Resonant ion-dip infrared spectroscopy of …Resonant ion-dip infrared spectroscopy of...

JOURNAL OF CHEMICAL PHYSICS VOLUME 113, NUMBER 6 8 AUGUST 2000

Resonant ion-dip infrared spectroscopy of benzene– „water …9:Expanding the cube

Christopher J. Gruenloh, Joel R. Carney, Fredrick C. Hagemeister,and Timothy S. Zwiera)

Department of Chemistry, Purdue University, West Lafayette, Indiana 47907-1393

John T. Wood III and Kenneth D. JordanDepartment of Chemistry, University of Pittsburgh, Pittsburgh, Pennsylvania 15260

~Received 7 September 1999; accepted 30 March 2000!

The techniques of resonant two-photon ionization~R2PI!, UV-UV hole-burning, and resonantion-dip infrared~RIDIR! spectroscopy have been employed along with density functional theory~DFT! calculations to characterize the hydrogen-bonding topologies of three isomers ofbenzene–~water!9. Isomers I and II, with R2PI transitions shifted, respectively, by177 and163cm21 from the benzene monomer, have similar intensities in the R2PI spectrum. The signal from thethird isomer~isomer III, shifted160 cm21! is present at about one-fourth the intensity of the othertwo. The experimental RIDIR spectrum of isomer I bears a strong resemblance to the spectrum ofthe benzene–~water!8 D2d-symmetry cubic structure identified in earlier work, but possessing anextra single-donor transition associated with the ninth water molecule. Using theS4 and D2d

symmetry forms of the water octamer as base structures to which the ninth water molecule can beadded, a total of nine ‘‘expanded-cube’’ structures are identified for W9 arising from two distinctinsertion points in the W8(D2d) cube (D1,D2) and three such points in the W8(S4) cube (S1-S3).DFT calculations predict these to be spread over an energy range of less than 1 kcal/mol. Given thateach of the nine ‘‘expanded-cube’’~water!9 structures contains five symmetry-inequivalent free OHgroups, a total of 45 ‘‘expanded-cube’’ benzene–~water!9 conformational isomers are predicted.Structural and vibrational frequency calculations have been performed on seven of these todetermine how the~water!9 structural type and the attachment point of benzene to the structureaffect the total energy and vibrational frequencies of the cluster. Based on a comparison of theexperimental RIDIR spectrum with the calculated vibrational frequencies and infrared intensities,isomer I is attributed to the BW9(D1) structure in which benzene attaches to W9(D1) at the freeOH of the water molecule which donates a H-bond to the ninth water. This structure has a calculatedbinding energy that is about 0.13 kcal/mol greater in magnitude than any other benzene–~water!9

isomer studied. The experimental spectra of isomers II and III are of insufficient quality to assignthem to specific BW9 structures with confidence. However, isomer II is most consistent with anS4-derived expanded cube structure~either S1 or S2), while isomer III shows characteristicsconsistent with a secondD1-derived BW9 structure in which benzene is attached at a position on theexpanded cube remote from the ninth water. ©2000 American Institute of Physics.@S0021-9606~00!01024-2#

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I. INTRODUCTION

In the pursuit of quantitatively accurate descriptionshydrogen bonding in water, the study of gas-phase~water!n

clusters~shortened to Wn hereafter! can play an importanrole as a testing ground for intermolecular potentials. A uful feature of these clusters is that their energeticapreferred structures sample a range of H-bonding topologvarying from cyclic for n53 – 5 to the first three-dimensional networks whenn56 and 7 and then to cubic an58.1–3

The unusual stability and high symmetry of the cubwater octamer have made it a particular focus of recent sies. Aside from the early work of Stillinger and David,4 allrecent calculations3,5–16 agree that the lowest energy stru

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ture of the W8 cluster is nominally cubic with the oxygeatoms of the water molecules taking up positions at the cners of the cube. There are 14 cubic W8 isomers, that differprimarily in the orientations of the 12 H-bonds.17,18 Two ofthese cubic structures, withS4 and D2d symmetry, are cal-culated to be nearly isoenergetic and about 2 kcal/mol mstrongly bound than the next nearest energy cuisomer.13,19 The S4 and D2d structures may be viewed asfusion of two cyclic tetramers, differing primarily in the direction of H-bond donation in the tetramer sub-units, wdonation occurring in the same direction in theS4 speciesand in the opposite direction in theD2d species.3,13

