Hydrogen bond breaking dynamics in the water pentamer: Terahertz VRTspectroscopy of a 20 µm librationWilliam T. S. Cole, Raymond S. Fellers, Mark R. Viant, and Richard J. Saykally

Citation: J. Chem. Phys. 146, 014306 (2017); doi: 10.1063/1.4973418View online: http://dx.doi.org/10.1063/1.4973418View Table of Contents: http://aip.scitation.org/toc/jcp/146/1Published by the American Institute of Physics

http://aip.scitation.org/author/Cole%2C+William+T+Shttp://aip.scitation.org/author/Fellers%2C+Raymond+Shttp://aip.scitation.org/author/Viant%2C+Mark+Rhttp://aip.scitation.org/author/Saykally%2C+Richard+J/loi/jcphttp://dx.doi.org/10.1063/1.4973418http://aip.scitation.org/toc/jcp/146/1http://aip.scitation.org/publisher/

THE JOURNAL OF CHEMICAL PHYSICS 146, 014306 (2017)

Hydrogen bond breaking dynamics in the water pentamer:Terahertz VRT spectroscopy of a 20 µm libration

William T. S. Cole, Raymond S. Fellers,a) Mark R. Viant,b) and Richard J. Saykallyc)Department of Chemistry, University of California, Berkeley, California 94720, USA

(Received 19 October 2016; accepted 16 December 2016; published online 5 January 2017)

Hydrogen bonds in solid and liquid water are formed and broken via librational vibrations, hencecharacterizing the details of these motions is vital to understanding these important dynamics. Herewe report the measurement and assignment of 875 transitions comprising 6 subbands originatingfrom out-of-plane librational transitions of the water pentamer-d10 near 512 cm�1. The preciselymeasured (ca. 1 ppm) transitions reveal bifurcation splittings of ∼1884 MHz, a ∼4000× enhancementover ground state splittings and 100× greater than predicted by theory. The pentamer is thus thethird water cluster to display greatly enhanced bifurcation tunneling upon single quantum excitationof librational vibrations. From the intensity pattern of the observed transitions, the mechanism ofbifurcation is established by comparison with theoretical predictions. Published by AIP Publishing.[http://dx.doi.org/10.1063/1.4973418]

INTRODUCTION

The out-of-plane librational band is the most prominentfeature in the intermolecular vibrational spectrum of bulkwater, and has important consequences for hydrogen bonddynamics.1–4 Excitation of this vibration, which occurs in the500-800 cm�1 region, has been shown to comprise motionsthat break and reform hydrogen bonds,5–7 and the hydrogenbond breaking process has been shown to be highly local,and largely unaffected by hydrogen bond order.8 Thus, waterclusters present a convenient route for examining details ofthese hydrogen bond dynamics.9 Additionally, analysis of themany-body expansion of the water-water interaction potentialhas shown that the most significant terms are the 2 and 3 bodyterms, which comprise ∼99% of the interaction energy.10–12Towards the development of improved water models, VRTexperiments on water clusters have been shown to accuratelyprobe the short-range interactions.13,14 The key distinctionsbetween water clusters and the bulk are the free hydrogensof the clusters. These hydrogens are predicted to have littleeffect on the librational motions, as evidenced by low reso-lution spectroscopy studies of small clusters (n = 10-100).15

Here we report the high resolution terahertz VRT spectrum of alibrational vibration near 500 cm�1 for the water pentamer-d10,excitation of which produces a dramatic increase in the bifur-cation tunneling rate and consequent hydrogen bond breakingdynamics.

As for the water trimer and tetramer, the lowest energyform of the water pentamer is a quasi-planar ring structure(Figure 1(a)) with all hydrogen bonds directed in the samesense (CW or CCW).16 The free hydrogens of each water

a)Present address: Picarro, 3105 Patrick Henry Drive, Santa Clara, California95054, USA.

b)Present address: School of Biosciences, University of Birmingham,Edgbaston, Birmingham B15 2TT, UK.

c)Author to whom correspondence should be addressed. Electronic mail:saykally@berkeley.edu

monomer, directed either above or below the plane of themolecule, are labeled with “u” for up or “d” for down, andthe global minimum for the pentamer is labeled (ududd).This structure was predicted by ab initio calculations17–19

and confirmed by Liu et al.’s observation of the pentamer-d10species in 1996.20,21 Liu measured parallel-type transitions ofa torsional vibration and showed that a rigid oblate symmetricrotor model fits the data well; however, parallel transitions canonly rigorously determine the B rotational constant and statedifferences for the corresponding C rotational constant.20,21

