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Disentangling the Complex Vibrational Mechanics of the Protonated Water Trimer by Rational Control of Its Hydrogen Bonds Chinh H Duong, Nan Yang, Mark A. Johnson, Ryan J. DiRisio, Anne B. McCoy, Qi Yu, and Joel M Bowman J. Phys. Chem. A, Just Accepted Manuscript • DOI: 10.1021/acs.jpca.9b05576 • Publication Date (Web): 20 Aug 2019 Downloaded from pubs.acs.org on August 25, 2019

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The Journal of Physical Chemistry

Disentangling the Complex Vibrational Mechanics of the Protonated Water Trimer by Rational Control of Its Hydrogen Bonds Chinh H. Duonga, Nan Yanga, and Mark A. Johnsona,* aSterling Chemistry Laboratory, Yale University, New Haven, CT 06520, USA *M. A. Johnson. Tel: +1 203 432 5226, Email: [email protected] Ryan J. DiRisio,b Anne B. McCoyb,§,* bDepartment of Chemistry, University of Washington, Seattle, Washington 98195, USA §A. B. McCoy. Tel: +1 206 543 7464, Email: [email protected] Qi Yu,c Joel M. Bowmanc,#,* cDepartment of Chemistry and Cherry L. Emerson Center for Computational Science, Emory University, Atlanta, GA 30322, USA #J. M. Bowman. Tel: +1 404 727 6592, Email: [email protected] Abstract The vibrational spectrum of the protonated water trimer, H+(H2O)3 , is surprisingly complex, with many strong features in the expected region of the fundamentals associated with two H-bonded OH groups on the H3O+ core ion. Here we follow how the bands in this region of the spectrum evolve when the energies of the fundamentals in the H-bonded OH stretches are systematically increased by the attachment of increasingly strongly bound “tag” molecules (He, Ar, D2, N2, CO, and H2O) to the free OH position on the hydronium core ion of H+(H2O)3, as well as by replacement of the hydrogen atom in the non-bonded OH group on hydronium with methyl and ethyl groups. This allows for the incremental transformation of the complex band pattern observed in H+(H2O)3 into that of the “Eigen” structure of the protonated water tetramer. Differences among the trajectories of the various bands provide an empirical way to disentangle features primarily due to the displacements of the OH stretches bound to the hydronium core from those arising from anharmonic coupling to states involving one or more quanta in lower frequency modes. The latter are found to be dramatically enhanced when the nominal frequencies of the intermolecular OH stretching modes approach those of the intramolecular bends of the H3O+ and H2O constituents in both H and D isotopologues.

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I. Introduction The molecular distortions that accompany attachment of a proton to a water cluster have recently come into sharp focus with the application of temperature-controlled ion spectroscopy to size-selected H+(H2O)n cluster ions.1-27 Surprisingly, among the most complex spectral patterns is that displayed by one of the smallest clusters, the protonated water trimer, H+(H2O)3, hereafter denoted 3H. Its calculated structure, presented at the top of Figure 1, is that of an incomplete hydration shell around the H3O+ Figure 1. Top insets show the structures of H+(H2O)3 hydronium ion, leaving one of its OH groups (blue (3H), highlighting the rotation angles of the water in Figure 1) non-bonded. The strong hydrogen molecule off of the axis defined by the shared bonds to the flanking water molecules break the proton and the oxygen atoms (12˚) and by the free C3v symmetry of hydronium, causing the OH bond off of the plane containing the other three absorptions nominally due to the OH stretching atoms that make up the hydronium ion (28.5˚). (A) fundamentals of the bound OH groups (bands a5-8 Harmonic spectrum of H+(H2O)3 computed at the in Figure 1B) to occur at about half the frequency CCSD(T)-F12a/VTZ level of theory, and (B) bare of the free OH group (Figure 1, a3). In essence, linear spectrum of 3H compared with (C) 18-mode the strongly anharmonic potential energy curves VSCF/VCI calculations of bare 3H. All three traces that govern these vibrational levels result in large are reproduced with permission from ref. 26. amplitude motions upon vibrational excitation 28 that partially drive intra-cluster proton transfer. The mechanics at play in the 3H spectrum have recently been addressed with advanced theoretical methods that explicitly treat 18-dimensional motions on an accurate potential energy surface.26 The spectrum calculated with that approach is displayed in Figure 1C, and it indeed recovers the complexity in the experimental spectra of both H and D isotopologues. A similar comparison to Figure 1 with the all D isotopologue (denoted 3D) is presented in Figure S1. These calculations provide a quantitative description of the states accessed by infrared excitation in a normal mode representation. In the traditional picture of intramolecular vibrational redistribution (IVR), the oscillator strength of the “bright” H-bonded OH stretching fundamentals in the double harmonic approximation is widely distributed among the “dark” zero-order states by anharmonic couplings to the bright states. Although the detailed anharmonic analysis of the vibrational bands26, 29 is compelling, the assignments of transitions to excitations of specific vibrational motions can depend on the details of the calculation, particularly the choice of coordinates. In cases such as 3H where one of the fundamentals is strongly coupled to several near-by excited states, it is informative to consider how this complex spectral pattern would evolve in a scenario where the bright, zero order states are gradually displaced to higher energies, effectively scanning them through the background levels. In this study, we demonstrate how this can be accomplished experimentally by exploiting two approaches10, 30 that effectively “tune” the frequencies of OH groups engaged in strong H-bonds. 2 ACS Paragon Plus Environment

