How the Zundel (H5O2+) Potential Can Be Used to Predict the Proton

Nov 28, 2016 - To further test the predictions of the results in Table 1 for the proton stretch frequencies, we compare those predictions with previou...
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How the Zundel (H5O+2 ) Potential Can Be Used to Predict the Proton Stretch and Bend Frequencies of Larger Protonated Water Clusters Qi Yu and Joel M. Bowman* Department of Chemistry and Cherry L. Emerson Center for Scientific Computation, Emory University, Atlanta, Georgia 30322, United States S Supporting Information *

ABSTRACT: From a series of seminal experiments on the IR spectra of protonated water clusters and associated theoretical analyses, it is clear that the energies and spectral features of the proton stretch and bend modes are very sensitive functions of the cluster size. Here we show that this dynamic range can be understood by examining the sensitivity of these modes in the potential of the Zundel cation, H5O+2 , as the separation of the two water monomers is varied. As this distance increases, the proton increasingly localizes on a monomer, and this is encoded in the IR spectrum of the proton vibrational modes. The quantitative predictions from this simple correlation are verified for the H7O+3 and H9O+4 clusters, for which new benchmark harmonic frequencies are reported. The predictions are also in good accord with trends seen experimentally and previous calculations for these and five other clusters, including H+(H2O)21.

T

The Zundel cation stands out in contrast to the Eigen cation because in the former the proton is equidistant between the two monomers, at the global minimum, and thus evenly shared by these monomers. In the Eigen form, the proton is bound to one monomer. In larger protonated water clusters, a major question has been which cation motif is the relevant one. A major step in addressing this question was made in a series of joint experimental and theoretical studies of protonated water clusters ranging in size from 2 to 28.21−27 Zundel and Eigen motifs were used to interpret the vibrational signature of protonated water clusters, especially in the proton stretching region. In joint experimental/theoretical work that appeared in 2004,21 and updated and reviewed in a recent Feature Article,28 the IR spectra of protonated water clusters (H2O)n=2−28, with special emphasis on n = 2−6, 8, 10, and, 21 were reported over a spectral range of 800−4000 cm−1. The important theoretical work, which consisted of ab initio geometry optimization of the clusters followed by harmonic and recent VPT2 calculations, revealed a complex pattern of Zundel and Eigen motifs with respect to cluster size (and, more relevantly, geometry). A major indicator of the dominant motif was the location of the proton stretch band, which shifts and broadens considerably with the various clusters. In Zundel, the proton stretch band is around 1000 cm−1, as noted already, whereas in the Eigen motif, it occurs in a broad range from around 2000 to 2800 cm−1 and a broad band contour. This transformation is qualitatively explained using the structures of clusters that a

he hydrated proton is of central importance in chemical and biological systems, and thus, it has been the subject of numerous experimental and theoretical studies, with, arguably, the most detailed ones coming from IR spectroscopy of protonated water clusters. An excellent review and overview of progress and challenges in the field (including hydrated OH−) has just appeared.1 Of course, the smallest example of the hydrated proton is H3O+, and the IR spectroscopy of this cation is well established,2−6 as are the ab initio potential energy surface (PES) and full-dimensional vibrational calculations using these PESs.7−10 (A PES that dissociates diabatically to H+ and H2O has just been reported by us.11) In the context of larger protonated water clusters and in the condensed phase, H3O+ is referred to as the Eigen form of the hydrated proton.12 Next in size is the protonated water dimer, H+(H2O)2, also denoted H5O+2 , known as the Zundel cation. There has been a substantial body of work, both experimental and theoretical, on the IR spectrum of this cation. Theoretical work of relevance here has made use of a full-dimensional, CCSD(T)/aug-ccpVTZ ab intio PES that dissociates with full permutational invariance to H2O + H3O+.13 The PES and corresponding dipole moment surfaces have been used in a number of calculations of the IR spectrum from 0 to roughly 4000 cm−1,14−17 motivated by detailed experimental spectra in this range.15,18−20 The work of Meyer and co-workers stands out as an essentially exact calculation of the IR spectrum, in nearperfect agreement with the complex spectrum reported by Johnson and co-workers.15 In this work, a prominent band, actually a doublet, due to the proton stretch at around 1000 cm−1 has come to serve as the signature of the Zundel motif of larger protonated water clusters. © 2016 American Chemical Society