Until the present work, only parallel-type transitions have beenmeasured for the pentamer, limiting the possible structuralcomparisons with theory.20–24

The pentamer behaves similarly to the trimer in the waythat hydrogen bond tunneling motions affect the energy levelstructure.25,26 The most facile process is termed “flipping” andinvolves a free hydrogen switching from one side of the planeto the other, as shown in Figure 1(b). Previous experimentsand theory revealed that this motion, in combination withpsuedorotation of the ring pucker, results in fast vibrationalaveraging to a planar, symmetric (C5h) pentamer structure.This process results in a “torsional-puckering” manifold ofenergy levels, described by Wales et al. and Graf et al., andelaborated by Harker et al.17,24,27 This energy level manifoldis shown on the left of Figure 2. The levels can be labeled bythe irreducible representation of the C5h point group. Experi-ments have shown the separation of these levels to be ca. a fewwavenumbers.24

A second tunneling motion, which had previously beenobserved only in the (H2O)5 pentamer isotopomer, is “bifur-cation,” sometimes referred to as “donor tunneling,” whereinthe hydrogen participating in the hydrogen bond interchangeswith the corresponding free hydrogen. This tunneling motionbreaks and reforms the hydrogen bond and is of particu-lar interest in studying the effect of cooperativity in waterdynamics, as this tunneling path has been characterized exper-imentally in the dimer, trimer, pentamer, and hexamer, but

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FIG. 1. Structure of the water pentamer. (a) Oxygen atoms are red and hydrogens are grey. The oxygen framework deviates from planarity by 15.5◦, but thevibrationally averaged rotational constants have been shown to be well-approximated by a semi-rigid, oblate symmetric top model. (b) One proposed mechanismof bifurcation tunneling A single monomer switches the hydrogen participating in the hydrogen bond, and an adjacent monomer flips its free hydrogen withrespect to the plane. The hydrogens involved in the pathway are colored blue.

not for the octamer.2,3,22,23,28–37 It is currently unclear fromrecent observations if bifurcation tunneling is observed in thetetramer. This tunneling motion further splits the torsionalenergy levels, shown on the right of Figure 2, which arenow labeled by the irreducible representation of the molec-ular symmetry group G320.38 A detailed study by Wales andWalsh elucidated two possible mechanisms for bifurcationtunneling, but determining which one is correct requires exper-imental study.17 Further examination by Gregory and Clarypredicted tunneling splittings of 220-700 MHz for (H2O)5and 70-140 MHz for (D2O)5 on variants of the ASP poten-tial surface.39 Brown et al. observed bifurcation tunneling in(H2O)5, of magnitude ∼5 MHz, but due to the small numberof observed lines, a definitive determination of the tunnel-ing mechanism was not possible.22 Readers interested in thedetailed group theory of the water pentamer are referred to thework of Balasubramanian.38

Here we report the measurement of 875 VRT transi-tions belonging to 6 perpendicular subbands originating from(D2O)5 at ∼512 cm�1 and the assignment to a librational

FIG. 2. Pseudorotational manifold of the water pentamer. The diagram on theleft shows the result of the “flipping” motion, shown as a red arrow, whichgenerates a manifold of 10 energy levels, labeled by the irreducible represen-tations of the C5h point group. A pseudo-quantum number, k, defined in thetext, also labels the levels. On the right, the splitting caused by bifurcationtunneling is shown for a single pseudorotational level. These states can belabeled by the irreducible representations of G320, as shown by Wales et al.The reader is referred to Wales and Walsh for a detailed discussion of therelevant group theory.17

vibration. The subbands reveal an increase in the bifurcationtunneling splittings of at least 3 orders of magnitude uponsingle quantum excitation, suggesting a strong coupling ofthe librational motion to the tunneling pathway. Analysis ofthe fitted constants provides the first characterization of theC rotational constant as well as the DJK and DK centrifugaldistortion terms.