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One strategy to control the frequency of a bound OH group X involves incrementally increasing the binding energy of an atom or R molecule (X) that is attached to the free OH group on the embedded hydronium ion, as illustrated in Figure 2. This acts to weaken the bonds to the flanking water molecules due to the anti-cooperativity displayed among H-bonds to the same core ion.31-34 This is a variation on the control scheme recently used10 to incrementally Figure 2. Schematic structure + distort the H (H2O)4 Eigen ion through a series of structures that of the complex R+(H2O)3·X, encode the response of all five OH stretches proximal to the charge where X denotes an adduct defect as the system approaches the transition state for bound to the central free OH 10 intermolecular proton transfer. In the second method, the nongroup (He, Ar, D2, N2, CO, bonded OH group on the hydronium ion is replaced with an alkyl H2O) when R = H or substituent, R in Figure 2. This is an adaptation of the approach used alternatively, ROH2+(H2O)2·X, earlier to monitor the character of the intermolecular proton bond where X = H2 when R = CH3 + in the H2O(H )OH2 “Zundel” ion when each non-bonded OH is and CH2CH3. Arrows indicate 30 incrementally replaced by a methyl group. Alkyl substitution the evolution of the bond effectively increases the basicity of the lone pair of electrons on the lengths with increasingly oxygen atom to which the shared proton is attached. In that case, strongly bound adducts (X) or the bridging proton frequencies were observed to follow the same larger alkyl derivatives (R). trend as that obtained when adducts (X) were attached to each free OH group on the Zundel scaffold. The magnitude of the frequency shifts upon alkylation were observed to be much larger than those induced by the series X=He, Ar, D2, N2 and CO, and were in fact on the same order as that found when an exterior OH group is complexed to a water molecule.30 Thus, by combining tagging and alkylation, we can follow the incremental evolution of the bound OH band pattern from 3H to 4H. This information also allows us to analyze the implications of these results on the assignments of the features in both the 3H and 4H spectra that occur near the expected locations of the intramolecular HOH bending modes. II. Experimental Section For the 3H·X experiments, cluster ions are produced with electrospray ionization (ESI) of 1 mM HCl in H2O within a humidity-controlled chamber through a 100 μm diameter ESI needle. These ions are then passed through several stages of differential pumping and then stored in a 3D Paul trap (Jordan TOF Products, Inc.) using He buffer gas mixed with ~15% messenger tags of either D2, N2, or CO. Depending on the gas mixture, the trap was held at 15, 35, and 63 K for D2, N2, and CO respectively, with a closed cycle He cryostat (Sumitomo Heavy Industries, Ltd.) to condense tag adducts onto the cold cluster ions. After approximately 98 ms in the trap, the ions are extracted and intersected with one tunable IR laser (LaserVision) for one-color predissociation or two IR lasers for both two-color, isotopomer-selective double-resonance and linear spectroscopy of the cold, bare 3H(D) clusters. Substitution of HCl and H2O with D2SO4 and D2O/HDO were used for the 3D·X and 3D6H·D2 experiments. MeOH and EtOH were leaked into the first octopole guide to collisionally exchange (ligand switch) an H2O molecule for MeOH or EtOH to obtain the alkyl derivatives MeOH2+(H2O)2 (denoted as 2H·MeOH) and EtOH2+(H2O)2 (denoted as 2H·EtOH). Further experimental details for acquisition of the 3H bare 3 ACS Paragon Plus Environment


spectrum are described in ref. 26, while the experimental apparatus and double resonance, photobleaching spectroscopy technique can be found in ref. 35. Procedures for obtaining the single OH isotopologue HD6O3+ (denoted 3D6H) are analogous to those found in ref. 27, which also describes the computational details for the anharmonic vibrational self-consistent field/vibrational configuration interaction (VSCF/VCI) calculations. The VPT2 and harmonic calculations described below and in the SI were performed at the MP2/aug-cc-pVDZ level of theory and basis as implemented in the Gaussian program package.36 Cartesian coordinates for each of the R+(H2O)3·X species, where X = He, Ar, D2, N2, CO, H2O when R = H and ROH2+(H2O)2 where R = CH3 and CH2CH3 can be found in Table S1. III. Results and Discussion The effect of weakly perturbing adducts on the 3H spectrum was addressed at length in ref. 26 in the context of the behavior of the cold, bare ion, which was obtained using a two-color IR-IR double resonance method.26 That study established that the low energy bands near 2000 cm-1 displayed minimal distortion upon complexation of 3H with either D2 or Ar ligands, as demonstrated by the comparison in Figure S2. We therefore focus here on the D2 messenger tag spectrum to assess the nature of the atomic displacements at play in the most intense vibrational bands. The sharp features at the high frequency side of the 3H·D2 spectrum (Figure 3C) are readily assigned to the antisymmetric (a1) and symmetric (a2) OH stretches of the flanking water molecules, while the feature to the left of a2 (a3, blue) arises from the D2-bound OH group on the hydronium core. The latter occurs at 3668 cm-1 in the 3H·He complex (Figure 3A) as well as in the bare 3H cluster (Figure 1B). Lowest in energy, the a11 feature in Figure 3C is due to the fundamental in the out-of-plane vibration of the H-bonded OH groups in the hydronium core. This motion resembles the umbrella fundamental of the hydronium ion, although it primarily involves motions of two of the three OH bonds. In the 3H cluster, this umbrella motion corresponds to displacement of the bound OH bonds in the hydronium core off of the O···O axis. Although the complex series of bands (a4-10) in the range 1600 to 2600 cm-1 fall in the expected locations of the HOH bending and bound OH stretching fundamentals, these have been traced to complex vibrational motions involving extensive mixing between the bend and stretch displacements as well as to combination bands involving various soft modes of the ion-molecule scaffold.26 Based on ref. 26, for example, the strongest feature, a8, near 1900 cm-1 is assigned to extensively mixed states involving the out-of-plane frustrated rotation of hydronium, the H3O+ umbrella mode and IHB symmetric and asymmetric stretch. IIIA. Incremental spectral evolution from 3H to 4H with tagging and alkyl substitution. Figure 3 presents the evolution of the 3H·X spectra for X=He, Ar, D2, N2, CO, and H2O with increasing binding energy of the tags in traces 3A-3E and 3H, along with those for the alkyl derivatives 2H·MeOH and 2H·EtOH in traces 3F and 3G, respectively. This combination of H-bonding anticooperativity and chemical modification (replacement of H by CH3 and CH3CH2) acts to incrementally weaken the H-bonds to the flanking water molecules in traces 3A-3H. Note that the band arising from the OH group bound to the tag, denoted a3 (Figure 3, blue), is readily identified at the high energy side of the spectra. Its increasing red shift and intensity enhancement (relative to the sharp free OH bands near 3700 cm-1) follow the expected trends with increasing proton affinities of the tagging atom or molecule (X), which are included in Table S2. Note that the character of the lower energy a4-8 bands 4 ACS Paragon Plus Environment

