra of the latter isomers are expected to contain a peak associated with a free or weakly perturbed OH stretch in the range of 3500–3700 cm⁻¹. The lack of such features when X = Cl and Br and the very weak feature near 3650 cm^-1 when X = I [denoted by * in Fig. 2(c)] leads us to conclude that the carrier of the spectra shown in Figs. 2(a)–2(c) is indeed the hydrogen bonded X⁻ · HOCl structures. Very recently, the results of additional analysis of the spectrum shown in Fig. 2(c), which focused on the carrier of the * feature, identified its origin as the free OH stretching vibration in the halogen-bonded Cl⁻ · IOH complex.⁵⁹ 

Like the spectra of the X⁻ · HOD clusters, those of the X⁻ · HOCl series [Figs. 2(a)–2(c)] above 2500 cm⁻¹ are similarly dominated by a strong band with halide-dependent shifts that are assigned to the $vOHb$fundamentals of the bound OH group (again highlighted in red). Note that the shifts of these bands [relative to the free OH band of bare HOCl,³³ black arrow labeled $vOHfbare$ in Fig. 2(a)] are much larger (∼3×) than the shifts in the $vOHb$ bands of X⁻ · HOD, while the linewidths (with the exception of that in Cl⁻ · HOD) are comparable. As such, these complexes do not display the typical behavior of strong H-bonds where the linewidths increase along with the relative intensity.³⁴ 

In the lower energy region near the HOD bend fundamental (1400 cm⁻¹ in bare HOD), the X⁻ · HOD spectra [Figs. 2(d)–2(f)] do not exhibit a dominant band, but rather appear with two features of comparable intensity. These have been assigned to the bend fundamental (v_HOD, blue) and the v = 0 → 2 overtone of the frustrated out-of-plane rotation (⁠$2voopH$⁠, green) of the water molecule. Weaker combination bands are also present that arise from excitation of the bend fundamental with one quantum in the in-plane frustrated rotation (v_HOD + v_ip, orange). Note that the bend fundamental displays a gradual red shift down the halide series (∼20 cm⁻¹ per halogen from Cl⁻ to I⁻) and appears farthest above the bend in the bare HOD molecule³⁵ [black arrow in Fig. 2(d) denoted $vHODbare$] in the Cl species (by 105 cm⁻¹). The incremental shifts in the $2voopH$ feature, on the other hand, are much larger with changes of 142 and 159 cm⁻¹ from Cl⁻ to Br⁻ to I⁻. The lower energy range of the X⁻ · HOCl spectra also displays multiplet structures (for Cl and I) near the bend fundamental of bare HOCl³⁶ [black arrow in Fig. 2(a) denoted $vHOClbare$], which are strongly dependent on the halide such that bands red-shift down the series. In this case, however, it is not obvious by inspection which of these are primarily due to the bend fundamentals of the X⁻ · HOCl complexes. We postpone discussion of the mechanics underlying these qualitative trends in the OH bending region to Sec. III C after first considering the electronic character of the strong ionic H-bond.

Very large $vOHb$ red shifts have been reported in the B⁻ · H₂O complexes (B = O, OH, and F) and analyzed in the context of the increasing electric field around the smaller ions, which is, in turn, correlated with the stronger basicities of the lighter halides.⁴ The extreme case of OH⁻ · H₂O, for example, occurs as a quasi-symmetrical [HO⋯H⋯OH]⁻ structure with an equally shared proton,^37,38 thus corresponding to a three-center, two electron covalently bound system akin to the classic case of FHF⁻.³⁹ From the perspective of acid–base interactions, the bound OH stretching fundamental energies reflect the energetics of the so-called “frustrated intra-cluster proton transfer” (FPT) reactions.^4,40 These are the cluster analogs of the familiar base hydrolysis reactions in aqueous electrolyte chemistry,

The mechanics associated with FPT qualitatively account for both the large intensity and extreme red shift of the bound OH stretching fundamental relative to the behavior of a generic free OH group with frequency $vOHf$ ∼ 3700 cm⁻¹.⁴¹ This is illustrated by the shapes of the potential energy curves calculated for the parallel displacement of the shared proton from the oxygen (O) atom to the Cl⁻ ion displayed in the lower panel of Fig. 3 (red and black curves for Cl⁻ · HOCl and Cl⁻ · HOD, respectively). In particular, the attractive outer region on the potential curve calculated for the HOCl system displays an inflection point near 1.35 Å. This occurs when the system adopts electron configurations associated with the ClH⋯OCl⁻ partial proton transfer, thus driving down the v = 1 energy level in the more acidic OH group of HOCl (proton affinities of OH⁻ and OCl⁻ of 1633⁴² and 1502⁴³ kJ/mol, respectively). As is seen by the energy levels calculated based on these one-dimensional cuts, in the case of Cl⁻ · HOCl, the level with one quantum in the OH stretch samples this region of the potential, while for Cl⁻ · HOD, the wave function remains localized in the part of the potential that corresponds to the Cl⁻ · HOD complex.