EXPERIMENTAL

Our previous investigations of water dimer and trimerlibrational motion in the 500 cm�1 region prompted us tosearch for transitions from larger clusters.1,3 The Berkeleydiode laser/supersonic beam spectrometer used in this studyhas been described in detail elsewhere and only a shortdescription is provided here.3,40–42

A helium-cooled spectrometer (Spectra Physics) usinglead-salt diodes (Laser Photonics) was used to produce infraredradiation from 509 to 514 cm�1. The beam was multipassed18-22 times through a pulsed planar supersonic expansion of amixture of H2O and He using a Herriot cell and detected usinga helium-cooled (Si:B) photoconductive detector (IR Labs).The supersonic expansion was produced by bubbling pure Hegas, with a backing pressure of 1-2 atm through liquid D2O(Cambridge Labs, 99.96% purity), and then expanding througha 101.6 mm long slit at a repetition rate of 35 Hz into a vac-uum chamber maintained at ∼200 mTorr by a Roots blower(Edwards 4200) backed by two rotary pumps (E2M 275).Simultaneously, the fringe spacing of a vacuum-spaced etalonand an OCS reference gas spectra were detected with a liq-uid He cooled (Cu:Ge) detector (Santa Barbara ResearchCenter) and recorded to enable precise frequency calibra-tion. The observed linewidths of ∼30-40 MHz full-width halfmaximum (FWHM) are somewhat larger than the Doppler-limited linewidths extrapolated from earlier experiments usingargon expansions. Typical frequency measurement accuracy is10-20 MHz, limited by both linewidths of the cluster absorp-tions and laser drift. Spectra were detected in direct absorp-tion using a time-gated phase sensitive signal processingapproach.

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FIG. 3. (a) All 1063 observed transitions in the experimental range of509.258–513.820 cm�1. There are two major laser gaps in the spectrum:from 510.357 to 510.901 cm�1 and 511.360–511.719 cm�1, as well as sev-eral smaller gaps, typically less than 0.01 cm�1. The spectrum also shows thedrastic intensity fluctuations of the lead salt diode laser, most notably around509.6 and 512.0 cm�1. (b) The remaining 188 unassigned transitions. Thebottom of the figure shows the experimentally probed region imposed underthe libration band of liquid water.

Accessing the 500 cm�1 region of the electromagneticspectrum has generally been notoriously difficult. The spec-tra reported here required the use of 10 separate laser diodes,each scanned across several modes to cover the specifiedspectral range. Moreover, large laser gaps are present in thespectra, which causes considerable difficulty in the assign-ment. Additionally, the spectrum reflects several distinct laserintensity fluctuations across different devices that are appar-ent in the complete spectra shown in Figure 3(a). Specifi-cally, between 512.4 cm�1 and 513.2 cm�1 the intensity isenhanced and between 509.5 cm�1 and 510 cm�1 the intensityis depressed.

RESULTS AND ANALYSISAssignment

We were able to assign 875 of the 1063 recorded transi-tions to the pentamer-d10 using a pattern recognition algorithmbased on the oblate symmetric top model. A similar program

has been used to aid in the assignment of water dimer andwater octamer spectra.1,30 The above-mentioned intensity fluc-tuations make it difficult to rely on relative intensities acrossmore than 0.5 cm�1, and complicated the assignment pro-cess. The full spectrum, along with the remaining unassignedlines, is shown in Figure 3. Lines were assigned to a total of6 perpendicular (∆K= ±1) subbands originating from a singlydegenerate ground state and terminating in a singly degenerate“torsional-puckering” excited state. A typical band structureis shown in Figure 4. The assigned spectra evidenced a largebifurcation tunneling splitting.

Fit results

The assigned transitions were fit to a standard oblate sym-metric top energy level expression (Equation (1)). This modelhas been previously shown to correctly model the VRT tran-sitions of the water pentamer by Harker et al.24 Each subbandwas fit to a separate expression to simplify the analysis. Theaverage RMS of the 6 subbands was ∼8.5 MHz, which is wellbelow the observed linewidths of ∼30 MHz and comparableto the wavelength accuracy of ca. 10 MHz,

E = B ∗ J (J + 1) + (C − B) ∗ K2 − DJ [J (J + 1)]2

−DJK ∗[J (J + 1) K2

]− DK ∗ K4. (1)

In Eq. (1), B and C are the usual rotational constants ofthe structure and DJ, DJK, and DK are the centrifugal distor-tion constants. The transitions displayed no Coriolis splitting,suggesting a transition from a singly degenerate state; thesestates are well-studied by Harker et al., Liu et al., Cruzan et al.,and Brown et al. and display no Coriolis splittings in the groundstate.20–24 The 6 subbands appear to be evenly spaced with anaverage separation of ∼0.052 cm�1(∼1.559 GHz). The resultsof the fit are shown in Table I. Correlation matrices and theexplicit transition frequencies included in the fit can be foundin Tables S1 and S2 of the supplementary material.