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changes dramatically as the centroids of the diffuse absorptions (red arrows, defined as ∑ ωjIj/∑ Ij, the j

j

average intensity (I) weighted frequency (ω) within a select spectral region specified in Figure 3 and 4 captions) evolve toward the dominant absorption (a5-7) near 2600 cm-1 (Figure 3H, red band adapted from ref. 5) in the 4H spectrum. The latter band has been studied at length with isotopomer selectivity and double resonance methods,27 and is due to the OH stretching fundamentals of the embedded hydronium ion in the 4H·D2 (so-called “Eigen”) ion. We remark that this overall behavior, where the bands derived from the OH stretches bound to the flanking water molecules and that to the tag evolve in opposite directions with increasing tag binding energy, is the spectroscopic manifestation of H-bond anticooperativity.31-34, 37 An important trend revealed by the survey in Figure 3 is the fact that the low Figure 3. Vibrational predissociation spectra of energy bands do not simply blue shift, as R+(H2O)3·X, where X denotes an adduct bound to the might be expected from the systematic red free OH group of the hydronium ion and is (A) He, (B) shifts of the sharper a3 bands of the OH group Ar, (C) D2, (D) N2, (E) CO, (H) H2O when R = H (3H). For bound to the tags. Instead, a feature in the cases of ROH2+(H2O)2·X when R = (F) CH3 (2H·MeOH) location of the dominant peak in the bare and (G) CH2CH3 (2H·EtOH), X = H2. Green bands show spectrum (a8) remains essentially fixed in the evolution of the H2O bends (dark green, a10) and energy as the intensity profile shifts onto H3O+ bends (light green, a9), while the grey dashed line other peaks that lie higher in energy (as highlights the evolution of the features appearing shown by the red arrows in Figure 3, which closest to the dominant a8 feature in the 3H and 3H·D2 indicate a blueshift of the position for the spectra. Blue dashed lines trace the redshift of the tag centroid of the intensity in the region bound free OH, both as a function of different adducts between 1600 and 3000 cm-1). In fact, the and alkyl substituents. Traces A and C were feature that appears in the vicinity of the a8 reproduced from ref. 26 with permission from ACS, band gradually weakens going down the tag while H is adapted from ref. 5 with permission from series (gray dashed line in Figure 3), while the AAAS. Red arrows for B-G indicate the centroid of dominant band envelope evolves toward the bands between 1600 and 3000 cm-1, while the range a5-7 features in the 4H spectrum (Figure 3H).5 for H was from 2000- 3200 cm-1, computed by The persistence of intensity in the region of obtaining the average intensity weighted frequencies the a8 feature, as the bound OH stretch is for that region. Band labels, experimental frequencies, shifted to the blue is consistent with and assignments can be found in Tables S3 and S4. observation of similar two-quanta transitions in modes that correspond to displacement of the bound OH bond off of the O···Y– axis seen in the halide



