Tag-Free and Isotopomer-Selective Vibrational ... - ACS Publications

Article Cite This: J. Phys. Chem. A 2018, 122, 9275−9284

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Tag-Free and Isotopomer-Selective Vibrational Spectroscopy of the Cryogenically Cooled H9O4+ Cation with Two-Color, IR−IR DoubleResonance Photoexcitation: Isolating the Spectral Signature of a Single OH Group in the Hydronium Ion Core Chinh H. Duong, Nan Yang, Patrick J. Kelleher, and Mark A. Johnson* Sterling Chemistry Laboratory, Yale University, New Haven, Connecticut 06520, United States

J. Phys. Chem. A 2018.122:9275-9284. Downloaded from pubs.acs.org by UNIV OF WINNIPEG on 12/20/18. For personal use only.

Ryan J. DiRisio and Anne B. McCoy* Department of Chemistry, University of Washington, Seattle, Washington 98195, United States

Qi Yu and Joel M. Bowman* Department of Chemistry and Cherry L. Emerson Center for Computational Science, Emory University, Atlanta, Georgia 30322, United States

Bryan V. Henderson and Kenneth D. Jordan* Department of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260, United States S Supporting Information *

ABSTRACT: We report vibrational spectra of the cryogenically cooled H9O4+ cation along with those of the D2 tagged HD8O4+ isotopomers using two variations on a two-color, IR−IR double-resonance photoexcitation scheme. The spectrum of the isolated H9O4+ ion consists of two sharp features in the OH stretching region that indicate exclusive formation of the “Eigen” cation, the H3O+·(H2O)3 isomer that corresponds to the filled hydration shell around the hydronium ion. Consistent with this structural assignment, the spectrum of the HD8O4+ isotopologue is resolved into contributions from two isotopomers: one with the single OH group on one of the three solvent water molecules and another in which it resides on the hydronium core ion. The latter spectrum is dominated by a broad feature assigned to the isolated hydronium OH stretching fundamental with an envelope that is similar to that displayed by the H3O+·(H2O)3 isotopologue. The feature appears with a diffuse band ∼380 cm−1 above it, which is assigned to a combination band involving the hydronium OH stretching vibration and the frustrated translation mode of the HD2O+ core and one of the solvating water molecules. These trends are analyzed with anharmonic calculations involving four-mode coupling on a realistic potential surface and interpreted in the context of vibrationally adiabatic potentials based on insights acquired from analysis of the ground state probability amplitudes obtained from diffusion Monte Carlo calculations. “tagging” approach in which weakly bound adducts (H2 or Ar) are photoevaporated to record the spectrum by mass loss.12,13,21 Such measurements necessarily raise the issue of whether attachment of the tag perturbs the cluster ion structure,22−24 and indeed tag-induced distortions have been exploited in the spectra of the D9O4+ (denoted hereafter 4D) to reveal the cooperative response of the local H-bonded

1. INTRODUCTION The H9O4+ cluster ion, commonly referred to as the H3O+(H2O)3 “Eigen” ion (hereafter denoted 4E and displayed in Figure 1a) has been the focus of intense study by theory and experiment over the past three decades1−18 since the first spectroscopic observation of it in the infrared by Schwarz.19 The most direct probe of the structure of this cluster has been through analysis of its vibrational spectrum, which now extends over the range 200−7400 cm−1.1,2,7,9,11−13,17,20 To date, all linear spectra of the key bands in the fundamental region arising from cold ions have been obtained with the messenger © 2018 American Chemical Society

Received: August 31, 2018 Revised: October 7, 2018 Published: October 11, 2018 9275

DOI: 10.1021/acs.jpca.8b08507 J. Phys. Chem. A 2018, 122, 9275−9284

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The Journal of Physical Chemistry A