Received: November 2, 2016 Accepted: November 28, 2016 Published: November 28, 2016 5259

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Figure 1. Potentials from the H5O+2 PES13 as a function of the proton−O distance for fixed OO distances, relative to the global minimum.

as ROO increases, the barrier increases relative to the local minimum, indicating an increased tendency for localization of the proton on one monomer. To provide some quantitative results, we performed normalmode analyses, with a focus on the proton stretch and bend modes at various OO distances, with the flanking water monomer configurations fixed at the global minimum, equilibrium value. To do this analysis, the position of the proton was optimized and a standard normal-mode analysis was conducted at each configuration. Note that only at the global minimum are all of the vibrational frequencies real. However, at all values of ROO, the intramolecular modes have real frequencies. Results are given in Table 1 for the proton stretch and bend modes. As seen, the harmonic frequency of the proton stretch changes significantly for ROO between roughly 2.46 and 3.0 Å and the corresponding range of ROH+ 1.15 and 1.01 Å. In this range, the harmonic stretch increases from roughly 850 to 3000 cm−1. The proton stretches and bending modes are all of interest in this work. As seen, one bending mode varies considerably with the configuration and ultimately correlates with the hydronium umbrella mode, and therefore, that mode is labeled “umb”. There is another bend that remains nearly constant and in the range of around 1600−1650 cm−1 That mode correlates with the hydronium deformation mode, and therefore, that label is used in the table. It should also be noted that the two flanking water monomers, although not geometry-optimized, have bending modes in the range of

solvated Zundel structure shows when n = 6−8 and then generates the 1000 cm−1 Zundel motif. The quantitative relationship between the frequency and the proton-adjacent oxygen distance was investigated by analyzing computational results.28 A near-linear correlation of this signature frequency, actually the shift relative to the bare H3O+ stretch, versus the corresponding shift of the equilibrium OH+ distance for the various clusters was uncovered and identified as conforming to Badger’s rule. This simple correlation indicates an apparently smooth transition from the Zundel to the Eigen motif. This inspired us to investigate whether the potential for the bare Zundel cation can capture this transition. We do that here using the ab initio H5O+2 PES, which was developed more than 10 years ago.13 At first glance, it may seem contradictory to use the H5O+2 PES for this purpose. This is not the case because this PES dissociates to H2O + H3O+, and therefore, a transition from the Zundel to Eigen motifs is described by this PES. This transition is illustrated in Figure 1, where potential curves as a function of the OH+ distance for fixed OO distances are plotted, with the two H2O monomers fixed at the configurations at the minimum. Starting with the minimum configuration, there is a single flat minimum. As the OO distance increases, a barrier develops, creating a symmetric double-well potential. (This is a well-known result.) Note, the energy at the minima increases as ROO increases, reflecting the dissociation of the complex to H3O+ + H2O. More significantly, 5260

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The Journal of Physical Chemistry Letters Table 1. Harmonic Frequencies (cm−1) of the Proton from the Zundel PES13 as a Function of the OO Distance and Shorter OH+ Distance (Å) ROH+

ROO

proton stretch

bend → umb

bend → def

1.193 1.198 1.208 1.188 1.154 1.139 1.119 1.070 1.044 1.027 1.011 1.001 0.992 0.990 0.980 0.974 0.974

2.386 2.401 2.415 2.444 2.461 2.473 2.491 2.596 2.701 2.806 3.016 3.226 3.436 3.579 4.772 7.159 9.545