(Y–) water systems.38-39 As in the case of the tagged 3H·X ions, the intensities of these transitions are comparable to those of the bend fundamentals. Another indication that the band structure in the protonated water trimer is not simple is that the shape of the overall band contour in the region of the H-bonded OH stretch is not preserved upon isotopic substitution. This effect was analyzed earlier, with the spectrum of the D+(D2O)3·D2 (3D·D2) isotopologue displayed in Figure 4A and compared with the photon energy scaled 3H·D2 spectrum in Figure S3. We therefore carried out a similar survey of the tag dependence of the 3D·X bands, which are displayed in Figures 4B and 4C, along with the 4D·D2 spectrum in Figure 4D. This series also exhibits a gradual evolution of the band intensities from 3D to 4D. Note that the location of a dominant low energy band in the 3D spectrum (b8b) quickly falls off in intensity as the most intense absorptions blue shift toward the OD stretches of the embedded hydronium ion in the 4D·D2 spectrum (b5-7 Figure 4. Predissociation spectra of 3D·X, in Figure 4D near 2000 cm-1). where X = D2 (A), N2 (B), CO (C), and D2O The empirical spectral trends revealed in Figures (D). Red arrows for A-C indicate the 3 and 4 are consistent with the scenario inferred from the centroid of bands between 1250 and high level anharmonic calculations of the 3H spectrum.26, 2250 cm-1, while the range for D was 29, 40 Analysis of the wave functions obtained in these from 1775-2250 cm-1 computed by calculations indicated that the strong absorptions in the obtaining the average intensity weighted 3H spectrum near 1900 cm-1, long attributed to the bound frequencies for that region. Trace A is OH stretches,20, 41 are best considered excitations of adapted from ref. 26 with permission complex motions that act to distribute the oscillator from ACS and trace D is adapted from strength derived from the bound OH fundamentals over ref. 10 with permission from AAAS. Band many energetically proximal vibrational levels. Although labels, experimental frequencies, and the anharmonic effects in the 3H(D) systems were assignments can be found in Table S5. accurately treated in the VSCF/VCI calculations, it is not straightforward to apply that level of theory to the higher dimensionalities at play in the tagged and alkylated systems of interest here. Therefore, we turn to the more limited, but widely available second order vibrational perturbation theory (VPT242-43) approach, as implemented in Gaussian 16,36 to gauge how the band structures are predicted to evolve in the 3H·X, 3D·X, and 2H·ROH·H2 systems. The results of these calculations are reported in Tables S6 and a comparison of the calculated anharmonic (VPT2) spectra with the experimental spectra is available in Figure S4. Consistent with the measured spectra, the intensities of the bands near the maxima in the bare clusters decrease with increased tag binding strength but retain some intensity throughout the series (see Table S6). We refrain from extracting specific assignments to the various bands in light of an earlier report29 indicating that VPT2 predicts dramatically different vibrational degrees of freedom to be responsible for the strong bands in the 3H and 3H·D2 spectra even though the experimental patterns are similar as illustrated in Fig. S2. We remark 6 ACS Paragon Plus Environment

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that the approximate energy of the anharmonic local OH stretch frequency can also be obtained by analyzing the ground state wave function obtained using diffusion Monte Carlo (DMC) methods on the same potential energy surface used in the VSCF/VCI calculations.40, 44 Applying this analysis, we find that the nominal frequency of the out-of-phase vibrations of the bound OH stretch is predicted to be near 1807 cm-1 (1665 cm-1 in 3D), close to the observed centroids.40 This is consistent with the bright state mixing model where most of the oscillator strength is derived from the displacement of the bound OH(D). IIIB. Spectral signature of an isolated bound OH oscillator with isotopomer-selective, two-color IR-IR double resonance spectroscopy. Given the broad range of activity derived from the bound OH stretching motion in the 3H spectrum, it is useful to consider where the v=1 level of a hypothetical, uncoupled OH group would appear. This issue can be addressed experimentally by measuring the spectral behavior of a single, bound OH group on the hydronium core of the HD2O+(D2O)2 isotopomer donating an H bond to a flanking water (hereafter denoted 3D6Hbound). Three isotopomers of 3D6H are available that differ according to whether the OH group resides on the free OH position of the hydronium core (3D6Htag bound), one of its two bound OH groups (3D6Hbound), or on a non-bonded OH group on one of the two flanking water molecules (3D6Hfree). The unresolved Figure 5. Comparison of the predissociation 3D6H·D2 spectrum (i.e., due to contributions from spectra of (A) 3D·D2, (B) 3D6H·D2, (C) the all three isotopomers) is displayed in Figure 5B, VSCF/VCI calculated spectrum of 3D6Hbound (D) where it is compared with those of 3D·D2 and 3H·D2 the double resonance depletion spectra of in Figures 5A and 5E, respectively. As mentioned 3D6Hbound·D2 isolating the position of the H atom above in the experimental section, the spectra of donating an H bond to a flanking water molecule, each isotopomer can be obtained using selective and (E) 3H·D2. The structure corresponds to the photobleaching of each contribution to the 3D6Hbound·D2, with the shared proton position spectrum in Figure 5B. This is accomplished with highlighted with a red circle. The red arrow in (B) two-color, IR-IR double resonance, an advanced indicates the probe position (2049 cm-1) for the method that requires three stages of mass double resonance experiment which produced selection in addition to the two laser interaction 2 3 trace C. Band labels, experimental frequencies, regions, and is hence denoted an IR MS class of 27, 35 and assignments can be found in Table S7. secondary analysis. The isolated (D2-tagged) spectra of the three isotopomers are included in Figure S5, while that of the key isotopomer with the single OH group in the H-bond donor position (3D6Hbound) is presented in Figure 5D, and the excitation energy used to obtain the spectrum is shown with the red arrow in 5B. Note that there is a minor contribution from the isotopomer with the OH 7 ACS Paragon Plus Environment