Observation of Table I shows that the excited state con-stants for all 6 subbands are in close agreement, indicating that

FIG. 4. A typical subband structure observed in the experiment. The P branchregions are severely affected by the two large laser gaps described in the text.

ftp://ftp.aip.org/epaps/journ_chem_phys/E-JCPSA6-146-001702

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TABLE I. Results from the fit of all 875 observed transitions to an oblatesymmetric top energy level expression. All values are given in MHz, with theexception of the number of transitions. Subbands are labeled 1-6 from low tohigh frequency to distinguish the 6 subbands. Single prime values representthe excited state value and double primed constants are associated with thelower state.

Subband 1 Subband 2 Subband 3Value (MHz) Value (MHz) Value (MHz)

v 15 361 732(9) 15 363 247(5) 15 364 722(2)B′ 1 767.28(50) 1 767.03(29) 1 767.36(10)C′ 941.38(76) 941.28(44) 940.99(13)Dj′ 1.10(76) × 10−2 1.152(65) × 10−2 1.246(22) × 10−2Djk′ 1.97(33) × 10−2 1.66(13) × 10−2 1.527(42) × 10−2Dk′ 3.18(31) × 10−2 3.723(87) × 10−2 3.521(36) × 10−2B′′ 1 750.15(46) 1 749.68(28) 1 750.020(99)C′′ 907.15(79) 906.93(42) 906.72(13)Dj′′ 7.31(12) × 10−3 7.09(55) × 10−3 7.61(21) × 10−3Djk′′ �8.72(32) × 10−3 1.17(11) × 10−2 �1.223(42) × 10−2Dk′′ �4.70(41) × 10−2 �4.054(97) × 10−2 �4.283(39) × 10−2RMS 11.53 9.61 4.21

Number oftransitions 71 137 199

Subband 4 Subband 5 Subband 6Value (MHz) Value (MHz) Value (MHz)

v 15 366 285(2) 15 367 659(3) 15 369 321(7)B′ 1 767.36(14) 1 767.12(21) 1 768.25(37)C′ 941.02(19) 941.12(27) 941.47(49)Dj′ 1.205(29) × 10−2 1.171(46) × 10−2 1.438(92) × 10−2Djk′ 1.517(60) × 10−2 1.60(11) × 10−2 1.43(17) × 10−2Dk′ 3.529(42) × 10−2 3.648(83) × 10−2 3.55(11) × 10−2B′′ 1 750.10(13) 1 749.81(20) 1 750.65(34)C′′ 906.72(18) 906.76(27) 907.03(46)Dj′′ 7.74(27) × 10−3 7.57(40) × 10−3 9.06(75) × 10−3Djk′′ �1.284(57) × 10−2 �1.140(99) × 10−2 �1.28(16) × 10−2Dk′′ �4.232(45) × 10−2 �4.200(99) × 10−2 �4.26(13) × 10−2RMS 6.05 8.42 11.16

Number oftransitions 207 163 98

the excited vibrational state is the same for all bands. Like-wise, the lower state constants indicate a common vibrationalground state, which is in good agreement with the results ofHarker et al. and Liu et al. for the D2O pentamer.20,21,24

Tunneling dynamics

As shown in Figure 2, the tunneling dynamics of the waterpentamer lead to a tenfold increase in the number of energylevels; to determine the origin of the 6 observed subbands,we consider the feasible tunneling mechanisms in turn. Themost facile tunneling process in the pentamer is “flipping,”which leads to the pseudorotation manifold shown in Figure 2.Selection rules for these “flipping” transitions are similar tothose for the trimer pseudorotation manifold:25,26 ∆K − ∆k= 5 + 10n; here n is an integer and k is the pseudorota-tion quantum number, shown on the left of Figure 2.17,27,35

For our observed transitions, ∆K=±1; this implies ∆k=±4,which would result in two subbands in the experimentalregion instead of the 6 we actually observe. Additionally, the

splitting due to flipping in the ground state has been observedto be ca. 1 cm�1, very distinct from the ∼0.051 cm�1 separa-tion observed for the 6 subbands. Moreover, the bands orig-inating from transitions between pseudorotational level with∆K=±1 would not be equally spaced.17 We are thus forced toconsider bifurcation tunneling as a second feasible tunnelingmotion.