Our group has recently provided spectral evidencethe S4 and D2d cubic water octamers using the size- aconformation-selectivity afforded by resonant ion-dip infrred spectroscopy~RIDIRS!.2,3,20–24By incorporating a ben-zene molecule into the cluster as a weakly-interacti

0 © 2000 American Institute of Physics

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2291J. Chem. Phys., Vol. 113, No. 6, 8 August 2000 Spectroscopy of benzene–(water)9

surface-attached probe molecule, individual vibronic trantions of a cluster of a given size and conformation caninterrogated with both mass and wavelength selectivity usresonant two-photon ionization~R2PI! time-of-flight massspectroscopy~TOFMS!.25,26 Hole-burning methods3,22,27 arethen used to divide complicated R2PI spectra into subspearising from different species present in the same mass cnel. The infrared~IR! spectra of each species can thenrecorded free from interference from one another usRIDIR spectroscopy. Because the OH group vibrates direagainst the H-bond, the vibrational frequencies and IR intsities of the OH stretch fundamentals are sensitive functiof the number, type, and strength of H-bonds in which eOH group participates. When combined with density funtional theory ~DFT! calculations of the low-energy structures, harmonic vibrational frequencies, and IR intensitdefinite assignments of theS4 andD2d symmetry water oc-tamers of~benzene–water!8 @hereafter shortened to BW8(S4)and BW8(D2d)] were possible.

The anticipation, based on the structure of ice, is tfurther structural changes will accompany the formationlarger Wn and BWn clusters. One intriguing possibilityraised by recent calculations is that fused-cubic structuwill be among the lowest-energy forms of water clusters wn512, 16, and 20.6,13,28 Whether such structures do indeecompete with more compact networks and how the evoluof these structures occurs whenn is not an integral multipleof four are open questions that are just beginning toaddressed.10,29

Buck and co-workers have recently reported results frtheir investigation of intermediate-sized Wn clusters (n58 – 10) using a size-selected IR depletion scheme basemolecular scattering.10,29 They present an infrared spectrufor n58 that results from an inseparable mixture of theS4

andD2d symmetry isomers of W8 that are both present in thsupersonic expansion. Forn59, they ascribe their IR spectrum to aD2d-derived water nonamer structure, which canformed by expanding the cubic structure of W8.

In the present paper we present results that utilize R2UV-UV hole-burning, and RIDIR spectroscopies to recoIR and ultraviolet spectra of three isomers of BW9. As withBW8, the comparison with calculations plays a crucial roletheir assignment to particular structural isomers of BW9. Afirm assignment for one of these BW9 isomers is made asD2d-derived structure in which the ninth water expands oof the cyclic tetramer subunits to a cyclic pentamer, content with the assignment of Buck and co-workers10,29 on thebare W9 clusters. The two other observed BW9 species aretentatively assigned to anS4-derived expanded cube andsecondD2d-derived structure in which benzene attaches tdifferent OH group on the expanded cube.

II. METHODS

The experimental apparatus employed in this workbeen described previously.25 The experimental methods anexpansion conditions used to form the BW9 clusters are simi-lar to those used in our studies of BW8, to which the readeris referred for details.27


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In order to assist in the assignment of the experimenIR spectra, DFT calculations of the structures, binding engies, harmonic vibrational frequencies, and IR intensitiesseveral isomers of W9 and BW9 have been carried out. ThDFT calculations employed the Becke3LYP functional30–32

and either the 6-311G(d)/6-31G(d) ~Refs. 33–35! or aug-cc-pVDZ ~Ref. 36! basis sets. The former basis set emploa 6-311G(d) description of the water molecules and6-31G(d) description of the benzene molecule, whereaslatter employs an aug-cc-pVDZ description of all atoms.these two basis sets, aug-cc-pVDZ is considerably more flible, and the smaller 6-311G(d)/6-31G(d) basis set wasadopted due to computational demands of large basiscalculations on BW9. Several prior studies37–40 have shownthat Becke3LYP calculations, even when using t6-311G(d)/6-31G(d) basis set, give structures and Ostretch frequency shifts for Wn and BWn clusters close to thecorresponding MP2 results.