a two-color IR−IR excitation scheme where a first laser (IR1) is scanned through non-dissociative resonant transitions in the cold ion and a second laser (IR2) is fixed at a frequency for which the cold ions are transparent, but once excited, exhibit dissociative absorption that is not strongly dependent on the color of the first photon. This is carried out with a protocol involving three stages of mass selection and hence denoted an MS3IR2 method of secondary mass analysis. The overall twocolor, IR−IR photofragmentation strategy was introduced by Yeh et al.34 in the 1980s using mid-IR excitation followed by multiple photon dissociation with a line-tuned CO2 laser, but has since been used sparingly in ion spectroscopy.35,36 The IR−IR scheme has recently undergone a renaissance, however, with the implementation using two mid-IR lasers so that fewer photons are required to dissociate the excited cluster.37,38 For example, a recent report describes the application of this IR1− IR2 scheme to the H7O3+ system to establish that the spectrum of the free ion is indeed remarkably close to that obtained with He tagging.6 Here we extend that study by applying it to the 4H system. Cluster ions are produced with electrospray ionization (ESI) of 5 mM HCl in H2O in a humidity-controlled chamber that houses the ESI needle (100 μm inner diameter). They are then passed through several stages of differential pumping and loaded into a 3D Paul trap (Jordan TOF Products, Inc.) held at 10 K for D2 and 37 K for N2, with a closed cycle He cryostat (Sumitomo Heavy Industries, Ltd.). Ions in the trap are tagged with D2 or N2 for the one-color predissociation and isotopomer-selective double-resonance experiments or cooled with pure He to generate cold, bare ions for the two-color photodissociation experiments. Spectra of the bare ion were taken at 10 and 20 K to establish that the band patterns do not change over this range (see Figure S1), and the extended scans required for the two-color, IR−IR experiments were carried out at 20 K to avoid accumulation of ice on the walls of the trap (from impurities in the He buffer gas line), which limits the useful data acquisition time. We emphasize that the relatively slow cooling of the ions prepared in this way circumvents kinetic trapping of high-energy isomers, which is known to occur in the case of supersonic jet ion sources.39−43 The ions are then transferred to a triple focusing TOF photofragmentation mass spectrometer, displayed schematically in Figure S2, for one- and two-color IR excitation experiments that are described in detail in ref 37.

Figure 1. Two isomers of the H9O4+ cation: (a) the H3O+(H2O)3 “Eigen” (4E) form, and (b) the H5O2+(H2O)2 “trans-Zundel” (4Z) form, both computed at the MP2/aug-cc-pVDZ level of theory. The different colors of hydrogen atoms (two for (a) and four for (b)) indicate the unique sites that a single proton can occupy in 4D8H-D2.

network during the transfer of an “excess” proton between two water molecules.7 The degree to which the tags affect the intrinsic band pattern of the H9O4+ (4H) ion has recently risen in importance in the effort to experimentally pin down the possible role of other isomeric structures,2 in particular, the trans-Zundel isomer (4Z) displayed in Figure 1b.2,4,5,7 The 4Z isomer is calculated to lie about 672 cm−1 above 4E, but the two isomers are predicted5 to yield surprisingly similar spectra, raising the question of how the two forms can be distinguished experimentally. Subsequent theoretical efforts2,4 with more complete treatments of anharmonic effects indicated that the splitting behavior of the free OH groups should provide a useful means to distinguish the two forms. This occurs because the 4E arrangement has three equivalent water molecules while 4Z yields two classes of bands in the free OH region: one arising from the terminal water molecules that are single Hbond acceptors (A) and the other from the interior molecules in an H-bonding acceptor−donor (AD) configuration. A complication of the previous experiments using messenger tagging, however, is that a multiplet structure is observed in the free OH region that could either be induced by the tags or reflect the different OH contributions from different isomers.2,9,11−13,21 Here we revisit the 4H spectrum with a set of two-color, IR−IR double-resonance experiments designed to isolate the spectrum of the cold, bare ion, thereby eliminating complications arising from tag perturbations. A variation on the two-color scheme is then used to follow the evolution of the spectra upon incorporation of a single H atom into the cluster in an isotopomer−selective study of the HD8O4+ isotopologue, where the H atom is either on the core hydronium or on an exterior water (henceforth denoted 4D8Hcore and 4D8Hfree, respectively). These new data provide fresh insights into the nature of the diffuse band centered near 2650 cm−1, which is associated with excitation of the OH groups in the hydronium core ion of the 4E structure and unambiguously establish that it is the only species formed under all experimental conditions used thus far.

3. RESULTS AND DISCUSSION 3a. Comparison of Two-Color IR−IR Spectrum of 20 K Bare 4H with One-Color (Linear) Spectra Obtained with H2 and N2 Tagging. Because the dissociation energy of the H9O4+ cluster (with loss of H2O) is about 6000 cm−1,44 photodissociation by excitation in the hydrogen-bonded OH stretching region (∼2650 cm−1) requires absorption of three photons. As such, the vibrational spectrum of the bare ion has been limited to ensembles of warm ions that provide sufficient internal energy to drive one-photon dissociation or to onecolor IRMPD of cooler (but not temperature controlled) ions.45,46 A typical IRMPD spectrum is displayed in Figure 2d, where the dominant features (a5−7) near 2650 cm−1 have traditionally been assigned to the OH stretches of the embedded H3O+ ion in the 4E structure. The D2 tagged spectrum is presented in Figure 2b, demonstrating that the IRMPD band structure is largely intact under the better defined tagging conditions. An exception, however, is the

2. EXPERIMENTAL SECTION The experimental challenge of primary concern here is to recover the intrinsic vibrational spectrum of the cold (vibrational zero-point) 4H ion. One way to minimize complications arising from tag perturbations is through the use of very weakly bound He atoms,23,25−33 and this has been exploited in the H5O2+ (2H) and H7O3+ (3H) systems23 to quantify the perturbations caused by Ar and Ne tag atoms. Here, we turn to another approach in which we obtain the linear spectrum of the bare, isolated ion through application of 9276