861 762 680 669 852 986 1196 2075 2464 2737 3046 3227 3400 3416 3573 3644 3644

1495 1497 1499 1486 1442 1415 1374 1226 1106 1011 882 799 725 716 657 628 625

1575 1576 1578 1589 1612 1622 1634 1590 1629 1635 1636 1635 1632 1630 1616 1618 1616

five protonated water clusters.28 The results in the table and figure are significant and relevant to general protonated water cluster spectroscopy because the harmonic frequencies are in the range of those calculated for a variety of clusters. The strong dependence of the harmonic proton stretch and umbrella frequencies on the OH+ distance is in accord with observations from experiment and corresponding theoretical analysis.21−28 In addition, the strong dependence on the OO distance implies strong coupling with that mode. Thus, significant broadening of the proton stretch band is expected due to that coupling (and probably also to coupling to other low-frequency intermolecular modes). The dependence is especially strong for OO distances in the range of 2.5−2.7 Å, which is a range of direct relevance to experiment. This broadening is a challenge for theory to predict; however, the present results provide at least a qualitative understanding of its source. Indeed, the variation of several hundred wavenumbers with just a 0.1 Å change in the OO distance suggests a broadening of this order of magnitude. To summarize thus far, the harmonic analysis of the proton stretch and bend modes using the H5O+2 PES is in good qualitative accord with the large body of experimental and theoretical analysis (harmonic and VPT2) of a range of protonated water clusters. Next, we consider quantitative comparisons for larger clusters. We begin with the non-Zundel clusters H7O+3 and H9O+4 , using new CCSD(T)-F12/aug-cc-pVTZ calculations reported here. (These high-level calculations are now benchmark calculations, as previous ones were done at the MP2 and/ or DFT level of theory.) The structures of these two clusters are given in Figure S1 of the Supporting Information (SI), and the Cartesian coordinates are given in Table S1 of the SI. In H7O+3 , the hydronium core is bonded to two water monomers and has one free OH stretch. This results in two OH bond lengths, 0.964 Å for the free OH and 1.029 Å for the shared proton−O bond. For H9O+4 , the hydronium core is equally shared with three waters, with three equal OH bond lengths of 1.005 Å. As a result, this fully hydrated hydronium cluster is sometimes referred to as the Eigen cluster. Using Table 1 as a look-up table, the predicted harmonic frequencies were obtained using these bond lengths, and the harmonic frequencies are given in Table 2, along with the “exact” ab initio results for each cluster. As seen, there is good agreement with these results, especially for the signature proton stretch. For H7O+3 , there are two inequivalent proton stretches and a bend (a symmetric and asymmetric one) and of course just one from Table 1. The umbrella mode is the lowest-frequency mode, as correctly predicted from Table 1. Similar agreement is seen for H9O+4 , and the trends in both clusters are accurately captured by the model. There certainly are quantitative differences. However, we note that the MP2 frequencies for the proton stretches are roughly 60−90 cm−1 below the CCSD(T) ones for these clusters. Also, we recall that the “umbrella” mode is really only well-defined for H9O+4 , where the harmonic frequency is roughly 400 cm−1 above the predicted value from Table 1. This large upshift makes sense as the umbrella motion in this cluster is strongly hindered owing to the full hydration. The harmonic frequency of the umbrella mode for isolated H3O+ is 888 cm−1.11 Given that the potential cuts in Figure 1 are double wells for the Eigen case, whereas they are not for the H7O+3 and H9O+4 clusters, it is reasonable to ask if the good correspondence between the predicted harmonic frequencies is accidental. To

1600−1700 cm−1 and, depending on the OO distance, interact with the high-frequency proton bend. This observation is in agreement with conclusions of previous work on protonated water clusters. Finally, note that in limit of large ROO, the proton stretch and bend frequencies are in accord with the harmonic frequencies of isolated H3O+ from the PES,13 even without fully relaxing the flanking water monomers. The correct harmonic frequencies (for the PES) are about 70 cm−1 higher for the stretch and the deformation bend but 200 cm−1 higher for the umbrella mode. This relatively large difference for the umbrella mode is mainly due to the fixed monomer configurations. However, these asymptotic frequencies are not of direct interest in this study because the relevant OO distances are not larger than around 3.3 Å. Returning to the proton stretch, the harmonic frequency is plotted in Figure 2 as a function of ROH+ in the range of greatest variation. As seen, there is a near-linear correlation with large negative slope, in accord with a previous Badger’s rule correlation reported by examining the numerical results for

Figure 2. Harmonic frequency, ω, of the proton stretch versus ROH+. 5261

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The Journal of Physical Chemistry Letters Table 2. Comparison of Ab Initio and Predicted Harmonic Hydronium Frequencies (in cm−1) for H7O+3 and H9O+4 H7O+3 , (ROH+ = 1.029 Å) mode +