To illustrate the changes in the electronic wave functions along the FPT coordinate, the upper panel of Fig. 3(a) compares the natural charges^44–51 on the Cl⁻ anionic center for Cl⁻ · HOD (black) and Cl⁻ · HOCl (red). The magnitude of the effective charge on the Cl⁻ ion decreases as the shared proton approaches it (i.e., as r_OH increases), forming a partially covalent interaction in the early stage of the FPT reaction. The intrinsically more responsive HOCl system with respect to charge redistribution, combined with the larger amplitude of the OH displacement in the v = 1 level, accounts for the increased IR transition moment for the OH stretching fundamental in the X⁻ · HOCl systems. Thus, both the degree of charge displacement and the lowering of the potential are directly reflected in the intensity (see calculated values in Table II) and red shift of the $vOHb$ fundamental in the Cl⁻ · HOCl spectrum.

The directional nature of the strong H-bonds in both HOD and HOCl systems has important consequences on spectral behavior in the 1000–1500 cm⁻¹ region of OH bending fundamentals. The role of anharmonicities is immediately clear, for example, by the fact that only a single fundamental in the HOCl bend is expected in this region and is in all cases calculated to fall quite close to that of the isolated HOCl molecule as indicated in Table II. Although a feature is indeed observed near $vHOClbare$ for all three ions, this band [labeled a₁ in Fig. 2(a) and c₂ in Fig. 2(c)] is much weaker than the very strong band [labeled a₃ in Fig. 2(a)] higher in energy at 1564 cm⁻¹ in Cl⁻ · HOCl and similar in strength to a band lower in energy at 1206 cm⁻¹ [labeled c₁ in Fig. 2(c)] in I⁻ · HOCl. For both X = Cl and I, this extra band lies very close to the calculated v = 0 → 2 overtone transition associated with the out-of-plane (oop) frustrated rotation of the HOCl moiety relative to the X–O axis (denoted $2voopH$⁠) with displacements illustrated schematically at the top right of Fig. 2. The observation that one of the features lies close to the harmonic value for $2voopH$ and that it retains its large intensity as its frequency is tuned through the vicinity of the bend fundamental (⁠$vHOClbare$ rule out intensity borrowing through mechanical anharmonicity as the primary cause for the unusually strong oscillator strength for this feature. The $2voopH$ overtone transitions were also found in the X⁻ · HOD spectra (green in the right panel of Fig. 2) with intensities that were traced to the modulation of the large intra-complex charge-transfer contribution in the equilibrium configuration upon displacement along the oop coordinate. This motion rotates the OH group off the X-O axis, effectively breaking the strongly directional H-bond and therefore inducing relaxation of the charge back onto the X⁻ atom. This effect has been analyzed at length,⁶ and the large associated changes in the dipole moments along the X–O axes give rise to surprisingly strong v = 0 → 2 overtone transitions in the $voopH$ and in-plane rotation (⁠$vip$ modes. This is a manifestation of electronic anharmonicity, where the quadratic dependence of the dipole moment on nuclear displacements drives the transition moments for IR excitation. The strongly directional hydrogen bond is also responsible for the shift of v_HOCl to higher frequencies as the interaction with the smaller halide ion increases. Explicit details of the relative contributions to the fundamentals and overtones are presented in Sec. S5 of the supplementary material.