Wales and Walsh have shown that there are two possi-ble mechanisms for bifurcation tunneling.17 The net resultof the bifurcation pathway is the exchange of the hydrogenbonded and free proton within a single water monomer. In thefirst pathway, this results in the exchanged free proton local-ized on the opposite side of the pentamer plane. This pathwaywas predicted from ab initio calculations and two empiricalpotentials (TIP4P and ASP-W2), and will be referred to asMechanism A. The second pathway also produces this sameresult for the exchanged free proton, but this is accompaniedby an adjacent monomer flipping of its free hydrogen as well.The second pathway was observed for the ASP-W4 potential,and will be referred to as Mechanism B.17 These two path-ways are shown in Figure 5. Both result in an extension ofthe effective molecular symmetry group to G320; however thespectral intensity pattern changes depending on which mech-anism is active. In analyzing our results we considered bothmechanisms.

The presence of bifurcation tunneling induces a furthersplitting of the pseudorotation energy levels, as shown on theright of Figure 2. This splitting pattern for both mechanismsis shown in Table 8 of Wales and Walsh.17 In the G320 MSgroup notation, the new selection rule for electric dipole tran-sitions indicates that transitions occur between states whichchange parity with respect to inversion, but which maintaintheir overall symmetry (i.e., H1+ → H1�, E1� → E1+, etc.).From the fit, we can assume that the ground state is one ofthe singly degenerate energy levels (k = 0, +5), which weknow from the experiments of Harker et al.,24 Cruzan et al.,23

and Liu et al.20,21 which display no bifurcation tunneling. Werefer to the ground state as singly degenerate and neglect the

FIG. 5. The two proposed mechanisms for bifurcation tunneling in the waterpentamer. Oxygens are colored red and hydrogens are colored grey. Hydrogensinvolved in the motion are highlighted blue. (a) In Mechanism A, a single watermonomer exchanges its free and hydrogen bonded protons via the transitionstate (the middle image). The exchanged free proton lies on the opposite sideof the plane in the final state shown on the right. (b) In Mechanism B, a singlewater monomer exchanges its free and hydrogen bonded protons, with theexchanged free hydrogen again lying on the opposite side of the plane via thetransition state shown in the middle image. Additionally, an adjacent watermonomer flips its free hydrogen to the opposite side of the plane, as shown inthe final state (the right image).

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underlying tunneling levels, as these cannot be resolved withcurrent experiments. As a note, we neglect considering higherenergy, singly degenerate, pseudorotation manifold levels asGraf et al.27 show that these lie nearly 50 cm�1 above k = +5,and are therefore expected not to be populated in a supersonicexpansion. In G320 notation, the energy level label for k = 0or +5 will be A1± ⊕ H1± ⊕ H2± ⊕ H3± ⊕ H4± ⊕ H5± ⊕ H6±⊕ A1±, for which the parity can be deduced from Table 8of Wales and Walsh17 or from Figure 6(a) herein. Based onthe selection rules, the allowed transitions would be k = 0→ ±1, ±3, +5 or k = +5 → 0, ±2, ±4 for either mechanism.To determine which of the above transitions we are observing,we compare the unique splitting patterns to our experimentallyobserved pattern.

We can immediately rule out the transitions k = 0→ ±1,±3 and k = 5→ ±2, ±4 for two main reasons. The first is thatwe did not observe Coriolis splitting, which would be expectedif the transitions were to terminate in one of the doubly degen-erate pseudorotation levels (±1,±2,±3, and±4). It is possible,although unlikely, that the splitting is below the experimentalresolution, as previous studies of (D2O)5 found evidence ofCoriolis splitting of ca. 100s of MHz in these states in a lowfrequency band (∼27 cm�1). The second reason is that a tran-sition from k = 0 or +5 to one of the doubly degenerate stateswould result in at least 12 subbands appearing, for which wefind no evidence in the spectrum.