III. RESULTS AND ANALYSIS

A. R2PI spectra

One-color R2PI spectra were recorded in the orig@Figs. 1~a!–1~c!# and 60

1 @Fig. 3~a!# regions of theS1←S0

transition of benzene, monitoring the BWn1 mass channels

with n56 – 8, respectively. Vibronic frequency shifts for thclusters are reported with respect to either the 00

0 ~38 086cm21! or 60

1 ~38 609 cm21! transitions of the benzene monomer. Since theS1←S0 transition of benzene is electridipole-forbidden, the appearance of BWn transitions in theorigin region reflects the breaking of benzene’s symmetrythe Wn cluster. The 60

1 transitions of the BWn clusters,~which are vibronically-allowed in the benzene monome!,are about 20 times more intense. As indicated in Fig.

FIG. 1. One-color R2PI spectra of BWn clusters near theS1←S0 origin ofbenzene, monitoring the BWn

1 mass channels with~a! n58, ~b! n57, and~c! n56. The zero of the frequency scale corresponds to the electric diforbidden origin of benzene monomer~38 086 cm21!. Assignments to BW7,BW8, B2W8, and BW9 clusters are labeled in the figure. See the textfurther details.


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2292 J. Chem. Phys., Vol. 113, No. 6, 8 August 2000 Gruenloh et al.

much of the structure in the R2PI spectra has been assipreviously to BW7,

26 BW8,3,27 and B2W8 ~Ref. 27! clusters.

The three most prominent bands in the BW81 mass channe

have not been assigned to other clusters, and the assignand characterization of these bands as arising from B9

clusters form the focus of the present paper. They are labby 3, 4, and 7 in Fig. 1 to match with the numbering usedthe more intense 60

1 region in Fig. 3.A characteristic shared by all BmWn neutral clusters is

that they fragment following photoionization, thereby complicating the assignment of a set of transitions in a particumass channel to a given neutral cluster size. Figure 2plays histograms of the amount of fragmentation occurrin one-color R2PI studies of BWn clusters withn51 – 9. Forclusters with up to five water molecules, there is efficiefragmentation by loss of a single water molecule.25,26,41 InBW6 and BW7, loss of a second water molecule also is oserved, suggesting that an energetic threshold to this prois being reached atn56. The ionized clusters have verdifferent minimum-energy structures than do the startneutral clusters.42 The Franck–Condon factors to the adibatic ionization threshold are therefore very poor, hindertwo-color R2PI and producing ionized clusters in one-coR2PI with substantial internal energy, which can fragmsubsequently.

There are several characteristics of transitions 3, 4, anthat lead us to assign them as arising from three BW9 iso-mers.

FIG. 2. Fragmentation of BWn clusters into the mass channels:~a! BWn1 ,

~b! BWn211 , and~c! BWn22

1 after one-color resonant two-photon ionizatioSmaller BWn clusters (n<5) efficiently fragment by losing one water moecule following photoionization. The loss of a second water moleculecomes energetically favorable at BW6 and continues for larger clusters. Daon the individual isomers of BW8, and BW9 are included, showing thesimilar fragmentation for isomers of the same size.


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~1! The mass resolution of the measurement insures thacarriers of these R2PI transitions possess at leastbenzene and eight water molecules.

~2! The R2PI spectra in the BW81 mass channel in the origin

region @Fig. 1~a!# are dominated by the three featurassigned to BW9.

~3! All other features in the spectrum have been assigneother clusters, including those containing more than obenzene molecule, which carry a distinctly different bezene concentration dependence~e.g., as B2W8).

~4! The assignment of the remaining transitions to BW9 isconsistent with the fragmentation patterns observedsmaller clusters. We have carefully followed these framentation patterns up from smaller cluster sizes, efftively assigning all transitions in so doing.

~5! The alternative possibility would be that some of thetransitions are due to even higher BWn clusters~e.g.,BW10), but if so, they do not appear in the BW9

1 masschannel like one would anticipate.

~6! UV-UV hole-burning ~presented in the next section!prove that the three transitions assigned to BW9 are dueto unique species and not to vibronic transitions outthe same ground state.

~7! Finally, as we shall see in Sec. III C, transitions 3, 4, a7 each have unique infrared spectra which bear a cresemblance to the BW8 cubic structures~especially inthe case of isomer I!, consistent with expanded-cubBW9 structures.