To investigate the magnitudes of the electronic anharmonicities expected for the X⁻ · HOCl systems, we calculated the vector contributions to the dipole moment as a function of displacements along the out-of-plane coordinate (Q_oop), with the results presented in Fig. 4. In the Cartesian axes defined in the inset of Fig. 4(a), the dipole moment perpendicular to the bond, $μ⊥z$⁠, in the direction out of the plane defined by the equilibrium structure, is observed to depend linearly on Q_oop [Fig. 4(a)]. On the other hand, the component parallel to the O⋯Cl⁻ axis, $μ∥x$⁠, displays a quadratic dependence on Q_oop [Fig. 4(b)]. The third component, $μ∥y$ (y-axis), which is also in the heavy atom plane, is nearly zero for Cl⁻ · HOD and is an order of magnitude smaller than the x-component in Cl⁻ · HOCl, as shown in Fig. S5. Note that the magnitude of the change in $μ∥x$ is much larger for the HOCl complexes than for HOD, which is again consistent with the larger degree of charge transfer at the equilibrium geometry, while the change in $μ⊥z$ is only slightly larger for the HOD complex. The strong halide dependence of the $voopH$ frequency is evident in the $2voopH$ bands in the X⁻ · HOD complexes [green in Figs. 4(c), 4(e), and 4(g)], while the bend fundamental (v_HOD, blue) is only weakly dependent on the halide. Thus, the response of the $voopH$ mode directly reflects the stronger H-bonds in the lighter halides that act to stiffen the force constants for the out-of-plane vibrations. With the X⁻ · HOD behavior in mind, it is straightforward to assign the strongly halide-dependent bands in the X⁻ · HOCl complexes [green in Figs. 4(d), 4(f), and 4(h)] to the $2voopH$ transitions, while those that appear close to the neutral HOCl bend are due to the bend fundamentals of the HOCl moieties (v_HOCl, blue).

Closer inspection of the calculated anharmonic behavior of the X⁻ · HOCl complexes in the bending region indicates that the v = 2 levels of the $2voopH$ mode and the v = 1 level of the HOCl bend, which both have A′ symmetry, are coupled through a Fermi interaction. The approximate magnitude of this effect is encoded in the $12FoobQoop2×Qbend$ cubic term in the Taylor expansion of the potential energy. Incorporation of this term in a degenerate perturbation theory calculation yields coupling matrix elements of 9, 13, and 17 cm⁻¹, respectively (see Table III) for Cl, Br, and I. In contrast to the prototypical situation where the overtone transition has a small cross section, both the unperturbed v_HOCl and $2voopH$ transitions are calculated to occur with significant intensities. In the Cl⁻ · HOCl case, the oop overtone transition carries about three times the intensity of that calculated for the bend fundamental (see Table II). This results in an interference term that alters the distribution of oscillator strength among the two bands that result from excitation of the perturbed excited state levels. To gauge how this effect impacts the observed spectra, the calculated zero-order $2voopH$ level was shifted to recover the observed position of this band in the spectra for each of the X⁻ · HOCl complexes, and the Fermi analysis was repeated using the calculated zero-order v_HOCl and Fermi coupling constant. This procedure recovers the intensities of the two bands in the Cl⁻ · HOCl and I⁻ · HOCl complexes [green and blue inverted bars in Figs. 4(d) and 4(h); the spectra obtained without this shift are provided in Fig. S6]. Interestingly, this procedure predicts that the transition moment to one of the two transitions is effectively canceled by the interference term [inverted blue v_HOCl bar in Fig. 4(f)], accounting for the fact that only one band is observed for the Br⁻ · HOCl complex in the bending region (as opposed to being a case of accidental degeneracy). As such, we report in Table II the expected frequency of the fundamental that is too weak to be observed here. Note that the deperturbed levels (i.e., calculated energies used in the 2 × 2 Fermi analysis) yield a smooth evolution of the zero-order bends (decreasing from Cl to I) similar to that observed for X⁻ · HOD, while the observed transitions in HOCl are nearly identical in the Cl and Br spectra and then red-shift in the I complex.

Close inspection of Fig. 4(d) reveals that there is one additional feature in the Cl⁻ · HOCl spectrum in the bending region (orange) that is anticipated by the VPT2 calculation. This feature is traced to the combination band involving excitation of the bending fundamental along with one quantum of the in-plane frustrated rotation (v_HOCl + v_ip). This is again similar to the situation encountered in X⁻ · HOD clusters and arises due to the strong dependence of the electric dipole surface on both the HOD bending and the in-plane displacement of the OH group.⁶ As such, this represents a case where the oscillator strength for a band forbidden in the double harmonic approximation is activated by electronic anharmonicity. Having assigned the $2voopH$ transitions, we note that there is a pronounced anti-correlation between the frequencies of the $voopH$ and $vOHb$ fundamentals. In particular, as the stronger interactions with the acid act to lower the bound OH stretching potentials due to the emergence of the FPT shelf [see Fig. 3(b)], these stronger bonds are harder to break by modes whose displacements are perpendicular to the bond and, thus, lead to blue shifts in the oop fundamentals (as evidenced by the observed behavior of the overtones).