group located on a flanking water molecule (3DHfree), as evidenced by the weak, but sharp peak at 3685 cm-1 (c1). The explicit spectrum of the 3DHfree isotopomer is presented in Figure S5D, and its weak contribution does not affect the qualitative conclusions about the character of the bands associated with the 3D6Hbound species. The 18-dimensional anharmonic calculation for the bare 3D6Hbound is included in Figure 5C. The comparison of the D2-tagged 3D6Hbound spectrum with those of the 3D (Figure 5A) and 3H (Figure 5E) isotopologues is interesting, in that the dominant peak at 1830 cm-1 (c12 label in Figure 5D) appears redshifted by only 48 cm-1 relative to that (a8) in the 3H spectrum shown in Figure 5E. This is reminiscent of the behavior reported earlier for the case of the single bound OH isotopomer of the H+(D2O)4 isotopologue, denoted 4D8Hcore,27 where the diffuse, asymmetrical shape of the 4D8Hcore·D2 spectrum was observed to be quite similar in breadth and location to the bands displayed by 4H in the region of the bound OH stretch. As such, it is empirically evident that the complex character of the 3H spectrum arises largely from the local vibrational mechanics of an isolated OH oscillator in the hydronium core. The high-level calculation (Figure 5C) recovers this overall band pattern displayed by 3D6Hbound·D2, again in the context of highly coupled OH(D) displacements with soft modes, as was the case in the 3H system. The primary conclusion from this part of the study is that the contribution of the OH group is complex in this region of the spectrum, where the very large redshifts bring its nominal OH stretching frequency closer to those of the H2O and H3O+ bends, while at the same time interacting strongly with background states based on soft modes that break the H-bonds that bind the core hydronium ion to the flanking water molecules. It seems likely that much of this complexity arises because the v=1 level of the bound OH stretch explores frustrated proton transfer regions of the potential surface that drive structural deformations concomitant with partial intracluster charge transfer. This behavior is therefore related to the extreme broadening reported earlier when the HD2O+ ion is sequestered in the binding pocket of crown ether hosts or fully coordinated in water clusters.27, 45 IIIC. Evolution of the HOH bending manifold in the tag series. Finally, we turn to the behavior of the bending modes associated with the flanking water molecules as well as those of the hydronium core. Here it is valuable to recall the situation encountered in the H5O2+ “Zundel” ion, where the bending modes of the two water molecules tethered by the shared proton display bending fundamentals at ~1750 cm-1. This lies ~155 cm-1 above that of an isolated water molecule46 and 120 cm-1 above the bends in H3O+.47 That effect has been traced to the strong coupling between the bridging proton parallel stretch and the bends,6, 48-49 which leads to strongly coupled vibrations in which the lower energy band near 1000 cm-1 corresponds to an in-phase collective motion between the stretch and bend while the upper level results from excitation of the out-of-phase partner. When cast in a local mode picture involving isolated bend and stretch, the observed levels can be reconstructed by applying an effective harmonic mixing matrix element of about 750 cm-1. Very recently, Dzugan et al.40 also considered the 3H spectrum in this context, which offers the variation where the proximal bound OH stretch now lies above the energy of the bends, in contrast to the situation encountered in the Zundel ion. The nominal bending fundamentals of the flanking water molecules in 3H are thus pushed lower in energy than those observed in cases where the bound OH stretches are much higher in frequency, this time with an effective harmonic matrix element of 201 cm-1. 8 ACS Paragon Plus Environment

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The capability of systematically displacing the bound OH stretches higher in energy with increasingly strongly bound tags enables a direct test of the coupling model for the frequencies of the bending fundamentals. Figure 6 presents an expanded display of the bending region, with the bands nominally assigned to the bends highlighted in green (a9,10 for 3H). Indeed, the two bands arising from the bending modes blue shift down the series. The two bends evolve such that the lower energy member of the doublet is converging toward the bends of the dangling water molecules in the 4H spectrum, while the higher energy feature trends toward the HOH bending fundamental of the embedded H3O+ core ion in the Eigen structure (attributed7 to a11 in Figure 6E). Interestingly, the a10 feature in the 4H spectrum falls close to the a8 feature in the 3H spectrum, whose Figure 6. Predissociation vibrational intensity dramatically decreases down the tag series. The spectra showing an expanded view of latter effect is important, as it has been challenging to the water bending region for (A) identify the origin of this 4H feature with anharmonic 3H·Ar, (B) 3H·D2, (C) 3H·N2, (D) 3H·CO, theory.10, 20, 50 and (E) 4H·D2. Green bands trace the Analysis of the evolution of the bending movements of the H3O+ (a9) and H2O transitions at the VPT2 level indicates that the blue shifts (a10) bends in 3H·Ar to those of the down the tag series occur from two dominate effects: 4H·D2 (a11 and a12 for H3O+ and H2O, one due to the decoupling of the free OH group on the respectively) across the tag series. hydronium upon attachment of the adducts and the second to the displacement of the bound OH stretching frequency to higher energies that reduces the mixing between the two degrees of freedom. As the results in Table S8 and S9 indicate, at the harmonic level both effects have similar contributions to the overall shift. However, when the large anharmonicity of the bound OH stretch is included in the analysis, the shift due to changes in the mixing of these two vibrations becomes the more important contributor. Based on these results, it would be useful to address the origin of various features that appear near the bending fundamentals in the H+(H2O)n=5-8 clusters that have thus far eluded compelling assignments.41 This is especially true in the case of 5H, where “extra” bands in this this region (i.e., not expected from the pattern of fundamentals) has complicated the assignment of the shared proton in the spectrum.4, 34, 41, 51 IV. Summary We demonstrate how a series of increasingly strongly bound tag molecules, in conjunction with alkyl substitution, can be used to unravel the nature of the strong transitions in the vibrational spectrum of the protonated water trimer. The suppression of the strongest band in the 3H·D2 spectrum with increasing strength of the tag is consistent with anharmonic vibrational calculations that suggested that it involves a large contribution from a combination band with a soft mode of the scaffold. The complex 9 ACS Paragon Plus Environment


