IR Spectra of the Water Hexamer - American Chemical Society

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Letter

IR Spectra of the Water Hexamer: Theory, with Inclusion of the Monomer Bend Overtone, and Experiment are in Agreement Yimin Wang, and Joel M Bowman J. Phys. Chem. Lett., Just Accepted Manuscript • DOI: 10.1021/jz400414a • Publication Date (Web): 19 Mar 2013 Downloaded from http://pubs.acs.org on March 20, 2013

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The Journal of Physical Chemistry Letters

IR Spectra of the Water Hexamer: Theory, with Inclusion of the Monomer Bend Overtone, and Experiment are in Agreement Yimin Wanga and Joel M. Bowmanb Department of Chemistry and Cherry L. Emerson Center for Scientific Computation Emory University, Atlanta GA 30322

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ABSTRACT Signature IR spectra of isomers of the water hexamer in the spectral range 3000-‐ 3800 cm-‐1 have been reported by experimentalists but crucial theoretical interpretation has still not been definitive. Using ab initio potential and dipole moment surfaces and a fully coupled quantum treatment of the intramolecular modes, the ring and book are assigned to spectra obtained in the He nanodroplet and Ar tagging experiments, respectively. The overtone of the intramolecular bend at ca 3200 cm-‐1 is a new calculated feature that completes an important missing piece in previous experimental and theoretical comparisons and leads to a consistent assignment of these two experimental spectra. Calculated IR spectra for the lowest energy forms of the water heptamer and octomer are also presented and compared to experiment. In all the calculated spectra the bend overtone is demonstrated to be a noticeable feature and this is one important conclusion from the work. Also, the danger in using scaled double-‐harmonic spectra to assign spectra is demonstrated. Keywords: water book hexamer, ring hexamer, heptamer, octomer, local-‐monomer, bend-‐overtone


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The water hexamer has both fascinated and bedeviled theorists and experimentalists for more than twenty years, because it is the smallest water cluster that exists in numerous nearly iso-‐energetic isomeric forms. The lowest energy forms, the prism and cage, are space-‐filling and have the largest number of hydrogen bonds and are thus most “ice-‐like”. Curiously, while high-‐level electronic structure calculations are unanimous in finding the prism to be slightly lower in electronic energy than the cage,1-‐4 only the latter had been seen experimentally. This was first reported in seminal high-‐resolution supersonic jet experiments,5 which were reported prior to the high-‐ level ab initio studies. Very recently, the prism was observed for the first time, along with the cage, and to a small extent the higher energy book isomer, in high-‐resolution supersonic jet experiments.6 The higher-‐energy forms of the hexamer, such as the book and ring have fewer hydrogen bonds and thus are floppier and thermodynamically more populated as the temperature increases.7-‐10 However, is should be stressed that there is no evidence to suggest that the experiments in supersonic jet expansions follow a Boltzmann distribution of isomers. Indeed, signature IR spectra of the hexamer isomers in the “OH-‐stretch region”, i.e., roughly 3000 -‐ 3800 cm-‐1, have been reported by experimentalists11-‐14 and assigned to the high-‐energy book11,12 and even the higher-‐energy ring isomers.13,14 Theoretical interpretation of these spectra, mostly based on scaled double-‐harmonic analysis (harmonic-‐oscillator wavefunctions with a linear approximation to the dipole moment in the normal modes), unfortunately are still not definitive. The spectrum of the hexamer in He nanodroplets was reported roughly 10 years ago13,14 and, based on several arguments, including a scaled ab initio double-‐harmonic analysis, was assigned to the high-‐energy ring isomer. However, the assignment of a band at 3229 cm-‐1 was noted to be problematic. Those authors assigned it to the lower-‐energy cage isomer and indeed a scaled double-‐harmonic