H3O umbrella H3O+ bend H3O+ stretch

H9O+4 , (ROH+ = 1.005 Å)

prediction

MP2/aVTZ

CCSD(T)-F12/aVTZ

prediction

MP2/aVTZ

CCSD(T)-F12/aVTZ

1011 1635 1635 2754 2754

1261 1687 1700 2462 2618

1242 1699 1709 2551 2702

833 1635 1635 3141 3141 3141

1216 1728 1729 2928 2932 3024

1186 1731 1733 2995 2998 3089

Figure 3. Ab initio OH+ potential energy curves (in red) of H7O+3 and H9O+4 and the related OH+ curve (in blue) from the Zundel potential with matching ROH+. In Zundel potential cuts, ROO = 2.802 Å for the H7O+3 case and 3.112 Å for H9O+4 . The ab initio and Zundel potential cuts have the same ROH+ at its own minimum.

investigate this, comparisons of these 1d potentials for the two clusters are given in Figure 3. The Zundel potential curves for H7O+3 and H9O+4 obtained at the corresponding ROO show good agreement with ab initio cuts for these clusters around the local minimum, even though the Zundel potential is a symmetric double well. Therefore, these comparisons demonstrate that the Zundel PES behaves well in describing the proton stretch around the minimum and thus gives realistic harmonic frequencies. In fact, it also appears that anharmonicity of the 1d cluster potential may also be captured by the Zundel potentials. We return to this below. To further test the predictions of the results in Table 1 for the proton stretch frequencies, we compare those predictions with previously reported harmonic proton stretch frequencies from the literature (obtained using B3LYP/aug-cc-pVTZ calculations) for the indicated protonated water clusters.22,28−30 In order to make the predictions, we used the value of ROH+ reported in that literature. Note, for n = 3,4, we chose the OH distance and harmonic frequencies from ref 28 rather than the CCSD(T) data in Tables 2 and S1. These comparisons are given Table 3, along with experimental peak positions and 1d anharmonic calculations that we explain and discuss below. As seen, the predicted harmonic frequencies are in good agreement with the previously directly calculated ones. Note that in some cases there is more than one proton stretch frequency, and of course, the model produces a single frequency. Next, we consider the comparison of the harmonic frequencies with experiment, where, as noted previously in the literature, large downshifts are seen for the Eigen clusters. Also, a systematic trend of increasing downshift, relative to the

Table 3. Harmonic, 1d Anharmonic and Experimental Fundamentals of the Proton Stretch (in cm−1) in H+(H2O)n, n = 3−6, 8, 10, 21 n

ROH+a

3 4 5

1.043 1.014 1.005 1.049

6 8

1.199 1.156 0.991 1.018 1.035 1.030

10 21

ab initio harmonic

predicted harmonic

1d anharmonic

2493, 2627 2936, 3009 3080, 3110 2454

2528 2996 3141 2431

1885 2568 2860 1901

1209 -

762 852 3367 2931 2657 2738

1175 1198 3161 2460 1921 2013

2962 2862, 2576 2816, 2600, 2567

expt 1880b 2665b 2860b 1490c/ 1885b 1055b 1055c 3200c 2650c 1920c 1950c

a

For the OH+ bond length,n = 3−5, 10, and 21 are from ref 28, and n = 6 and 8 are optimized using B3LYP/aVDZ. For ab initio harmonic frequencies, n = 3−6 are from ref 22, n = 10 is from ref 29, and n = 21 is from ref 30. bExperimental data from ref 22. cExperimental data from ref 28.

harmonic frequency, with increasing ROH+ is seen. This increasing anharmonicity can be understood by inspection of Figure 3, where the 1d potential cuts for H+(H2O)3 [H7O+3 ] are significantly “softer” than those for H+(H2O)4 [H9O+4 ]. This is true for both the Zundel PES cut and directly for the two clusters. The softer potential for H+(H2O)3 correlates with the smaller proton transfer barrier height, as seen in the figure. As already noted, the 1d PES cuts display a single well for the 5262

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Figure 4. Harmonic, anharmonic 1d, and experimental proton stretches fundamental of Eigen structures with respect to ROH+ in Å.