The transitions assigned to BW9 are shifted 60.0, 63.3and 77.1 cm21 from theS1←S0 origin of benzene monomerrespectively. The corresponding transitions in the 60

1 region,@also labeled 3, 4, and 7 in Fig. 3~a!#, show a somewha

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FIG. 3. ~a! One-color R2PI spectrum of BW71 in the 60

1 region of theS1

←S0 transition of benzene.~b!–~e! Ultraviolet hole-burning spectra of transitions with the UV hole-burning laser tuned to transitions 1~46.1 cm21!, 4~61.7 cm21!, 5 ~67.6 cm21!, and 7~78.1 cm21!, respectively. BW9 transi-tions were detected in BW7

1 mass channel after ionization-induced fragmetation of two water molecules. Transitions 1, 2, and 8 result from B2W8,transitions 5 and 6 from BW8, and transitions 3, 4, and 7 from isomersBW9. See the text for further discussion.


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greater fragmentation than do the corresponding origin trsitions, appearing most strongly in the BW7

1 mass channe@Fig. 3~a!#. This reflects the additional 1040 cm21 of energypotentially available to the cluster when ionization occursthe 60

1 rather than the origin vibronic transition.

B. UV-UV hole-burning spectra

UV-UV hole-burning spectroscopy in the 601 region is

used to distinguish whether the three transitions are dudifferent BW9 isomers, or whether transitions 4 and 7 coube vibronic bands built off of transition 3. Hole-burninspectra are collected in the BW7

1 mass channel with the holeburning laser tuned to transitions 1, 4, 5, and 7, are showFigs. 3~b!–3~e!. The lower intensity and spectral congestiof transitions 2, 3, and 6 made it difficult to collect analogohole-burning scans for these transitions. The hole-burnscans indicate that the congested R2PI spectrum of Fig.~a!is the sum of several sub-spectra due to different specieeach case, the spectrum is dominated by a 60

1 doublet whichis present due to the breaking of the degeneracy of vibtional moden6 ~of symmetrye2g in the isolated benzenmolecule! by Wn . The lack of intermolecular progressionsthe hole-burning scans indicates that the geometry chain the clusters upon electronic excitation of benzenesmall. As shown in previous work,27 transitions 5@Fig. 3~d!#and 6 are 60

1 transitions of BW8(S4) and BW8(D2d). Tran-sitions 1 and 8 are 60

1 transitions of the two benzene moecules in the B2W8(S4) cluster, while transition 2 is thaanalogous to 1 in the B2W8(D2d) isomer.

Most importantly for the present work, the UV-UV holeburning spectra shown in Figs. 3~c! and 3~e! prove that tran-sitions 3, 4, and 7 arise from distinct structural isomersBW9, and not from intermolecular combination bands osingle isomer. The 60

1 splittings ~3.8 and 2.9 cm21! of thetwo dominant isomers~4 and 7! are similar to those in theisomers of BW8 ~2.2 cm21!. The lack of a hole-burning scafor transition 3 leaves the 60

1 splitting of this isomer under-mined and suggests the possibility that one member of th0

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doublet of 3 may lie underneath the 601 transitions of

isomer 4.The similar frequency shifts, 60

1 splittings, and fragmen-tation patterns of the three isomers of BW9 suggests that theyare close structural analogs of one another. Furthermoretransitions straddle those of BW8, suggesting that the interactions between the benzene molecule and the various9

isomers are similar to those between benzene and W8, in itsS4 andD2d structural forms.

C. RIDIR spectra

RIDIR spectra of the three isomers of BW9 in the OHand CH stretch region of the IR are shown in Figs. 4~a!–4~c!.The RIDIR spectra were recorded with the UV laser tunedtransitions 7, 4, and 3 in Fig. 3~a!, respectively, while moni-toring the BW7

1 mass channel. The frequencies and wid~FWHM! for each kind of OH stretch vibration are given fothe three species in Table I. Like their BW8 counterparts, allthree BW9 IR spectra show OH stretch absorptions assiable to one of four categories of O–H groups:~i! the free


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~nonbonded! OH stretch transitions appearing around 37cm21 and marked by an F in Fig. 4,~ii ! thep H-bonded OHstretch of the water molecule that is complexed to benzenp cloud and shifted down in frequency to about 3650 cm21,~iii ! the double-donor interwater H-bonded OH stretchesthe 3450–3600 cm21 region ~D!, and ~iv! the single-donorinterwater H-bonded OH stretches in the 3100–3250 cm21

region~S!. The CH stretch fundamentals of the benzene mecule in each isomer are just barely observable as a Fresonance triad at 3048, 3074, and 3100 cm21, essentiallyunshifted from their values in free benzene.