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calculation did find a peak in the cage spectrum, at around 3280 cm-‐1. However, those authors concluded cautiously “Unfortunately, a definitive assignment of this spectral feature has not been made…” More recently, Diken et al.12 reported the spectrum of the water hexamer using Ar tagging and electron attachment and tentatively assigned it to the book isomer, based on previous scaled double-‐harmonic calculations.15 (By varying experimental conditions Diken et al. argued that multiple isomers of the hexamer were unlikely.) The assignment of the book in these experiments was recently questioned by Tainter and Skinner, who presented new calculations of the IR spectrum in the OH-‐stretch region, based on a local OH-‐stretch model that includes anharmonicity in that mode. They assumed a thermal distribution of hexamer isomers and concluded that the Diken et al. spectrum was a mixture of book and cage isomers. Thus, the current status of the understanding of the hexamer IR spectra is still unsettled. We believe this has been hampered to a large extent by the use of scaled double-‐harmonic analysis (and also using relatively low-‐level ab initio theory) to interpret the spectra. And, while the recent work of Tainter and Skinner has advanced theory, its lack of consideration of the monomer bend, specifically the overtone of the bend, is a concern. There is solid evidence in smaller clusters, e.g. the trimer, of significant bend-‐overtone intensity.16,17 Very recently, we reported a significant contribution of this overtone in the OH-‐stretch region of IR spectrum of clusters of 192 monomers, representing two ice models.18 These calculations were done using the Local Monomer (LMon) model, briefly reviewed below, which does describe the coupling of the stretch and bend modes of each monomer in a cluster. Here we focus on comparisons between calculated LMon spectra for the hexamer and experiment and show the importance of the bend overtone band in the IR spectra. More significantly, inclusion of this band does lead to a resolution in assigning the experimental spectra to a single hexamer isomer. An ancillary part of


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this Letter is a calculation of the IR spectra for the lowest energy forms of the water heptamer and octomer and comparison with experimental action spectra. The present calculations use full-‐dimensional ab initio potential energy surface (PES) and dipole moment surface (DMS), referred to as WHBB.19 The potential is a permutationally invariant representation in terms of all 1, 2, and 3-‐ body interactions. The 1-‐body potential is a spectroscopically accurate potential, the 2-‐body potential is a precise fit to roughly 30 000 CCSD(T)/aug-‐cc-‐pVTZ electronic energies and the 3-‐body potential is a similar fit to roughly 40 000 MP2/aug-‐cc-‐ pVTZ. The dipole moment surface is a sum of all 1 and 2-‐body dipole moments, obtained from fitting 30 000 MP2/aug-‐cc-‐pVTZ dipole moments. Detailed tests of the surfaces have been given elsewhere19 and for use in quantum calculations of the IR spectrum, these surfaces are currently the most accurate ones available. The calculation of the IR spectra has been described in detail previously,19,20 so only a brief summary is given here. After optimization to a given isomeric form of the hexamer , using the WHBB PES the LMon calculation of vibrational energies, wavefunctions and IR spectrum are done for each monomer in the cluster. The LMon calculations employ the Watson Hamiltonian in mass-‐scaled “lormal modes”19-‐21 and in fully-‐coupled three-‐mode (bend and two stretches) calculations for each of the six monomers in the hexamer cluster. Specifically, the 3-‐mode Schrodinger equation for monomer m

[Tˆ

m

]

+ U m (Qm ) − E m ϕm vib (Qm ) = 0

is solved in parallel using a modification of the code MULTIMODE.22 In this equation, Qm represents the three high-‐frequency normal modes for monomer m (which we € also term the “lormal modes”), Tˆm is the kinetic energy operator (including the vibrational angular momentum terms) and Um is corresponding potential for monomer m, perturbed by all other monomers. To be clear, Um is the full WHBB PES in the three lormal modes of monomer m in the field of all other monomers held


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fixed. With the WHBB DMS intensities for the all transitions involving the three intramolecular modes are calculated rigorously and the resulting stick spectra are then smoothed using a Gaussian of width comparable to the width in experiment. It is perhaps worth noting that the present calculations do not consider the coupling to low-‐frequency intermolecular modes, which are not expected to play a signficant role in these low-‐resolution spectra. The first set of results is shown in Figure 1, where LMon and scaled-‐double harmonic (s-‐dbl-‐HO) spectra (both using the WHBB PES and DMS) are given for the four isomers indicated. The dlb-‐HO scaling factor is 0.95 (a commonly used factor) and, as seen, it brings the latter into agreement with the LMon results for the highest-‐ frequency free-‐OH band. Even with this scaling, there are substantial differences between the LMon and s-‐dbl-‐HO spectra. This lack of agreement, post-‐scaling, has been reported previously for water clusters.23 However beyond this disagreement, the most glaring one is the absence of the bend overtone in the s-‐dbl-‐HO, which by definition cannot be described in the dbl-‐HO model. Note that that band is found in the LMon spectrum for all the isomers, but in particular notice that is the only feature in the most red-‐shifted portion of the “OH-‐stretch” region of the ring spectrum, at 3220 cm-‐1. Also note that the s-‐dlb-‐HO spectrum has, incorrectly, an intense feature at around 3200 cm-‐1 for the cage (and also the prism).