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larger in the 4H-N2 spectrum (Figure 2a). We confirmed that this pattern was homogeneous with double-resonance hole burning experiments (see Figure S3) thus ruling out any contribution from isomers arising from different tagging sites. The mechanics underlying these multiplets are considered in detail below. Although compelling, the structural implications of observing only the sharp a1 and a3 doublet and not the a2 and a4 features in the IRMPD spectrum are complicated because the nonlinearities inherent in the method are known to result in “missing” bands arising from “IRMPD transparency”.47 It is therefore important to establish the degree of splitting in the high-energy OH stretching bands in the linear spectrum of the cold, bare ion. To accomplish this, we next turn to two-color IR−IR spectroscopy of the cryogenically cooled ion to eliminate complications arising from both tags and IRMPD. Acquisition of the tag-free spectrum of a cold water cluster ion with two-color IR−IR photodissociation requires a favorable circumstance in which absorption of the first photon creates a warm cluster that has a broadened spectrum corresponding to the internal energy imparted by the photon. This condition is satisfied when IVR is sufficiently fast that energy is randomized before absorption of the second photon. This scenario has been shown to be operative in the I−·(H2O)2 and 3H systems reported so far with the Yale instrument.6,37 In both cases, a second excitation frequency (IR2) could be identified that is not absorbed by the cold ions but can drive one- or twophoton dissociation of the photoexcited clusters in such a way that the photodissociation cross-section is not strongly dependent on the energy of the resonance excited by the first photon. The identification of an appropriate IR2 frequency requires a survey step in which IR1 is fixed on a known transition, while IR2 is scanned through the spectrum of the excited ion to identify features that are induced through resonant excitation by IR1 (in addition to the three-photon photodissociations arising from IRMPD with IR2 alone). In the case of 4H, the spectrum of the cold ion was obtained by monitoring absorption at the IR2 location indicated by the arrow in Figure 2c at 3690 cm−1, just to the blue of the symmetric stretch fundamental. The photodissociation spectrum of the excited 4H clusters is included in Figure S4 and free displays considerable broadening between the sharp νOH and s free bands in the tagged spectra. The photoexcited ions also νOH as display extended absorption from the a5−7 feature toward the free OH region. The resulting tag-free spectra of the 4H ion at a trap temperature of 20 K is presented in Figure 2c. This spectrum is indeed very similar to those obtained by D2 tagging and IRMPD (Figure 2b,d, respectively) with the exception that both the band doubling of the free OH fundamentals and the extra features near 3529, 3450, and 3380 cm−1 (denoted ‡n=1−3) disappear in the tag-free trace. An expanded view of the high-energy band structure is presented in Figure 3. The collapse of the doubling in the 20 K, bare 4H spectrum (Figure 3c) confirms that the remaining two peaks in this trace arise free free from the νOH and νOH modes of the three solvent water s as molecules in the 4E structure, as originally suggested by Lee and co-workers in 1986.21 For completeness, we note that the IR−IR spectrum of the cold, bare 4D system was recently reported48 in the region near the dominant band assigned to the OD stretches of the embedded D3O+ ion, and the extended scan obtained in the course of this work is included in Figure S5, along with those of the 4D-D2 and 4D-N2 complexes. Like

Figure 2. Messenger tagged vibrational predissociation spectra of (a) 4H-N2, (b) 4H-D2, and (c) 4H bare, where 4H denotes the H+(H2O)4 and 4H-X corresponds to the tagged complexes with X = N2 and D2. Dashed lines emphasize the evolution of analogous vibrational modes in this series. MS3IR2 denotes the isotopomerselective experimental approach that involves three stages of mass selection and two-color, IR−IR multiple photon dissociation as described in the text, while IRMPD corresponds to the one-color IR multiple photon dissociation experiment. The level diagram of the IR2MPD scheme used to collect the spectra is included in Figure S4, where the probe laser (IR2) was fixed at hν2 = 3690 cm−1 (black arrow in (c)). The red spectral region corresponds to the OH stretch of the H3O+ ion, while green highlights bands due to the tag-bound exterior water molecule symmetric (a4) and antisymmetric stretches (a2). Band labels a1−9, energies and their spectral assignments are included in Table 1.

behavior of the free OH bands (a1 and a3) that are nominally free free assigned to the symmetric (νOH ) and antisymmetric (νOH ) s as modes of the two OH groups on each of the three water molecules tethered to the core ion by accepting a single Hbond (denoted an “A” water site for single H-bond acceptor) in the 4E structure. These features are split apart in the 4H-D2 spectrum to give the appearance of a pair of closely spaced doublets separated by 85 cm−1, with two new features (a2 and a4) appearing ∼10 cm−1 to the red of each of the unperturbed positions. Note that the D2 (or Ar) tag is calculated to attach preferentially to only one of the free OH groups in the 4E structure (see insert Figure 2b). The multiplet splittings are 9277