Considering only k = 0→ +5 and k = +5→ 0, we comparethe predicted splitting patterns to what is observed experi-

mentally. It is important to note that the group theoreticaltreatment rigorously predicts that there should be 8 separatesubbands for any of the singly degenerate→ singly degener-ate transitions; however, the separation between the 3rd and4th levels is so small that only a very large bifurcation tun-neling splitting would result in the levels separating in thespectrum. The 5th and 6th levels are also closely spaced andnot expected to be resolved. In order for the experiment todiscern such a splitting, the separation needs to be larger thanca. twice the resolution of 30 MHz. This corresponds to abifurcation magnitude of∼0.154 cm�1, which is 3× larger thanthe separation of the observed subbands. Thus we expect theseclosely spaced levels to remain unresolved in the spectrum,similar to what Brown et al. observed for (H2O)5 at 90 cm�1.22

The exact spacing between these levels predicted by theory canbe ascertained from Table 8 of Wales and Walsh.17

Analysis of the group theoretical treatment of Wales andWalsh shows that there are only two possible bifurcation pat-terns, distinguished only by opposite intensity variations.17

For the mechanism B, k = 0 → +5 and k = +5 → 0 havethe same pattern, which is also shared by the mechanismA, k = 0→+5, in which the expected ratio of bands from low tohigh frequency is 1:10:38:76:76:31. The alternative splittingpattern for mechanism A, k = +5 → 0 is 31:76:76:38:10:1.Determining the intensity ratio of the observed bands is diffi-cult due to the intensity fluctuations of the laser and the largelaser gaps which limit spectral coverage; however we do find agood qualitative agreement between the experimental pattern

FIG. 6. (a) The pseudorotational manifold for the ground and a general excited state of the water pentamer. The parity, with respect to the G320 inversion operator,is shown to the left of the levels. Blue lines represent possible transitions originating in k = +5 and terminating in a doubly degenerate level. Red lines representtransitions originating in k = 0 and terminating in a doubly degenerate level. Green lines show the possible transitions between two singly degenerate levels.The bolded line shows the transition observed in this study. (b) The bifurcation splitting pattern for the k = 0 level, assuming Mechanism A is the bifurcationmotion. The labels are for the irreducible representations of G320. The line spacing is not to scale; for the actual spacing see Table 8 of Wales and Walsh.17 (c)Comparison of the observed and predicted subband patterns. The first line for the experiment is fixed to be in the same relative position as the first predictedtransition. The intensities are scaled such that the most intense transition in both the observed and predicted spectrum has a magnitude of 1.

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and that expected from mechanism A, k = +5 → 0 transi-tion as shown in Figure 6. Based on this assignment, we canextract a value for the bifurcation tunneling of the excited state,0.062 83 cm�1, confirming that the 3rd/4th and 5th/6th levelswould not be resolved separately.

More evidence supporting this assignment can be obtainedfrom comparison to the results of Harker et al., who observed aparallel-type transition at 27.3 cm�1 that was assigned to orig-inate in k = +5 of the lowest energy pseudorotational manifoldof (D2O)5.24 The authors fit their data to an oblate top modelwithout the DK term, but we can still compare the B′′ and DJ ′′

values, since they have no K dependence. Harker et al. reporta B′′ value of 1750.870 MHz and a DJ ′′ value of 0.007 MHz,compared to our values of 1750.070 MHz and 0.008 MHz,respectively.24 These values are in excellent agreement witheach other suggesting that the lower state is indeed k = +5 ofthe lowest energy pseudorotational manifold, which would beexpected given the rotational cooling effective in the super-sonic expansion. Our analysis of the intensity pattern of the 6observed subbands can then be used to confirm that the excitedstate is indeed k = 0.