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Figure 1 Comparison of Local Monomer, solid blue line (see text for details), and scaled double-‐Harmonic, dashed green line, spectra of the indicated water hexamer isomers. The filled bands are due to the bend overtone Next, we present comparisons of LMon spectra with experiment and we begin with the ring. As we pointed out previously, the LMon model produces an artificially degenerate spectrum for the ring owing to its high symmetry.20 We introduced a simple and accurate method to split that degeneracy.21 For the ring the band-‐width increases from zero to at most 20 cm-‐1 for the three intramolecular modes. The intense IR mode in the split spectrum is at 3364 cm-‐1, in good agreement with the experimental band reported14 at 3335 cm.-‐1 Figure 2 shows the comparison of the LMon ring spectrum with the experimental spectrum.13,14 As carefully analyzed in


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references 13 and 14, that spectrum contains features from other-‐sized clusters, which were assigned. This is indicated in the present figure by showing the portion of the experimental spectrum assigned to the hexamer in red. The band centered at roughly 3720 cm-‐1 is the free-‐OH stretch, which appears in a 2.0 1.5 1.0 Exp - Ring Hexamer Exp - non Hexamer 0.5 Theory - RIng Hexamer 0.0 3200 3300 3400 3500 3600 3700 -1 ν (cm ) Intensity (arbitrary units)

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Figure 2 Present Local Monomer (Theory) and experimental, He nanodroplet, (refs. 13,14), IR spectra of the water ring hexamer. The green line portion of the experimental spectrum is due to other water clusters smaller than the hexamer. The feature at 3212 cm-‐1 in the theory spectrum is due to the bend overtone. The experimental spectrum is a digitized rendering of Figure 1 in reference 14.


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number of water clusters and so, as noted in the experiment, that band has contributions from other clusters. However, we indicate it in red and assign it othe ring, since it certainly is present in that spectrum. The calculated intensity is smaller than the experimental one at 3335 cm-‐1. This is probably due to, at least in part, to overlapping contributions from the other clusters. With that caveat in mind, the comparison between theory and experiment is very good and allows us to assign the entire spectrum to the ring, and in particular the experimental band at 3229 cm-‐1 to the bend-‐overtone of the ring isomer and not to the cage. Next consider the comparison between the LMon hexamer spectrum with the Ar-‐tagged one reported by Johnson and co-‐workers,12 shown in Figure 3. As noted 2.5 Exp - Hexamer Theory - Book Hexamer 2.0


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Figure 3 Present Local Monomer (Theory) and experimental, Ar-‐tagged IR spectra (ref. 12) of the book hexamer. The broad feature in the range 3150-‐3250 in the theory spectrum is due to the bend overtone(s), as pointed out in Figure 1.


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above, they tentatively assigned the spectrum to the book, but which Tainter and Skinner10 recently re-‐assigned to both the cage and the book, with the most red-‐ shifted feature assigned to the cage, as was done previously for the ring. Here we find that that feature, as in the ring, is due to the overtone of the bend. Further, the overall agreement with experiment12 is very good (perhaps a bit fortuitously so), leading us to assign this spectrum to the book isomer. We also note that there is very good agreement with the earlier molecular beam experiments of Buch, Buck and co-‐ workers11 who, as it turns out, correctly interpreted their spectrum as the book isomer.

Finally, consider the water heptamer and octomer. The spectra of these

clusters in the OH-‐stretch region were also reported by Buck and co-‐workers using action spectroscopy.25 In this case, mass-‐selected clusters were dissociated in a molecular beam following absorption of an infrared photon. The intensities are thus not directly the IR dipole intensities, but presumably roughly proportional to them. The lowest energy forms of these clusters were used in the calculations. These are depicted in the spectra shown below, first for the hepatamer and then for the octomer.. The theoretical spectrum is for the lowest energy form of the heptamer and the orange part of the theoretical spectra indicates the bend overtone contribution to the IR spectrum. The comparison between theory and experiment here is good but not as good as seen for the hexamer. The good agreement lends evidence, though not conclusive, that experiment also corresponds to the lowest energy form of the heptamer. The largest difference with experiment is below 3000 cm-‐1 and where the band in experiment is totally absent in the theory and we have no definitive explanation for this. Note that the weak band due to the bend overtone is evidently missing in experiment. This could be due to the weak intensity of this band or


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perhaps a long predissociation lifetime of the complex with excitation of the bend overtone relative to the stretch excitation. This is just a speculation of course.