The RIDIR spectra of the three BW9 isomers are similarto one another and bear a distinct resemblance to the RIspectra obtained previously3,27 for the two cubic water oc-tamer structures ofS4 and D2d symmetry in BW8(S4) andBW8(D2d). This strong similarity is most clearly evident icomparing the RIDIR spectrum of Fig. 4~a!, reproduced inFig. 5~a!, with that for BW8(D2d), shown below it in Fig.5~b!. Apart from an extra single-donor transition appearing3286 cm21 in the BW9 spectrum, the two spectra are nearidentical. One would surmise on this basis that the B9structure responsible for the spectrum is closely related toBW8(D2d) structure, but with a ninth water molecule producing the ‘‘extra’’ single-donor transition at 3286 cm21. W9

structures in which the W8(D2d) and W8(S4) cubes are ex-panded to incorporate a ninth water molecule into one eof the cube are most probable candidates for the structmotif present in the BW9 isomers observed here. In pure W9

clusters, the infrared spectrum observed recently by Saet al.10,29 has been assigned to a single expanded-cube9

structure. Based on the qualitative appearance of our spesimilar structures also appear to dominate in BW9 clusters.The analysis which follows focuses on this possibility, whiprovides strong support for this structure in isomer I. Aswill see, the other two isomers are less firmly assigned,

FIG. 4. Resonant ion-dip infrared spectra of the three isomers of B9

associated with UV transitions~a! 7, ~b! 4, and~c! 3 in Fig. 3. The top traceis the OPO power curve for the LiNbO3 crystal used in this study. Thespectra have not been corrected for OPO power.



TABLE I. Experimental vibrational frequenciesa and widthsb for the isomers of BW9.

Type ofOH group

Numberof OHgroups

I @BW9(D1)] II @BW9# III @BW9#

Freq. ~Width! Freq. ~Width! Freq. ~Width!

Free OH 4 3713 ~11! 3713 ~7! 3715 ~9!3704 ~4!

p H-bonded OH 1 3644 ~5! 3644 ~5! 3648 ~10!Double-donor OH 8

Asymmetric stretch 3561 ~30! 3555 c 3557 c3519 c

Symmetric stretch 3509 ~8! 3496 ~14! 3499 ~9!3493 ~10!3447 ~12!

Single-donor OH 5AD 3287 ~35! 3422d ~17! ;3200d cAAD 3202 ~33! 3279 c 3050–3230

3146 ~26! 3161 ~22!3078 ~12! 3130 ~32!

3098 ~24!3045 ~15!2989 ~24!

CH stretch region 3101 ~7! 3050 ~10!of benzene 3048 ~5! c c

aAll frequencies reported in wave numbers~cm21!. cDue to congestion, these transitions could not be assigned widths.bThe widths~in cm21! of the transitions are full-widths at half-maximum. dTentative assignment. See text for further discussion.

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D. The expanded-cube isomers of W 9

A first step in exploring expanded-cube structures for9

is to determine the number of different ways a ninth wamolecule can be inserted into theS4 andD2d symmetry cu-bic water octamers. As Fig. 6 shows, there are three unpositions for inserting a water molecule into theS4 octamer~labeled 1–3!, and two unique positions for doing so in thD2d octamer. In theS4 isomer positions 2 and 3 are distincwhile in theD2d isomer they are equivalent. In each case,ninth water molecule acts as single-acceptor/single-do~AD!, as anticipated. In addition, the free OH of the inserwater can assume axial or equatorial orientations as showFig. 7. For theD2d-derived W9 structure with the ninth watein position 1, the two orientations are equivalent, but forother isomers they are distinct, leading to a prediction of nexpanded-cube W9 isomers. A shorthand notation basedthese considerations will be used in the remainder ofpaper; namely,D2d-derived structures with the ninth watemolecule in thenth position (n51, 2, or 3! with free OHdangling either axial or equatorial will be denoted as ‘‘Dna’’or ‘‘ Dn,’’ respectively. The analogousS4-derived expandedcube will be denoted ‘‘Sna’’ or ‘‘ Sn.’’