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S6, which indicates that the observed trend can be readily accommodated by this local oscillator model in the approximation that the mixing matrix element remains constant at H12 = 50 cm−1. We next consider the origin of the breadth displayed by the dominant band at 2650 cm−1 (a5−7). First, we note that its shape in the MS3IR2 spectrum (Figure 2c) is very similar to that found in the 4H-D2 spectrum (Figure 2b), and that the 4H feature is significantly broader than that found in 4D (fwhm 120 vs 50 cm−1, respectively). There is, interestingly, a band labeled “*a” (for 4H-D2) and “*b” (for 4D-D2) that lies about 380 cm−1 (300 cm−1 in 4D-D2, shown in Figure S5) above the dominant bands whose origin is not clear. For example, recent high-level calculations4 (reproduced in Figure S7) attribute absorptions in this energy range to various overtone and combination bands. An important question in this regard is the role of the splitting between the symmetric core and and antisymmetric stretches of the hydronium ion (νOH s OHcore νas ) in the two isotopologues. Calculations completed at the MP2/aug-cc-pVDZ level of theory and basis using Gaussian0950 show that at the harmonic level, for example, the core νOH fundamental is predicted to occur 72.5 cm−1 above that s OHcore in 4H with about 3% of the intensity. Inclusion of of νas anharmonic corrections, however, suggests a more complex situation where many modes contribute to the strong absorption near 2600 cm−1.2,4 In the 4D case, the sharp feature near 2000 cm−1 has been analyzed in the context of the core dominant νOH fundamental in a scenario where the three OD as oscillators are nearly degenerate, in contrast to the behavior of the isolated D3O+ where they are calculated to split by ∼141 cm−1 from ref 51 (and experimentally shown to split by 87 cm−1 in H3O+ [refs 52−56]). The suggestion that this splitting is strongly suppressed in 4D was supported by the fact that the dominant feature splits into three distinct bands with increasing strengths of tag molecules attached to one of the exterior water molecules as reported in ref 7. This, in turn, raises the question of how the coupling between OH(D) oscillators depends on the H/D isotopic composition of the embedded hydronium ion. 3b. Isotopomer-Selective Spectra of H2 Tagged 4D8H: Isolating the Spectral Signatures of a Single OH Embedded in the Eigen Structure. The coupling between the OH(D) groups in the hydronium core of the 4E isomer can be addressed experimentally using a scheme in which only a single H atom is present (4D8H-D2). In that case, the OH group can occupy distinct locations according to the number of unique sites available in the cluster structure. When the barriers are large for interconversion between sites, this leads to the formation of spectroscopically distinct isotopomers. The spectra of each isotopomer can then be isolated using another two-color, IR−IR photofragmentation (i.e., double-resonance hole burning) as described in detail in previous applications to I−·(HDO)(D2O), D2O(H2O)5−, and Cs+·D2O(H2O)5 clusters.37,57,58 Note that there are two such sites in the 4E isomer of 4H and four in the 4Z isomer, as illustrated in Figure 1. When only a single H is available, we expect the doublet in the free OH region to collapse to a single line arising from the isotopomer with an HOD molecule in the “A” position, whereas incorporation into the hydronium core ion should remove all activity in the free OH range. Note that this is in contrast to the situation in the 4Z structure, where the free OHs on the “AD” and “A” water molecules should split to yield two features in the free OH region: one at the midpoint of the

Figure 3. Expanded view of the OH stretching region for 4H with messenger tags (a) N2 and (b) D2 and using (c) two-color MS3IR2 and (d) one-color IRMPD. For labels, see the Figure 2 caption and a more detailed list containing their corresponding energies and assignments is included in Table 1.

the case in the cold 4H spectrum, 4D displays a simple doublet in the OD stretching region with a splitting of 110 cm−1, again very close to that observed for bare D2O (117 cm−1 from ref 49). The similarities in the two systems, and the fact that the simpler 4D spectrum is convincingly assigned to the 4E structure,4,7,17 strongly support the conclusion that the 4H system exclusively adopts the 4E arrangement. The energies (in wavenumbers) of selected transitions in Figures 2 and 3 are included in Table 1. We next address the origin of the tag-induced doubling that occurs in the a1−4 series in the context of the 4E structure. As discussed above, two bands (a2 and a4) red shift in a tagdependent way, while the adducts are calculated to attach to only one of the OH groups on one of the “A” water molecules solvating the hydronium ion. This effect has been considered at length in the case of the 4D-X (X = D2, N2, CO, D2O) series,7 where it was treated with a model starting with a basis of two decoupled OD oscillators on the same water molecule. When the environment of the two OH oscillators in an “A” water molecule are identical, their local frequencies are also equal. The off-diagonal coupling matrix element (∼50 cm−1) that characterizes isolated water yields the observed transition free free locations that are associated with the νOH and νOH OH s as stretching normal modes. When the tag molecule attaches to one of the OH groups, the zero-order degeneracy is lifted such that the frequency of the bound OH group drops while the frequency of the other OH group is unaffected. Inclusion of the 50 cm−1 coupling now introduces a smaller mixing of these two zero-order states, and a smaller energy shift. When this occurs, the upper level of the mixed pair appears lower in energy than the antisymmetric stretch in an untagged “A” water molecule. This results in red shifts of both levels compared to unperturbed locations in the free ion. The explicit treatment of the shifts in the 4H-X (X = D2 and N2) is included in Figure 9278