bands in the 3H(D)·X series evolve toward the strongest features in the 4H(D)·D2 spectra, which are due to the OH(D) stretching bands of the embedded hydronium ion in the Eigen structure of the protonated water tetramer. These trends also reveal significant perturbations in the HOH bending modes of the flanking water molecules when the bound OH stretching frequencies are close by. The degree of coupling of the hydronium and water modes specific to the trimer depends sensitively on the tag species. A simple explanation for this, if it exists, appears to require a level of computational effort that is beyond the current state-of-the-art and would benefit from future studies as the field evolves. Lastly, bands associated with a single bound OH group in the 3D6Hbound isotopomer were isolated using IR-IR double resonance, and appear surprisingly similar to those displayed by 3H, illustrating the complex behavior is not simplified by suppression of intramolecular coupling between similar OH groups. Acknowledgements We thank Olga Gorlova and Lais Taveres for their contributions in acquiring the survey spectra that laid the foundation for this work. M.A.J. thanks the U.S. Department of Energy, Office of Science, Basic Energy Sciences, CPIMS Program under grant award DE-FG02-06ER15800 for funding the experimental research on the protonated water trimer and the Air Force Office of Scientific Research under grant FA9550-17-1-0267 for funding the two color IR-IR triple focusing cryogenic photofragmentation mass spectrometer. C.H.D. thanks the National Science Foundation Graduate Research Fellowship for funding under grant DGE-1122492. A.B.M acknowledges support from the Chemistry Division of the National Science Foundation (CHE-1619660). Parts of this work were performed using the Ilahie cluster, which was purchased using funds from a MRI grant from the National Science Foundation (CHE-1624430). Q. Y. and J. M. B. thank the National Science Foundation (CHE1463552) for funding. The authors also thank NASA, CXC, UMass, D. Wang et al, and Radio: NRF/SARAO/MeerKAT telescope for the use of their image on the cover photo. Supporting Information The Supporting Information is available free of charge on the ACS Publications website and contains: Additional figures and tables comparing the theoretical and experimental results, Cartesian coordinates, additional discussion of the VPT2 results, description of the DMC calculations, list of proton affinities, and an Excel file containing the full results of the VPT2 calculations.


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Okumura, M.; Yeh, L. I.; Lee, Y. T. The Vibrational Predissociation Spectroscopy of Hydrogen Cluster Ions. J. Chem. Phys. 1985, 83, 3705-3706. Okumura, M.; Yeh, L. I.; Myers, J. D.; Lee, Y. T. Infrared Spectra of the Cluster Ions H7O3+·H2 and H9O4+·H2. J. Chem. Phys. 1986, 85, 2328-2329. Douberly, G. E.; Walters, R. S.; Cui, J.; Jordan, K. D.; Duncan, M. A. Infrared Spectroscopy of Small Protonated Water Clusters, H+(H2O)n (n=2-5): Isomers, Argon Tagging, and Deuteration. J. Phys. Chem. A 2010, 114, 4570-4579. Fagiani, M. R.; Knorke, H.; Esser, T. K.; Heine, N.; Wolke, C. T.; Gewinner, S.; Schollkopf, W.; Gaigeot, M.-P.; Spezia, R.; Johnson, M. A., et al. Gas Phase Vibrational Spectroscopy of the Protonated Water Pentamer: The Role of Isomers and Nuclear Quantum Effects. Phys. Chem. Chem. Phys. 2016, 18, 26743-26754. Fournier, J. A.; Johnson, C. J.; Wolke, C. T.; Weddle, G. H.; Wolk, A. B.; Johnson, M. A. Vibrational Spectral Signature of the Proton Defect in the Three-Dimensional H+(H2O)21 Cluster. Science 2014, 344, 1009-1012. Hammer, N. I.; Diken, E. G.; Roscioli, J. R.; Johnson, M. A.; Myshakin, E. M.; Jordan, K. D.; McCoy, A. B.; Huang, X.; Bowman, J. M.; Carter, S. The Vibrational Predissociation Spectra of the H5O2+·RGn (RG = Ar, Ne) Clusters: Correlation of the Solvent Perturbations in the Free OH and Shared Proton Transitions of the Zundel Ion. J. Chem. Phys. 2005, 122, 244301. McCoy, A. B.; Guasco, T. L.; Leavitt, C. M.; Olesen, S. G.; Johnson, M. A. Vibrational Manifestations of Strong Non-Condon Effects in the H3O+X3 (X = Ar, N2, CH4, H2O) Complexes: A Possible Explanation for the Intensity in the "Association Band'' in the Vibrational Spectrum of Water. Phys. Chem. Chem. Phys. 2012, 14, 7205-7214. Mizuse, K.; Fujii, A. Infrared Photodissociation Spectroscopy of H+(H2O)6·Mm (M = Ne, Ar, Kr, Xe, H2, N2, and CH4): Messenger-Dependent Balance Between H3O+ and H5O2+ Core Isomers. Phys. Chem. Chem. Phys. 2011, 13, 7129–7135. 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. 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. Fournier, J. A.; Wolke, C. T.; Johnson, C. J.; Johnson, M. A.; Heine, N.; Gewinner, S.; Schollkopf, W.; Esser, T. K.; Fagiani, M. R.; Knorke, H., et al. Site-Specific Vibrational Spectral Signatures of Water Molecules in the Magic H3O+(H2O)20 and Cs+(H2O)20 Clusters. Proc. Natl. Acad. Sci. U. S. A. 2014, 111, 18132-18137. Heine, N.; Fagiani, M. R.; Asmis, K. R. Disentangling the Contribution of Multiple Isomers to the Infrared Spectrum of the Protonated Water Heptamer. J. Phys. Chem. Lett. 2015, 6, 2298-2304. Heine, N.; Fagiani, M. R.; Rossi, M.; Wende, T.; Berden, G.; Blum, V.; Asmis, K. R. Isomer-Selective Detection of Hydrogen-Bond Vibrations in the Protonated Water Hexamer. J. Am. Chem. Soc. 2013, 135, 8266-8273. Yeh, L. I.; Okumura, M.; Myers, J. D.; Price, J. M.; Lee, Y. T. Vibrational Spectroscopy of the Hydrated Hydronium Cluster Ions H3O+·(H2O)n (n=1,2,3). J. Chem. Phys. 1989, 91, 7319-7330. 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. 11 ACS Paragon Plus Environment