E. DFT calculations on W 9 and BW 9

1. Structures and binding energies of the W 9 isomers

Table II reports the relative energies of the niexpanded-cube W9 isomers calculated using both the 6-31G(d) and aug-cc-pVDZ basis sets. The relative energiethe nine isomers obtained using these two basis setsnearly identical, and, in the ensuing discussion, we will foc


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FIG. 5. Comparison of the RIDIR spectra of~a! BW9 transition 7 with~b!that for BW8(D2d). ~c! and ~d! Stick diagram of the calculated OH stretcvibrational frequencies and intensities for~c! the D1(O8) isomer of BW9,and~d! the corresponding BW8(D2d) isomer. The calculated results are DFcalculations using the Becke3LYP functional with a 6-31G(d)/6-31G(d) mixed basis set on water/benzene. The zero of thequency scale was taken to be the average of the symmetric and antisymric modes of the water monomer calculated at the same level of theory.labels on the traces indicate free OH stretch fundamentals~F!, p H-bondedOH stretches~p!, antisymmetric and symmetric stretch double-donor Ostretches (D-a and D-s, respectively!, single-donor OH stretches~S!, andsingle-donor stretch of the AD water molecule~AD!.


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on the results obtained with the aug-cc-pVDZ basis set.calculations predict the nine expanded-cube structures twithin 0.80 kcal/mol of one another, with theD1 speciesbeing most stable, followed by theS2, S2a, S1a, and S1clusters 0.34–0.37 kcal/mol higher in energy, and thenthe S3, D2, D2a, and S3a clusters, 0.65–0.80 kcal/mohigher in energy. The relative energies are essentially utered by inclusion of either counterpoise correctionsBSSE~Ref. 43! or the contributions of vibrational zero-poinenergies~calculated in the harmonic approximation!.

The main point of comparison between experiment atheory is the computed and experimental vibrational frequcies and infrared intensities. However, one also hopesreliable relative energies in the computations. In geneBecke3LYP calculations cannot be used to correctly ordifferent isomeric forms of water clusters that lie so closeenergy.44 However, the largest errors occur in comparistructures with very different hydrogen bonding topologiThe situation for the various inserted-cube W9 clusters isquite different as the different isomers are so closely relastructurally. In such a case, the Becke3LYP procedurebe much more reliable for predicting relative energies. Westimate that the relative energies are correct to within atenths of a kcal/mol.

The OO and OH distances of the Becke3LY6-311G(d) optimized structures for a subset of the W9 andBW9 expanded-cube isomers are summarized in Table

FIG. 6. Structures for~a! cubic W8(D2d) and~b! cubic W8(S4) showing theunique positions for substitution of a ninth water molecule as a sinacceptor/single donor water. Note that positions 2 and 3 in theS4 structureare equivalent in theD2d structure.


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@The results obtained with the 6-311G(d)/6-31 G(d) basisset rather than the aug-cc-pVDZ basis set are reportedcause we have a more complete set of results for the B9

isomers with the smaller basis set.# Comparison of the resultsin Table II and III reveals that the relative energies of tnine W9 isomers correlate closely with the magnitude of t

FIG. 7. Binding energies and structures for the nine unique ‘‘expandcube’’ W9 isomers. The shorthand notation for the isomers specifies whethe structure is expanded fromS4 or D2d water octamer, the position osubstitution~1, 2, or 3!, and whether the dangling hydrogen is axial~a! orequatorial~no designation!. The binding energies shown have not been crected for zero-point energy or basis-set superposition error. The ZPErection changes the energy ordering of theS1 andS2 structures~Table II!.

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TABLE II. Dipole moments, rotational constants, and relative energies of low energy W9 isomers fromBecke3LYP calculations.

StructureDipole

moment~D!Rotational

constants~cm21!Relative

energy~kcal/mol!a,b

W9(D1) 1.72 0.808 07 0.633 71 0.586 88 0.00~0.00!W9(S2) 1.99 0.799 73 0.646 64 0.583 96 0.31~0.48!W9(S2a) 1.90 0.800 24 0.645 65 0.584 46 0.32~0.51!W9(S1a) 1.70 0.795 98 0.644 14 0.580 43 0.36~0.45!W9(S1) 1.75 0.799 78 0.648 27 0.583 07 0.42~0.51!W9(D2) 2.05 0.789 72 0.657 81 0.576 49 0.51~0.75!W9(D2a) 1.92 0.789 11 0.656 81 0.577 58 0.55~0.78!W9(S3) 2.06 0.785 13 0.659 47 0.578 93 0.57~0.90!W9(S3a) 1.95 0.788 38 0.656 84 0.577 24 0.68~0.93!

aNumbers in parentheses include effects of vibrational zero point energies calculated in the harmonic amation.

bThe absolute binding energy of W9(D1) is 299.39 kcal/mol before ZPE correction.