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Figure 4 Present Local Monomer (Theory) and experimental action spectrum (ref. 25) of the water heptamer. The experimental spectrum is a digitized rendering of Figure 6 in reference 25). Consider next the comparison with the action spectrum for the water octomer. This is shown in Figure 5 and, as seen, agreement is good and now the lowest frequency band(s) in experiment are in the range 3050-‐3100 cm-‐1 with nothing reported below 3000 cm-‐1. Note in this cluster the calculated bend-‐overtone bands are fairly weak and evidently absent in the experiment, perhaps for the same


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reason speculated for their absence in the heptamer. Notice also the relative simplicity of the octomer spectrum compared to the heptamer one. This is evidently a consequence of the higher symmetry of the octomer compared to the heptamer. somewhat like the differences between the ring and book hexamer. 2.5


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Figure 5 Present Local Monomer (Theory) and experimental action spectrum (ref. 24) of the water octomer. The experimental spectrum is a digitized rendering of Figure 6 in reference 25). In summary, we used ab initio potential and dipole moment surfaces in

coupled three-‐mode calculations of the IR spectra of the book and ring isomers of the


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water hexamer in the 3000-‐3800 cm-‐1 region. By including the bend overtone in these calculations, we were able to firmly assign experimental spectra that tentatively made these isomer assignments. We also demonstrated substantial inaccuracies in the widely-‐used scaled double-‐harmonic approximation to assign and interpret these spectra. Calculated spectra of the water heptamer and octomer in this spectral range were also presented and compared to experimental predissociation action spectra, and with some caveats, agreement was good. The authors declare no competing financial interest. AUTHOR INFORMATION Corresponding Author *E-‐mail: [email protected] Acknowledgments: We thank the National Science Foundation (CHE-‐1145227) for financial support. We also thank Mark Johnson for sending the spectrum shown in Figure 3, and Gary Douberly for sending his He nanodroplet spectrum References 1. Dahlke, E. E.; Olson, R. M.; Leverentz, H. R.; Truhlar, D. G. Assessment of the Accuracy of Density Functionals for Prediction of Relative Energies and Geometries of Low-‐Lying Isomers of Water Hexamers. J. Phys. Chem. A 2008, 112, 3976-‐3984. 2. Santra, B.; Michaelides, A.; Fuchs, M.; Tkatchenko, A.; Filippi, C.; Scheffler, M. On The Accuracy Of Density-‐Functional Theory Exchange-‐Correlation Functionals For H Bonds In Small Water Clusters. II. The Water Hexamer And Van Der Waals Interactions. J. Chem. Phys. 2008, 129, 194111-‐194114.


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3. Bates, D. M.; Tschumper, G. S. CCSD(T) Complete Basis Set Limit Relative Energies for Low-‐Lying Water Hexamer Structures. J. Phys. Chem. A 2009, 113, 3555-‐3559. 4. Gora, U.; Podeszwa, R.; Cencek, W.; Szalewicz, K. Interaction Energies Of Large Clusters From Many-‐Body Expansion. J. Chem. Phys. 2011, 135, 224102-‐ 224119. 5. Liu, K.; Brown, M. G.; Carter, C.; Saykally, R. J.; Gregory, J. K.; Clary, D. C. Characterization Of A Cage Form Of The Water Hexamer. Nature 1996, 381, 501-‐503. 6. Pérez, C.; Muckle, M. T.; Zaleski, D. P.; Seifert, N. A.; Temelso, B.; Shields, G. C.; Kisiel, Z.; Pate, B. H. Structures of Cage, Prism, and Book Isomers of Water Hexamer from Broadband Rotational Spectroscopy. Science 2012, 336, 897-‐ 901. 7. Kryachko, E. S. Ab Initio Studies of the Conformations of Water Hexamer: Modelling The Penta-‐Coordinated Hydrogen-‐Bonded Pattern In Liquid Water. Chem. Phys. Lett. 1999, 314, 353-‐363. 8. Dunn, M. E.; Pokon, E. K.; Shields, G. C. Thermodynamics of Forming Water Clusters at Various Temperatures and Pressures by Gaussian-‐2, Gaussian-‐3, Complete Basis Set-‐QB3, and Complete Basis Set-‐APNO Model Chemistries; Implications for Atmospheric Chemistry. J. Am. Chem. Soc. 2004, 126, 2647-‐ 2653. 9. Wang, Y.; Babin, V.; Bowman, J. M.; Paesani, F. The Water Hexamer: Cage, Prism, or Both. Full Dimensional Quantum Simulations Say Both. J. Am. Chem. Soc. 2012, 134, 11116–11119. 10. Tainter, C. J.; Skinner, J. L. The Water Hexamer: Three-‐Body Interactions, Structures, Energetics, And OH-‐Stretch Spectroscopy At Finite Temperature. J. Chem. Phys. 2012, 137, 104304-‐104316.