(16) Jiang, J.-C.; Wang, Y.-S.; Chang, H.-C.; Lin, S. H.; Lee, Y. T.; Niedner-Schatteburg, G.; Chang, H.-C. Infrared Spectra of H+·(H2O)5-8 Clusters: Evidence for Symmetric Proton Hydration. J. Am. Chem. Soc. 2000, 122, 1398-1410. (17) Lin, C.-K.; Wu, C.-C.; Wang, Y.-S.; Lee, Y. T.; Chang, H.-C.; Kuo, J.-L.; Klein, M. L. Vibrational Predissociation Spectra and Hydrogen-Bond Topologies of H+·(H2O)9-11. Phys. Chem. Chem. Phys. 2005, 7, 938-944. (18) Wu, C. C.; Lin, C. K.; Chang, H. C.; Jiang, J. C.; Kuo, J. L.; Klein, M. L. Protonated Clathrate Cages Enclosing Neutral Water Molecules: H+(H2O)21 and H+(H2O)28. J. Chem. Phys. 2005, 122, 074315. (19) Shin, J.-W.; Hammer, N. I.; Diken, E. G.; Johnson, M. A.; Walters, R. S.; Jaeger, T. D.; Duncan, M. A.; Christie, R. A.; Jordan, K. D. Infrared Signature of Structures Associated with the H+·(H2O)n (n=6 to 27) Clusters. Science 2004, 304, 1137. (20) 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. (21) Miyazaki, M.; Fujii, A.; Ebata, T.; Mikami, N. Infrared Spectroscopic Evidence for Protonated Water Clusters Forming Nanoscale Cages. Science 2004, 304, 1134 - 1137. (22) Mizuse, K.; Mikami, N.; Fujii, A. Infrared Spectra and Hydrogen-Bonded Network Structures of Large Protonated Water Clusters H+(H2O)n (n=20-200). Angew. Chem. Int. Ed. 2010, 49, 1011910122. (23) Mizuse, K.; Fujii, A. Infrared Spectroscopy of Large Protonated Water Clusters H+(H2O)20-50 Cooled by Inert Gas Attachment. Chem. Phys. 2013, 419, 2-7. (24) Douberly, G. E.; Ricks, A. M.; Duncan, M. A. Infrared Spectroscopy of Perdeuterated Protonated Water Clusters in the Vicinity of the Clathrate Cage. J. Phys. Chem. A 2009, 113, 8449-8453. (25) Asmis, K. R.; Pivonka, N. L.; Santambrogio, G.; Brümmer, M.; Kaposta, C.; Neumark, D. M.; Wöste, L. Gas-Phase Infrared Spectrum of the Protonated Water Dimer. Science 2003, 299, 1375-1377. (26) 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. (27) Duong, C. H.; Yang, N.; Kelleher, P. J.; Johnson, M. A.; DiRisio, R. J.; McCoy, A. B.; Yu, Q.; Bowman, J. M.; Henderson, B. V.; Jordan, K. D. Tag-Free and Isotopomer-Selective Vibrational Spectroscopy of the Cryogenically Cooled H9O4+ Cation with Two-Color, IR-IR Double-Resonance Photoexcitation: Isolating the Spectral Signature of a Single OH Group in the Hydronium Ion Core. J. Phys. Chem. A 2018, 122, 9275-9284. (28) Rheinecker, J.; Xie, T.; Bowman, J. M. A Reduced Dimensionality Quasiclassical and Quantum Study of the Proton Transfer Reaction H3O++H2O → H2O+H3O+. J. Chem. Phys. 2004, 120, 7018-7023. (29) Samala, N. R.; Agmon, N. The Protonated Water Trimer and its Giant Fermi Resonances. Chem. Phys. 2018, 514, 164-175. (30) Roscioli, J. R.; McCunn, L. R.; Johnson, M. A. Quantum Structure of the Intermolecular Proton Bond. Science 2007, 316, 249-254. (31) Ludwig, R. The Effect of Hydrogen Bonding on the Thermodynamic and Spectroscopic Properties of Molecular Clusters and Liquids. Phys. Chem. Chem. Phys. 2002, 4, 5481-5487. (32) Albrecht, L.; Chowdhury, S.; Boyd, R. J. Hydrogen Bond Cooperativity in Water Hexamers: Atomic Energy Perspective of Local Stabilities. J. Phys. Chem. A 2013, 117, 10790-10799. (33) Guevara-Vela, J. M.; Romero-Montalvo, E.; Gomez, V. A. M.; Chavez-Calvillo, R.; Garcia-Revilla, M.; Francisco, E.; Pendas, A. M.; Rocha-Rinza, T. Hydrogen Bond Cooperativity and Anticooperativity Within the Water Hexamer. Phys. Chem. Chem. Phys. 2016, 18, 19557-19566. 12 ACS Paragon Plus Environment