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Table 1. Band Energies and Assignments for 4H-X (X = N2, D2), 4H Bare, 4D-D2, Bare 4D, and 4D8H-D2 along with the VSCF/VCI Calculations of Bare 4H, 4D, and 4D8H (Where H Is in Either the Free or Core Positions)a

a

The bare 4H and 4D experiments were obtained using the MS3IR2 technique described in the text.

free free νOH and νOH modes and another at the location of the AD s as

differences in the predicted OH patterns for the tagged 4E and 4Z isomers. The 4D8H-D2 spectrum is presented in Figure 4b. Highest in energy, it displays a single OH stretching feature at 3695

band in the 4H isotopologue. The calculated patterns are presented in Figure S8 to demonstrate the significant 9279


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D2 spectrum is not evident in the single H spectrum, which is expected since statistical weighting favors attachment of the D2 tag to an OD group over the single OH group by 5:1, and it has been reported earlier that zero-point energetics further suppress attachment to OH groups when ODs are present.59 Isolation of the 4D8Hcore isotopomer spectrum was achieved by setting the probe laser on the shoulder of the diffuse feature near c7 at 2605 cm−1 (red arrow in Figure 4b). This reveals the spectral signature of the single OH group on the embedded HD2O+ core ion in Figure 4d. Note that the c1 band is indeed missing, but the diffuse band is intact, along with a companion peak about 380 cm−1 above it (*ca). The fact that the breadth is retained in the IR−IR double-resonance depletion spectrum is significant because it establishes that this feature is homogeneous, and that the (*ca) transition is associated with excitation of a single OH group. As such, both bands are traced to the behavior of the vibrationally excited states rather than residual thermal broadening at low temperature. To address the qualitative trends revealed by the IR−IR double-resonance depletion spectra, we turn to recent highlevel anharmonic calculations based on inclusion of high-order mode coupling and large amplitude motion on an accurate potential energy surface.4 This extends the work published6 in 2017 which exposed the surprisingly complex nature of the band structure displayed by the related 3H and its deuterated isotopologue (3D). Details for the application of VSCF/VCI theory to the 4D8Hcore and 4D8Hfree isotopomers are presented in the Supporting Information (S12), with the results presented in Figure 5a,c. As was the case in 3H and 3D, these calculations predict that the nominal OH stretching fundamental associated with the isolated OH on the hydronium ion is heavily diluted upon inclusion of higher order terms, thus rationalizing its diffuse structure. The extent of this coupling makes it difficult, however, to draw qualitative conclusions regarding the dominant mechanisms driving the fast intramolecular vibrational redistribution signaled by the large energy range over which the oscillator strength derived from the single OH group is spread. Figure S9 emphasizes this point by plotting the number of admixtures of normal mode states for the upper levels of transitions in the 2400−4000 cm−1 spectral region. These admixtures are quantified by calculating the so-called “participation numbers”, defined in ref 6 and discussed in detail in ref 60. Note that this calculation also predicts absorptions in the vicinity of the observed *ca band, which has not been previously assigned. The calculated composition of the excited states involved in the *ca region includes a significant contribution from the translation of the HD2O+ ion toward the ligand bound by the OH group (i.e., the O−O stretching mode). The origin of the * feature is interesting in the context of the spectral behavior of the HD2O+ isotopologue embedded in the quasi-rigid 18-crown-6 ether (18C6) scaffold.48 The crown complex has a more open structure, with an O−O distance from the hydronium to the crown of 2.741 Å vs 2.565 Å in the 4E structure. The H3O+(18C6) spectrum displayed extremely broad OH bands (>500 cm−1 fwhm), even when only a single OH group was present in the hydronium core ion. This extremely diffuse envelope was observed to resolve into a discrete progression in the OD stretching region that involves a soft mode at about 85 cm−1 (Figure S10). That behavior led to a model in which the diffuse envelope was traced to strong coupling between the OH stretching frequency and the O−O distance from the hydronium oxygen to the nearest oxygen