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11. Steinbach, C.; Andersson, P.; Melzer, M.; Kazimirski, J. K.; Buck, U.; Buch, V. Detection of the Book Isomer from the OH-‐Stretch Spectroscopy of Size Selected Water Hexamers. PCCP 2004, 6, 3320-‐3324. 12. Diken, E. G.; Robertson, W. H.; Johnson, M. A. The Vibrational Spectrum of the Neutral (H2O)6 Precursor To The “Magic” (H2O)6-‐ Cluster Anion by Argon-‐ Mediated, Population-‐Modulated Electron Attachment Spectroscopy. J. Phys. Chem. A 2003, 108, 64-‐68. 13. Nauta, K.; Miller, R. E. Formation of Cyclic Water Hexamer in Liquid Helium: The Smallest Piece of Ice. Science 2000, 287, 293-‐295. 14. Burnham, C. J.; Xantheas, S. S.; Miller, M. A.; Applegate, B. E.; Miller, R. E. The Formation of Cyclic Water Complexes by Sequential Ring Insertion: Experiment and Theory. J. Chem. Phys. 2002, 117, 1109-‐1122. 15. Kim, J.; Kim, K. S. Structures, Binding Energies, and Spectra of Isoenergetic Water Hexamer Clusters: Extensive Ab Initio Studies. J. Chem. Phys. 1998, 109, 5886-‐5895. 16. Salmi, T.; Kjaergaard, H. G.; Halonen, L. Calculation of Overtone O-‐H Stretching Bands and Intensities of the Water Trimer. J. Phys. Chem. A 2009, 113, 9124-‐9132. 17. Tremblay, B.; Madebene, B.; Alikhani, M. E.; Perchard, J. P. The vibrational spectrum of the water trimer: Comparison between anharmonic ab initio calculations and neon matrix infrared data between 11,000 and 90 cm-‐1 Chem. Phys. 2010, 378, 27−36. 18. Liu, H.; Wang, Y.; Bowman, J. M. Quantum Calculations of Intramolecular IR Spectra of Ice Models Using Ab Initio Potential and Dipole Moment Surfaces. J. Phys. Chem. Lett. 2012, 3, 3671-‐3676. 19. Wang, Y.; Huang, X.; Shepler, B. C.; Braams, B. J.; Bowman, J. M. Flexible, Ab Initio Potential, and Dipole Moment Surfaces for Water. I. Tests and


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Applications for Clusters up to the 22-‐mer. J. Chem. Phys. 2011, 134, 094509. 20. Wang, Y.; Bowman, J. M. Ab Initio Potential And Dipole Moment Surfaces for Water. II. Local-‐Monomer Calculations of the Infrared Spectra of Water Clusters. J. Chem. Phys. 2011, 134, 154510. 21. Wang, Y.; Bowman, J. M. Coupled-‐Monomers in Molecular Assemblies: Theory and Application to the Water Tetramer, Pentamer, and Ring Hexamer. J. Chem. Phys. 2012, 136, 144113. 22. Bowman, J. M.; Carter, S.; Huang, X. MULTIMODE: A Code to Calculate Rovibrational Energies of Polyatomic Molecules. Int. Rev. Phys. Chem. 2003, 22, 533-‐549. 23. Watanabe, Y.; Maeda, S.; Ohno, K. Intramolecular vibrational frequencies of water clusters (H2O)n (n=2–5): Anharmonic analyses using potential functions based on the scaled hypersphere search method, J. Chem. Phys. 2008, 129, 074315. 24. Steinbach, C.; Andersson, P.; Melzer, M.; Kazimirski, J.K.; Buck, U.; Buch, V.; Detection of the book isomer from the OH-‐stretch spectroscopy of size selected water hexamers, PCCP, 2004, 6, 3320–3324. 25. Sadlej, J.; Buch, V.; Kazimirski, J.K.; Buck, U. Theoretical Study of Structure and Spectra of Cage Clusters (H2O)n, n = 7-‐10. J. Phys. Chem. A 1999, 103, 4933-‐ 4947.


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IR Spectra of the Water Hexamer - American Chemical Society

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