We next address the X⁻ · HOCl band patterns observed in the region of the strong $vOHb$ fundamentals near 2700 cm⁻¹. The appearance of extra bands in this region have been analyzed in the X⁻ · H₂O, X⁻ · HOD, and X⁻ · D₂O spectra and are remarkably complex in the case of the I⁻ · H₂O system reported in 2020.² The dominant effect here is the strong Fermi-type resonance interaction between the $vOHb$ and the v = 2 level of the corresponding OH bend, which in water occurs with a characteristic matrix element of about 35 cm⁻¹.⁵² In the X⁻ · HOD series, this accounts for the enhancement of the OH bend overtones [2v_HOD, blue in Figs. 2(d) and 2(e)] near 3000 cm⁻¹. The increase in the 2v_HOD band intensity from X = Br to Cl occurs because the $vOHb$ fundamental is lowered in the Cl⁻ · HOD complex, bringing its v = 1 level closer in energy to the v = 2 level of the bend. In addition to the bend/stretch Fermi resonances, the OH stretching bands in X⁻ · HOD also occur with weaker combination bands associated with the ion-water stretching (v_OX) and in-plane frustrated rotation (v_ip) soft modes. Because the fundamentals of these modes are typically out of the range of table-top IR laser systems, such as that used here, the combination bands are particularly useful because they provide benchmarks for intermolecular potentials that describe the ion–molecule interactions. In the X⁻ · H₂O series, for example, this procedure provided values for all six fundamentals.⁵³ 

Turning to the X⁻ · HOCl series, the analysis in Sec. III C regarding the assignments of the intramolecular HOCl bending levels provides information necessary to estimate the patterns of levels that occur near the $vOHb$ fundamentals (red in Fig. 2). We begin the spectral decomposition by approximating the energy of the v = 2 OH bending level in the harmonic limit (2 × v_HOCl) using the experimentally measured position of v_HOCl for Cl and I⁻ · HOCl and the calculated position of v_HOCl from Fig. 4 (blue) for Br⁻ · HOCl. These values are included as black arrows in Fig. 5, and it is clear that these levels effectively cross over the v = 1 levels of the bound OH stretch, becoming nearly degenerate in the Br complex. This behavior is, in fact, remarkably similar to that of Br⁻ · H₂O,⁵⁵ where the nominal $vOHb$fundamental appears as a doublet with nearly equal intensity in each member, split apart by about 60 cm⁻¹. Because in this case the zero-order 2v_HOH carries very little oscillator strength, the splitting immediately reveals the H_Fermi coupling matrix element to be ∼30 cm⁻¹ as discussed above. The Br⁻ · HOCl spectrum is more complex in that it displays a multiplet structure with a cluster of overlapping peaks near 2800 cm⁻¹. Because the zero-order levels are far apart in the Cl and I⁻ · HOCl complexes, a similar 2 × 2 deperturbation scheme to recover the separation and relative intensities of the observed $vOHb$ (red) and 2v_HOCl (blue) transitions yields effective H_Fermi values of 66 and 99 cm⁻¹, which are included in Table III. Like the case in the X⁻ · HOD spectra, weaker peaks appear above the dominant $vOHb$ features in the X⁻ · HOCl spectra. The displacements of these above the $vOHb$ fundamentals and their relative intensities are accurately recovered by an anharmonic VPT2 analysis, as indicated by the inverted bars in Figs. 5(a) and 5(c). These are assigned to combination bands involving one quantum of excitation in $vOHb$ and one quantum of excitation in either the in-plane rotation (v_ip, orange) or the ion-HOCl stretching motion (v_OX, pink). The band positions are collected in Table I and provide useful estimates of the soft mode fundamentals presented in Table IV.