Figure 4. Predissociation spectra of (a) 4D-D2, (b) 4D8H-D2, and (e) 4H-D2 are presented along with the MS3IR2 isotopomer-selective double-resonance depletion spectra of (c) 4D8Hfree-D2 and (d) 4D8Hcore-D2. The green (3695 cm−1) and red (2605 cm−1) arrows indicate the probed positions used to acquire traces (c) and (d), respectively. The top inset displays the 4E structure with the green (spectra in trace c) and red (spectra in trace d) hydrogen atoms identifying the two unique positions available in 4D8H-D2. A detailed list of band positions and their assignments for a1−7, b1-b4, c1−7, *a-c, and † are included in Table 1.

cm−1 (c1 in Figure 4b) that is close to the midpoint of the free free νOH and νOH bands (3702 cm−1) in the 4H-D2 spectrum s as (Figure 4e). This is consistent with the expectations for 4E, but not in agreement with a contribution from the 4Z isomer. Traces c and d in Figure 4 present the two distinct patterns recovered using two-color, IR−IR double-resonance depletion spectroscopy. The broad structure near the dominant a5−7 feature at 2650 cm−1 is retained in the 4D8Hcore-D2 spectrum (Figure 4d), which unfortunately partially overlaps with the free OD stretching bands as indicated by the 4D-H2 spectrum in Figure 4a. The latter accounts for the sharp features near 2770 cm−1, which appears as five bands (c2−6, †) in the 4D8Hfree-D2 spectrum (Figure 4c), as expected for the OD free free νOD (c5,6) and νOD (c2,3) fundamentals on the “A” type D2O s as molecules, as well as the OD band that falls between them when HOD occupies the third “A” site (c4), together with the † doublet that corresponds to a combination band that always occurs in this region.17 The fact that only two isotopomers are observed to contribute to the spectrum of the 4D8H isotopologue is consistent with the 4E structure but not the putative 4Z isomer, which should give rise to three distinct patterns as discussed above. The dip traces in Figure 4c,d were obtained by fixing the probe laser on the bands indicated by colored arrows in Figure 4b. Setting the probe on the exterior OH feature (c1) at 3695 cm−1 isolates the spectrum of the 4D8Hfree isotopomer, with the result shown in Figure 4c. This isotopomer-selective spectrum exhibits sharp bands associated with the free OH and OD stretches expected for the 4E isotopomer. The fact that these features occur over a flat background immediately establishes that all of the diffuse activity above 2400 cm −1 arises from the 4D 8 H core isotopomers. Note that the peak doubling found in the 4H9280


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Figure 6. Cuts through the calculated DMC probability amplitudes of the vibrational ground state of 4DHcore. The scans present the distributions of ROH bond lengths for a series of ROO values from 2.79 to 2.31 Å, with the labels defined by the arrows in the inset.

Figure 5. Comparison of the calculated VSCF/VCI spectra for (a) 4D8Hfree and (c) 4D8Hcore with the MS3IR2 isotopomer-selective double-resonance depletion spectra obtained for (b) 4D8Hfree-D2 and (d) 4D8Hcore-D2. The stick spectra for the VSCF/VCI calculations are overlaid with the convoluted spectra in (a) and (c) to qualitatively show the number of bands contributing to each feature. Refer to Table 1 for band labels, positions, and assignments of γ1−7, c1−7, *ca‑b, and *γa‑b.

and basis, as implemented in Gaussian 1668 and construct the OH adiabatic potential surfaces Uad(Roo)v that include the harmonic v = 0 and 1 excitations of the OH stretching degree of freedom at each ROO value. This approximation yields differently shaped potential energy functions that govern the eigenstates and energies associated with motion along the Roo degree of freedom for each OH stretching energy level (shown OH in Figure S11). These Uad(Roo)v curves were estimated by adding the harmonic zero-point energy in the OH stretch as well as the energy of the νOH = 1 level at each ROO value. Using OH these Uad(Roo)v potentials, we calculated the energies and wave functions for the νOO = 0 and 1 levels on both νOH (0 and 1) surfaces. These intermediate results were then used to calculate the soft mode activity in the spectrum through evaluation of the Franck−Condon factors for transitions from the ground state to states with νOH = 1 and νOO = 0 and 1. We find that the intensities of the combination band involving excitation of the O−O vibration is roughly 6% the intensity of the fundamental, while the combination band is blue-shifted from the OH fundamental by an amount that is 40 cm−1 larger than the ground state O−O stretch frequency. These results are therefore consistent with the experimental findings and support the qualitative assignment of the bands indicated with *a and *b in Figure 4 to combination bands involving the IHB or IDB and the associated O−O stretch, which are also consistent with theoretical calculations by Yagi and Thomsen.2