following results for the fundamental: 2039 and 2583 cm−1 for H7O+3 and H9O+4 , respectively. The latter result agrees very well with the 1d results using the Zundel double-well potential, 2568 cm−1, and both are in good agreement with experiment. (We note that a VPT2/B3LYP/6-31+G(d) calculation28 for n = 4 is in excellent agreement with experiment. This may be fortuitous as the same level of calculation produces results that are roughly 100 cm−1 below experiment for isolated H3O+.) However, for H7O+3 , the Zundel PES result is 1885 cm−1, which is considerably lower than 2039 cm−1. This may be due to overestimation of the potential anharmonicity that the low proton transfer barrier for H7O+3 is at the extreme edge of the 1d treatment using the H5O+2 PES. Nevertheless, the prediction of a very large downshift relative to the harmonic frequency for H7O+3 is correct. A final point about the n = 4 cluster is to contrast the two cuts shown in Figure 3 with the analogous figure in ref 28, where the OH stretch from H3O+ is compared to the cut for the n = 4 cluster. As expected, there is a much larger difference between these two than that seen in Figure 3. Thus, it is gratifying to see the much better agreement from the current model using the distorted H5O+2 PES. Finally, we applied the 1d anharmonic analysis to two Zundel clusters, namely, H+(H2O)n, n = 6 and 8. For these, we used optimized geometries (B3LYP/aVDZ) from Jordan. The results are also given in Table 3 together with 1d anharmonic results. As seen, the harmonic results are 200 and 300 cm−1 below experiment, and the 1d anharmonic ones are only 20 and 43 cm−1 above experiment, for n = 6 and 8, respectively. In summary, using a previous dissociable PES of the Zundel cation, we presented analyses of the proton stretch and bend frequencies of larger protonated water clusters. This potential morphs from a strictly Zundel motif at the global minimum to an Eigen motif as the OO distance increases, where the proton 1d potential morphs into a symmetric double well with an increasing barrier height separating the two wells. The proton stretches and bend fundamentals were obtained from normalmode analysis at a fixed OO distance and optimized OH+ distance over a range that is relevant for the larger clusters. A linear correlation between the harmonic proton stretch and

Zundel clusters or a symmetric double well for the Eigen ones. Of course, the actual 1d cuts for Eigen clusters do not display a double well. However, on the basis of the plots in Figure 3, we feel comfortable in claiming that the large downshift seen experimentally can be interpreted as a signature of the frustrated proton transfer. Given the large anharmonic downshift seen experimentally, we were motivated to extend the harmonic analysis using the H5O+2 PES to a simple anharmonic analysis of the proton stretch fundamental. This is done by obtaining the eigenvalues of a 1d Hamiltonian, using the potential cuts from the Zundel PES, with a fixed OO distance (like those shown in Figure 1) relevant to a given cluster and assuming infinite masses for the O atoms. For “Zundel” cases, there is a single minimum and the results of the calculation are directly comparable to those of the experiment. However, for “Eigen” cases, that is, double wells, there is a complication to deal with. As seen in Figures 1 and 3, the potentials are symmetric double wells, which produce energy doublets. In protonated Eigen water clusters, there is just a single well, as shown, for example, in Figure 3. Therefore, there is a question of how to relate the energy doublets to the actual 1d energies of the Eigen potentials. We do this by noting that in the elementary treatment of the symmetric double well as a 2 × 2 Hückel problem, one can extract the localized eigenvalue trivially as the average of doublets. Doing this for the ground and first excited states, we obtain the anharmonic fundamental energy that corresponds to the single-well case of the Eigen clusters. The results of these calculations are shown in Table 3, where satisfactory agreement with experiment is seen. (The near-perfect agreement for n = 3 is clearly fortuitous.) A summary of these 1d energies for Eigen clusters along with the harmonic and experimental ones is plotted in Figure 4 versus ROH+. Both the near-linear correlation and the large anharmonictiy are seen. To conclude this examination of Eigen clusters, it is worth noting that this 1d anharmonic analysis could be done directly for the 1d potential cuts for each cluster, for example, the ones shown in Figure 3. However, that is not the goal of the present analysis, which is to use the Zundel PES. Nevertheless, we did those calculations for the two cases shown in Figure 3 with the 5263