DISCUSSIONStructural characterization

This study represents the first time a perpendicular-typetransition has been measured for the water pentamer (any iso-topomer), and it allows us to extract an accurate measure ofthe C rotational constants. We average the C values from the6 subbands to give a value of 906.886 MHz for the groundstate and 941.211 MHz for the excited state. The ground statevalue can be compared to that obtained from ab initio cal-culations for (D2O)5. To our knowledge, the only existingcalculations for the (D2O)5 species are those from Graf et al.at the MP2/aug-cc-pVDZ level of theory,27 who obtain a Crotational constant of 922.0 MHz and a B constant value of1790.9 MHz in the ground state; both of which are in goodagreement with our observed values of 906.886 MHz and1750.070 MHz.27

Previous water pentamer experiments from Harker et al.,Liu et al., and Cruzan et al. provide more evidence forthe true water pentamer structure.20,21,23,24 Harker et al.recorded 5 low frequency torsional (D2O)5 parallel subbandswhich are supplemented by the one parallel (D2O)5 sub-band observed by Cruzan et al.,23,24 and one other parallel(D2O)5 subband observed by Liu et al.20,21 These studiesfound ground state B values in the narrow range of 1750.817–1751.976 MHz, which yield excellent agreement with ourpresent results. We do notice a marked contrast between ourresults, and those previously reported with respect to thechange in rotational constants between ground and excitedstates, however. The previous rotational constant changeswere at most a few MHz, whereas in our present study wereport changes of tens of MHz. This dramatic increase is dueto the vibrational nature of the excited state; i.e., all pre-vious observations were due to torsional vibrational modes,whereas the present study observes a libration, which engen-ders an increased intermolecular motion, as we have previouslyobserved.1,3

For completeness, Brown et al. observed a parallel transi-tion for the (H2O)5 isotopomer, which yielded a ground state Bvalue of 1992.467 MHz.22 This value can be compared to thecalculations of Graf et al., which predict a value of 2037.0 MHzfor the ground state.27

Vibrational assignment

The combination of the large number of vibrational modesof the water pentamer (24 intermolecular modes) with the inac-curacy of harmonic calculations makes it difficult to establishthe exact vibrational mode observed in this study. Nonetheless,we can make some general comparisons with recent harmoniccalculations for the (D2O)2 species. Again, Graf et al. have cal-culated the harmonic intermolecular frequencies and found 10modes between 300.8 and 712.4 cm�1 assigned to librationalvibrations.27 Noting that harmonic calculations overestimatethe vibrational frequency, we find two candidate librations,predicted at 572.2 and 577.4 cm�1. Both of these exhibitsignificant motions both parallel and perpendicular to the prin-cipal axis that would account for the relatively large changesobserved for both B and C rotational constants.

The intensity of the 577.4 cm�1 band is predicted to be∼7× higher than that of the 572.2 cm�1 band,27 making theformer assignment more likely. And if we are indeed observ-ing the 577.4 cm�1 vibration, the weak, unassigned lines at∼509.5 cm�1 would comprise evidence for an R branch of the572.2 cm�1 vibration.

Librational enhancement in bifurcation tunneling

Irrespective of the detailed vibrational assignment, asalient result of this study is the observation of a hugeenhancement in bifurcation tunneling rates. We have previ-ously observed a large increase in bifurcation tunneling ratesfor transitions occurring in the 500 cm�1 region for both theH2O dimer and trimer; ca. 40× and 400×, respectively.1,3 Asno experiment has yet quantified bifurcation tunneling forthe (D2O)5 ground state, we cannot yet establish the libra-tional enhancement observed herein as precisely. Cruzan et al.determined that there was no observable splitting resultingfrom bifurcation tunneling at the experimental resolution of450 kHz23 for (D2O)5. Taking that resolution as an upperlimit to the tunneling splitting, we would then be observing anenhancement of ca. 4000×. Such a large enhancement attestsa strong coupling between the librational motion and the tun-neling pathway, as discussed previously for both the dimerand trimer.1,3 Irrespective of whether the observed vibrationis the 577.4 or 572.2 cm�1 mode, both are predicted to have alarge component of motion in the plane perpendicular to theprincipal axis.27 Comparison with Figure 5 suggests that eitherbifurcation mechanism similarly exhibits significant motion inthat plane.