Finally, we address the more complex interactions in play near the $vOHb$ fundamental of the Br⁻ · HOCl complex [Fig. 5(b)]. To estimate the order of magnitude of the couplings, we first carried out a simple 2 × 2 deperturbation scheme by considering the zero-order bright $vOHb$ transition interacting with an effective dark partner that manifests as the centroid of oscillator strength in the observed multiplet structure near 2800 cm⁻¹. This procedure yields an effective H_Fermi matrix element of 88 cm⁻¹, which is indeed intermediate between those found for the other two systems (66 and 99 cm⁻¹ for Cl and I, respectively) and is included in Table III. Quantitative analysis of these interactions, however, requires treatment of the many levels involved as evidenced by the many transitions activated in this region. The occurrence of such multiplet structures in Fermi resonances is common^2,56 and results when several levels are in close proximity. One contribution to these arises in the Br⁻ · HOCl case because the bend fundamental is also engaged in a Fermi resonance interaction with the proximal $2voopH$ level. Consequently, three levels (⁠$4voopH$⁠, 2v_HOCl, and $vHOCl+2voopH$⁠) now appear close to the $vOHb$ fundamental in a classic example of a Fermi “polyad.”⁵⁷ We therefore used our VPT2 code to explore the couplings among the nearly degenerate levels in Br⁻ · HOCl in the region of $vOHb$⁠. The details of this analysis are presented in Sec. S3 of the supplementary material. To allow for comparison with the measured spectrum, the $vHOCl+2voopH$ and $4voopH$ energy levels were estimated using the $2voopH$ value obtained in the analysis of the bend. This procedure recovers three transitions in the calculated Br⁻ · HOCl spectrum with significant intensity, which are assigned to the $4voopH$⁠, 2v_HOCl, and $vHOCl+2voopH$ transitions and which fall close to the three closely spaced transitions in the observed spectrum. While the splittings among these peaks are roughly three times as large as those in the reported spectrum, this fine structure is expected to be very sensitive to both the magnitude of the Fermi coupling constant and the zero-order energies of the states. The existence of three transitions where only one is expected further supports the impact of the near degeneracy between v_HOCl and $2voopH$ in the lower frequency region of the spectrum. Finally, this analysis also recovers a fourth transition with appreciable IR intensity that is assigned to $vOHb+vOX$⁠, which is in good agreement with the feature observed at 2841 cm⁻¹.

As was found to be the case in the I⁻ · H₂O system, part of the pervasive multiplet character of the bands near the $vOHb$ fundamental arises from combination bands built on the bend overtone. When these fall near the v = 1 level of the OH stretch, they also undergo a Fermi resonance interaction, but with a much smaller matrix element. As with the Cl and I complexes, the Br⁻ · HOCl spectrum displays weaker bands displaced above the main features that are assigned to the in-plane rotation and ion–molecule translations and are included in Table IV. Note that the trends in these soft modes—decreasing from Cl to Br to I with values of 105 and 311, 83 and 235 (calculated), and 71 and 197 cm⁻¹, respectively—are in keeping with the qualitative picture of the H-bond becoming stronger and more directional for the smaller halides.

Anharmonic analysis of the vibrational band patterns displayed by the cryogenically cooled, H₂-tagged X⁻ · HOCl (X = Cl, Br and I) complexes indicates that both electronic and mechanical anharmonicities contribute on a similar scale to the intensities of “extra bands” that occur across the vibrational spectrum. These nominally forbidden IR transitions gain oscillator strength due to intrinsic properties of the strong anionic H-bond. Specifically, the directionality of this interaction is associated with unusually large charge transfer (CT) with displacement of the bound H-atom toward the halide ion, which enhances the intensities and red shifts of the acidic OH stretch fundamentals for the smaller and more basic halide ions. Soft mode displacements that act to break this H-bond generate surprisingly strong overtones because these motions modulate the CT contribution. On the other hand, the strength of the anharmonic coupling (Fermi resonance) between the v = 1 level of the OH stretch and the v = 2 level of the intramolecular HOCl bend is similar to that found in the more weakly interacting X⁻ · H₂O systems, as evidenced by the characteristic matrix elements required to recover observed behavior in a simple (reduced dimensionality) interaction model.

See the supplementary material for detailed descriptions of the experimental setup, HOCl sample preparation, and additional computational details.

M.A.J. and R.B.G. acknowledge support for this work by the NSF through the NSF Center for Aerosol Impacts on Chemistry of the Environment (CAICE) (Grant No. CHE-1801971). Any opinions, findings, and conclusions or recommendations expressed in this material are those of the author(s) and do not necessarily reflect the views of the National Science Foundation (NSF). Additionally, this work used the Extreme Science and Engineering Discovery Environment (XSEDE),⁵⁸ which is supported by Grant No. TG-CHE170064. A.B.M. acknowledges support from the Chemistry Division of the National Science Foundation (Grant No. CHE-1856125 for scientific work and Grant No. OAC-1663636 for perturbation theory code development). Parts of this work were performed using the Ilahie cluster at the University of Washington, which was purchased using funds from a MRI grant from the National Science Foundation (Grant No. CHE-1624430). This work was also facilitated through the use of advanced computational, storage, and networking infrastructure provided by the Hyak supercomputer system and funded by the STF at the University of Washington.

The authors have no conflicts to disclose.

The data that support the findings of this study are publicly available in a dataset hosted by the UCSD Library Digital Collections at: https://doi.org/10.6075/J0ZS2WPJ.