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subwave number accuracy for the inversion splittings. J. Chem. Phys. 2003, 118, 10929−10938. (11) Yu, Q.; Bowman, J. M. Ab Initio Potential for H3O+ → H+ + H2O: A Step to a Many-Body Representation of the Hydrated Proton? J. Chem. Theory Comput. 2016, 12, 5284. (12) Eigen, M. Proton Transfer, Acid-Base Catalysis, and Enzymatic Hydrolysis. Angew. Chem., Int. Ed. Engl. 1964, 3, 1. (13) Huang, X.; Braams, B.; Bowman, J. M. Ab initio potential energy and dipole moment surfaces for H5O+2 . J. Chem. Phys. 2005, 122, 044308. (14) McCoy, A. B.; Huang, X.; Carter, S.; Landeweer, M. Y.; Bowman, J. M. Full-dimensional vibrational calculations for H5O+2 using an ab initio potential energy surface. J. Chem. Phys. 2005, 122, 061101. (15) 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 H5O+2 · 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. (16) Vendrell, O.; Gatti, F.; Meyer, H.-D. Dynamics and Infrared Spectroscopy of the Protonated Water Dimer. Angew. Chem., Int. Ed. 2007, 46, 6918−6921. (17) Vendrell, O.; Meyer, H. D. A proton between two waters: insight from full-dimensional quantum-dynamics simulations of the [H2O-H-OH2]+ cluster. Phys. Chem. Chem. Phys. 2008, 10, 4692. (18) 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. (19) Fridgen, T. D.; McMahon, T. B.; MacAleese, L.; Lemaire, J.; Maitre, P. Infrared Spectrum of the Protonated Water Dimer in the Gas Phase. J. Phys. Chem. A 2004, 108, 9008−9010. (20) Headrick, J. M.; Bopp, J. C.; Johnson, M. A. Predissociation spectroscopy of the argon-solvated H5O+2 “zundel” cation in the 1000− 1900 cm−1 region. J. Chem. Phys. 2004, 121, 11523−11526. (21) 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. (22) 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. (23) Woutersen, S.; Bakker, H. J. Ultrafast Vibrational and Structural Dynamics of the Proton in Liquid Water. Phys. Rev. Lett. 2006, 96, 138305. (24) Vener, M. V.; Librovich, N. B. The Structure and Vibrational Spectra of Proton Hydrates: H5O+2 as a Simplest Stable Ion. Int. Rev. Phys. Chem. 2009, 28, 407. (25) Stoyanov, E. S.; Stoyanova, I. V.; Reed, C. A. The Structure of the Hydrogen Ion (H+aq) in Water. J. Am. Chem. Soc. 2010, 132, 1484. (26) Mandal, A.; Ramasesha, K.; De Marco, L.; Tokmakoff, A. Collective Vibrations of Water-Solvated Hydroxide Ions Investigated with Broadband 2D-IR Spectroscopy. J. Chem. Phys. 2014, 140, 204508. (27) 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. (28) 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. (29) Karthikeyan, S.; Kim, K. S. Structure, Stability, Thermodynamic Properties, and IR Spectra of the Protonated Water Decamer H+(H2O)10. J. Phys. Chem. A 2009, 113, 9237−9242.

ROH+ was found for different sizes of clusters. Tests at the harmonic level were presented for H7O+3 and H9O+4 using new benchmark harmonic frequencies for those clusters. Further comparisons between predicted harmonic and simple 1d anharmonic energies with experiment showed very satisfactory agreement, even semiquantitative agreement for the anharmonic energies. This result led us to interpret the extreme anharmonicity of the proton stretches in Eigen protonated clusters as a frustrated proton transfer.

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ASSOCIATED CONTENT

* Supporting Information S

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpclett.6b02561. Optimized global minimum geometries, ab initio harmonic frequencies, and coordinates for the studied species (PDF)

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. ORCID

Joel M. Bowman: 0000-0001-9692-2672 Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We thank Ken Jordan for sending the Cartesian coordinates of the H+(H2O)n, n = 6 and 8, clusters. We also thank the National Science Foundation CHE-145227 for financial support.

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REFERENCES

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