Bifurcation mechanism

The proposal of two distinct pentamer bifurcation mech-anisms from theory provides an opportunity to establish theactual mechanism responsible for the observed splittings.17,39

As mentioned above, the only previous experimental observa-tion of bifurcation tunneling in the water pentamer was from

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Brown et al., who observed splitting for the (H2O)5 species.Fortunately, the predicted splitting pattern does not changewith isotopic substitution, only the absolute splitting magni-tude and intensity patterns do (from the statistical weights).Therefore, combining the results presented herein with thoseBrown et al. will allow a reliable determination of whichproposed mechanism is responsible for the observed spectralsplittings.22

First, it is important to note that both the present resultsand those of Brown et al. are consistent with a VRT transi-tion between two singly degenerate pseudorotational states.22

As discussed in the Results section, the two distinct patternspredicted from group theory engender a single vibration-rotation transition split into an equally spaced sextet.17 Weagain note that there are 8 possible transitions, but due to thenear-degeneracy of the 3rd/4th and 5th/6th energy levels,only 6 separate transitions will be resolved in the presentexperiments. This sextet can have two possible intensitypatterns for (D2O)5, viewed from low to high frequency;31:76:76:38:10:1(Mechanism A) or 1:10:38:76:76:31(Mech-anism B), based exclusively on the spin statistical weightsof the energy levels. The analogous patterns for (H2O)5 are1:3:18:54:81:51(Mechanism A) and 51:81:54:18:3:1(Mecha-nism B).

As elaborated in Results, our observed intensity patternof 3:9:10:7:5:1 qualitatively agrees with the pattern predictedby mechanism A. The difference can be rationalized in termsof the intensity fluctuations of the laser. Brown et al. alsoreported an equally spaced sextet, but their intensity ratiowas not explicitly given,22 although they claimed that theirmeasured intensity pattern agreed with the predicted intensitypattern of Mechanism A for (H2O)5. As a note, the bifurcationmechanism of Brown et al. reported in Figure 1 of their paperdoes not correspond to mechanism A.

Based on the above information, we conclude that thebifurcation tunneling mechanism observed experimentally isthe predicted mechanism A (Figure 5(a)), as this is the onlymechanism that can account for both intensity patterns. Thismechanism was found by Wales and Walsh17 in ab initio,TIP4P, and ASP-W2 calculations and additionally by Gregoryand Clary39 on the ASP-P and ASP-NB surfaces. It is impor-tant to note that the bifurcation mechanism was incorrectlyreported by Brown et al. as mechanism B.22 The similarity ofmechanism A to the bifurcation mechanism in the water trimer,in addition to the dramatic increase in splittings observedupon excitation to a librational vibration, suggests that detailedexamination of the bifurcation tunneling motion would be apromising route to study hydrogen bond breaking/formationand the effect of cooperativity in both water clusters and inbulk water phases.

SUMMARY

We have observed 6 perpendicular subbands for the(D2O)5 isotopomer originating from the pseudorotationalk = +5 ground state level and terminating in the k = 0 levelof a librational vibration, split by bifurcation tunneling. Themagnitude of this bifurcation tunneling splitting was foundto be 0.062 83 cm�1 (1884 MHz), which is at least a 4000×

enhancement of this tunneling splitting in the ground state.We have also reported the first experimental measurement ofthe C rotational constant of the water pentamer, and estab-lish the mechanism for bifurcation tunneling. The dramaticincrease in bifurcation tunneling observed upon excitation ofthe librational vibration establishes the pentamer as the thirdwater cluster displaying such large enhancement in this spec-tral region. Further study of this librational enhancement willprovide further insight into details of the hydrogen bond break-ing/formation process and effect of cooperativity in both clus-ters and bulk water. Recent studies question the origin of thebifurcation splitting, and further examination of these spectralfeatures will require consideration of librational vibrations.43

Combining the results herein with the previous stud-ies of the H2O pentamer provides a comprehensive dataset spanning both torsional and librational bands of liquidwater.20–24 Additionally, bifurcation tunneling has now beendefinitively observed in the water dimer,1,28,29,33 trimer,2,3,25,38

pentamer,20–24 and hexamer;34–38 but not for the tetrameror octamer.30 Measurements of water tetramer spectra31,32

may possibly show bifurcation tunneling, but it appears to bedramatically quenched, relative to the trimer and pentamer.

SUPPLEMENTARY MATERIAL

See supplementary material for correlation matrices forthe fits, provided in Table S1. All the assigned transitions arepresented in Table S2.

ACKNOWLEDGMENTS

The Berkeley Terahertz project is supported by Chemi-cal Structure, Dynamics, and Mechanisms-A Division of theNational Science Foundation under Grant No. 1300723.

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