Page 12 of 26

Page 13 of 26 1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47 48 49 50 51 52 53 54 55 56 57 58 59 60


(34) Olesen, S. G.; Guasco, T. L.; Roscioli, J. R.; Johnson, M. A. Tuning the Intermolecular Proton Bond in the H5O2+ 'Zundel Ion' Scaffold. Chem. Phys. Lett. 2011, 509, 89-95. (35) Yang, N.; Duong, C. H.; Kelleher, P. J.; Johnson, M. A.; McCoy, A. B. Isolation of Site-Specific Anharmonicities of Individual Water Molecules in the I‾·(H2O)2 Complex Using Tag-Free, Isotopomer Selective IR-IR Double Resonance. Chem. Phys. Lett. 2017, 690, 159-171. (36) Frisch, M. J.; Trucks, G. W.; Schlegel, H. B.; Scuseria, G. E.; Robb, M. A.; Cheeseman, J. R.; Scalmani, G.; Barone, V.; Petersson, G. A.; Nakatsuji, H., et al. Gaussian 16 Rev. A.03, Wallingford, CT, 2016. (37) Olesen, S. G.; Hammerum, S. Redshift or Adduct Stabilization-A Computational Study of Hydrogen Bonding in Adducts of Protonated Carboxylic Acids. Eur. J. Mass Spectrom. 2009, 15, 239-248. (38) Roscioli, J. R.; Diken, E. G.; Johnson, M. A.; Horvath, S.; McCoy, A. B. Prying Apart a Water Molecule with Anionic H-Bonding: A Comparative Spectroscopic Study of the X·H2O (X = OH, O, F, Cl, and Br) Binary Complexes in the 600-3800 cm-1 Region. J. Phys. Chem. A 2006, 110, 4943-4952. (39) Horvath, S.; Mccoy, A. B.; Elliott, B. M.; Weddle, G. H.; Roscioli, J. R.; Johnson, M. A. Anharmonicities and Isotopic Effects in the Vibrational Spectra of X-H2O, ·HDO, and ·D2O [X = Cl, Br, and I] Binary Complexes. J. Phys. Chem. A 2010, 114, 1556-1568. (40) Dzugan, L. C.; DiRisio, R. J.; Madison, L. R.; McCoy, A. B. Spectral Signatures of Proton Delocalization in H+(H2O)n=1-4 Ions. Faraday Discuss. 2018, 212, 443-466. (41) 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. (42) Nielsen, H. H. The Vibration-Rotation Energies of Molecules. Rev. Mod. Phys. 1951, 23, 90-136. (43) Mills, I. M. 3.2 - Vibration–Rotation Structure in Asymmetric- and Symmetric-Top Molecules. In Molecular Spectroscopy, Rao, K. N.; Mathews, C. W., Eds. Academic Press: 1972; pp 115-140. (44) McCoy, A. B.; Diken, E. G.; Johnson, M. A. Generating Spectra from Ground-State Wave Functions: Unraveling Anharmonic Effects in the OH-·H2O Vibrational Predissociation Spectrum. J. Phys. Chem. A 2009, 113, 7346-7352. (45) Craig, S. M.; Menges, F. S.; Duong, C. H.; Denton, J. K.; Madison, L. R.; McCoy, A. B.; Johnson, M. A. Hidden Role of Intermolecular Proton Transfer in the Anomalously Diffuse Vibrational Spectrum of a Trapped Hydronium Ion. Proc. Natl. Acad. Sci. USA 2017, 114, E4706-E4713. (46) Shimanouchi, T. Tables of Molecular Vibrational Frequencies Consolidated Volume I, National Bureau of Standards. 1972; p 1-160. (47) Gruebele, M.; Polak, M.; Saykally, R. J. A Study of the Structure and Dynamics of the Hydronium Ion by High-Resolution Infrared Laser Spectroscopy. II. The 4 Perpendicular Bending Mode of H3O+. J. Chem. Phys. 1987, 87, 3347 - 3351. (48) Vendrell, O.; Gatti, F.; Meyer, H. D. Full Dimensional (15-Dimensional) Quantum-Dynamical Simulation of the Protonated Water Dimer. II. Infrared Spectrum and Vibrational Dynamics. J. Chem. Phys. 2007, 127, 184303. (49) McCunn, L. R.; Roscioli, J. R.; Johnson, M. A.; McCoy, A. B. An H/D Isotopic Substitution Study of the H5O2+·Ar Vibrational Predissociation Spectra: Exploring the Putative Role of Fermi Resonances in the Bridging Proton Fundamentals. J. Phys. Chem. B 2008, 112, 321-327. (50) 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. (51) Kulig, W.; Agmon, N. Deciphering the Infrared Spectrum of the Protonated Water Pentamer and the Hybrid Eigen-Zundel Cation. Phys. Chem. Chem. Phys. 2014, 16, 4933-4941.



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Disentangling the Complex Vibrational Mechanics ... - ACS Publications

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