atom on the ring. This coupling leads to an extensive progression involving excitation of the OH stretch with many quanta of the O−O translational soft modes.48,61−63 In the case of the 4H ion, two of these soft modes associated with the embedded H3O+ ion have been observed by Asmis and coworkers1 at 236 (H2O wag) and 316 cm−1 (H3O+ rattle or frustrated translation) using the free electron laser at the Fritz Haber Institute in Berlin. As these frequencies are much lower than the 380 cm−1 shift between the *a feature and the diffuse band (a5−7) in 4H-D2, it is not straightforward to assign the *a feature to a combination band involving v = 1 of the OH stretch with the O−O soft mode. To further explore the qualitative origin of the * band, we analyzed the couplings between the single OH stretching displacement in 4D8Hcore, ROH, and the distance between the two oxygen atoms that this hydrogen atom is sandwiched between, ROO. These couplings are manifested in the probability amplitudes for the ground vibrational state wave function calculated using the diffusion Monte Carlo (DMC) approach.64−66 This was computed on the same potential surface used for the VSCF/VCI calculations discussed above. The details of this calculation are presented elsewhere.67 Because DMC yields the many-body wave function without appealing to a separable basis, one has to reveal its character by extracting conditional probabilities along various slices through the multidimensional function. Figure 6 presents the interdependence of the probability amplitudes along the ROH and ROO coordinates defined above. On the basis of this analysis, as cuts in the probability amplitude for increasing values of ROO are analyzed, we find that, as ROO is increased, ⟨rOH⟩ and σrOH ∝ 1/ωOH1/2 both decrease. This implies that a vibrationally adiabatic calculation, performed in the same spirit as those used in our recent study of H3O+(18C6), can offer a qualitative picture of the important interactions. In this approach, we calculated a one-dimensional relaxed cut through the many-body Born−Oppenheimer potential energy surface UBO(ROO) along ROO at the MP2/aug-cc-pVDZ level of theory

4. CONCLUSIONS The spectra of the 4H and 4D isotopologues cooled to about 20 K in a cryogenic ion trap were obtained without the use of a perturbing messenger tag through application of two-color, IR−IR double-resonance spectroscopy. Most importantly, the isolated ion spectrum displays two sharp features in the highenergy OH(D) stretching region consistent with their assignment to the three dangling water molecules in the Eigen structure of the cluster. This is further reinforced by isotopomer-selective spectra of the 4D8H isotopologue, which reveals the presence of two distinct species that are readily assigned to the unique OH group residing either on a dangling water molecule or in the hydronium core. The band associated with excitation of the single OH group embedded in the 9281


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Foundation’s Center for Aerosol Impacts on Chemistry of the Environment (CAICE) under grant number CHE-1305427 for the development of the laser systems critical for these experiments. C.H.D. thanks the National Science Foundation Graduate Research Fellowship for funding under Grant No. DGE-1122492. Support from the Chemistry Division of the National Science Foundation (ABM: CHE-1619660) is gratefully acknowledged. Q. Y. and J. M. B. thank the National Science Foundation for funding the VSCF/VCI analysis under grant CHE-1463552. 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 (CHE-1624430).

hydronium core is still quite diffuse, indicating that this broadening is an intrinsic feature of the vibrationally excited states accessed in the 2650 cm−1 region. A second diffuse feature is also observed to occur upon excitation of the single embedded OH group that lies about 380 cm−1 above the dominant band. This feature is recovered by high-level anharmonic calculations on a realistic potential energy surface, which reveal an important contribution arising from a combination band with the O−O stretching translational mode between the hydronium ion and the water molecule to which the OH group is attached. A simple model of this anharmonic coupling that invokes vibrationally adiabatic potential energy curves provides a qualitative explanation for the observed behavior. This exercise is useful in that it offers a context to understand how coupling between the OH stretching degree of freedom and the soft modes associated with motions in the first hydration shell can impact the spectral signatures of embedded hydronium ions in a variety of different chemical environments.

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(1) Esser, T. K.; Knorke, H.; Asmis, K. R.; Schollkopf, W.; Yu, Q.; Qu, C.; Bowman, J. M.; Kaledin, M. Deconstructing Prominent Bands in the Terahertz Spectra of H7O3+ and H9O4+: Intermolecular Modes in Eigen Clusters. J. Phys. Chem. Lett. 2018, 9, 798−803. (2) Yagi, K.; Thomsen, B. Infrared Spectra of Protonated Water Clusters, H+(H2O)4, in Eigen and Zundel Forms Studied by Vibrational Quasi-degenerate Perturbation Theory. J. Phys. Chem. A 2017, 121, 2386−2398. (3) Yu, Q.; Bowman, J. M. Communication: VSCF/VCI Vibrational Spectroscopy of H7O3+ and H9O4+ Using High-level, Many-body Potential Energy Surface and Dipole Moment Surfaces. J. Chem. Phys. 2017, 146, 121102. (4) Yu, Q.; Bowman, J. M. High-level Quantum Calculations of the IR Spectra of the Eigen, Zundel, and Ring Isomers of H+(H2O)4 Find a Single Match to Experiment. J. Am. Chem. Soc. 2017, 139, 10984− 10987. (5) Wang, H.; Agmon, N. Reinvestigation of the Infrared Spectrum of the Gas-phase Protonated Water Tetramer. J. Phys. Chem. A 2017, 121, 3056−3070. (6) Duong, C. H.; Gorlova, O.; Yang, N.; Kelleher, P. J.; Johnson, M. A.; McCoy, A. B.; Yu, Q.; Bowman, J. M. Disentangling the Complex Vibrational Spectrum of the Protonated Water Trimer, H+(H2O)3, with Two-color IR-IR Photodissociation of the Bare Ion and Anharmonic VSCF/VCI Theory. J. Phys. Chem. Lett. 2017, 8, 3782−3789. (7) Wolke, C. T.; Fournier, J. A.; Dzugan, L. C.; Fagiani, M. R.; Odbadrakh, T. T.; Knorke, H.; Jordan, K. D.; McCoy, A. B.; Asmis, K. R.; Johnson, M. A. Spectroscopic Snapshots of the Proton-transfer Mechanism in Water. Science 2016, 354, 1131−1135. (8) Kulig, W.; Agmon, N. Both Zundel and Eigen Isomers Contribute to the IR Spectrum of the Gas-phase H9O4+ Cluster. J. Phys. Chem. B 2014, 118, 278−286. (9) Mizuse, K.; Fujii, A. Tuning of the Internal Energy and Isomer Distribution in Small Protonated Water Clusters H+(H2O)4−8: An Application of the Inert Gas Messenger Technique. J. Phys. Chem. A 2012, 116, 4868−4877. (10) Agmon, N. The Grotthuss Mechanism. Chem. Phys. Lett. 1995, 244, 456−462. (11) Okumura, M.; Yeh, L. I.; Myers, J. D.; Lee, Y. T. Infrared spectra of the Solvated Hydronium Ion: Vibrational Predissociation Spectroscopy of Mass-selected H3O+·(H2O)n·(H2)m. J. Phys. Chem. 1990, 94, 3416−3427. (12) Fournier, J. A.; Wolke, C. T.; Johnson, M. A.; Odbadrakh, T. T.; Jordan, K. D.; Kathmann, S. M.; Xantheas, S. S. Snapshots of Proton Accommodation at a Microscopic Water Surface: Understanding the Vibrational Spectral Signatures of the Charge Defect in Cryogenically Cooled H+(H2O)n=2−28 Clusters. J. Phys. Chem. A 2015, 119, 9425−9440. (13) Headrick, J. M.; Diken, E. G.; Walters, R. S.; Hammer, N. I.; Christie, R. A.; Cui, J.; Myshakin, E. M.; Duncan, M. A.; Johnson, M. A.; Jordan, K. D. Spectral Signatures of Hydrated Proton Vibrations in Water Clusters. Science 2005, 308, 1765−1769.

ASSOCIATED CONTENT

S Supporting Information *

This material is available free of charge on the ACS Publications Web site at The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpca.8b08507. Instrument diagrams, MS3IR2 spectra, double-resonance depletion spectra, N2 and D2 predissociation spectra, expanded view of the OH stretching region, VSCF/VCI calculated spectra, predicted tag induced spectral shifts, vibrational frequencies, vibrational predissociation spectra, adiabatic treatment of the OO and OH stretches, computational details for the VSCF/VCI calculations, and square of VCI coefficients (PDF)

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REFERENCES

AUTHOR INFORMATION

Corresponding Authors

*M.A.J. Tel: +1 203 432 5226. Email: [email protected]. *A.B.M. Tel: +1 206 543 7464. Email: [email protected]. *J.M.B. Tel: +1 404 727 6592. Email: [email protected]. *K.D.J. Tel: +1 412 624 8690. Email: [email protected]. ORCID

Nan Yang: 0000-0003-1253-2154 Mark A. Johnson: 0000-0002-1492-6993 Anne B. McCoy: 0000-0001-6851-6634 Joel M. Bowman: 0000-0001-9692-2672 Kenneth D. Jordan: 0000-0001-9178-6771 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS M.A.J. and K.D.J. thank the U.S. Department of Energy, Office of Science, Basic Energy Sciences, CPIMS Program, under Awards DE-FG02-06ER15800 and DE-FG02-00ER15066 for funding the experimental and theoretical research on the protonated water tetramer. M.A.J. also thanks the Air Force Office of Scientific Research under grant FA9550-18-1-0213 for funding the two-color IR-IR triple focusing cryogenic photofragmentation mass spectrometer. K.D.J. also thanks the Center for Research Computing at the University of Pittsburgh for computational resources. P.J.K. thanks the National Science 9282


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