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TABLE III. OO and OH distances~Å! of selected W9 and BW9 clusters as described by Becke3LYP calculations.a,b

Bond type

W9(D1) BW9(D1~O8!) W9(S2a) BW9(S2a~O8!) W9(S1a) BW9(S1a~O8!)

ROO ROH ROO ROH ROO ROH ROO ROH ROO ROH ROO ROH

ADD→AADO1–O5 2.842 0.982 2.844 0.982 2.836 0.983 2.852 0.982 2.845 0.983 2.852 0.O1–O6 2.838 0.983 2.842 0.982 2.821 0.985 2.834 0.983 2.844 0.982 2.847 0.O2–O5 2.837 0.982 2.834 0.982 2.836 0.983 2.830 0.984 2.839 0.983 2.838 0.O2–O6 2.833 0.983 2.832 0.983 2.839 0.982 2.837 0.983 2.833 0.983 2.831 0.O3–O7 2.837 0.982 2.845 0.982 2.835 0.982 2.838 0.982 2.838 0.983 2.845 0.O3–O8 2.847 0.983 2.818* 0.985* 2.843 0.982 2.852 0.981 2.843 0.983 2.812* 0.985*O4–O7 2.835 0.982 2.843 0.982 2.863 0.982 2.831* 0.985* 2.838 0.983 2.844 0.982O4–O8 2.839 0.982 2.808* 0.985* 2.666 1.005 2.668 1.005 2.848 0.982 2.819* 0.986*

AAD→ADDO5–O4 2.681 1.004 2.675 1.005 2.648 1.009 2.648 1.009 2.677 1.003 2.679 1.O6–O3 2.682 1.004 2.678 1.005 2.686 1.003 2.680 1.004 2.677 1.004 2.673 1.O7–O2 2.672 1.004 2.675 1.004 2.660 1.008 2.688* 1.002* 2.668 1.005 2.664 1.006

AAD→ADO8–O9 2.676 1.001 2.696* 0.997* 2.782 0.987 2.781 0.987 2.676 1.002 2.696* 0.997*

AD→ADDO9–O1 2.685 1.001 2.694 0.999 2.775 0.986 2.752* 0.989* 2.683 1.001 2.694 0.999

aResults for W9 and BW9 obtained with the 6-311G(d) and the mixed 6-311G(d)/6-31G(d) basis sets, respectively. See Fig. 8 for numbering schemebDistances associated with the water molecule attached to the benzene are designated by asterisks.

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structural distortions induced by insertion of the water mecule into the W8 cubes. This can be seen by comparingresults in Figs. 8~a! and 8~b!, which summarize the changein the OO distances in going from W8(D2d) and W8(S4) toW9(D1) and W9(S2a), respectively. The distortions argreater in the W9(S2a) cluster than in the W9(D1) cluster,consistent with the greater stability of the latter. This corlation between the amount of distortion of the cube andstability of the W9 isomer carries over to the other sevisomers.

Formally, the W9(D1) and W9(S1) clusters can be constructed by inserting a water molecule into the 1 positionthe corresponding W8 clusters~Fig. 6!. In analyzing the en-ergetic consequences of this insertion, one can view it atwo-step process in which a H-bond in the W8 structure isfirst broken in distorting the W8 cluster into the configurationit takes in the W9 isomer. In a second step, the two H-bonto the ninth water molecule are formed upon its insertionposition 1, the H-bond broken is an AAD→ADD(AAD5double acceptor/single donor; ADD5single


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acceptor/double donor! bond of the octamer. On-the-othehand, inserting a water molecule into the 2 or 3 positionsthe octamers requires breaking an ADD→AAD bond. Sincethe AAD→ADD bonds are appreciably stronger than tADD→AAD bonds, it is, at first sight, somewhat surprisinthat the nine W9 isomers are so close in energy. To addrethis issue, the inserted~9th! water molecule was deleted fromeach of the nine isomers, and single-point calculations wperformed on the resulting distorted W8 clusters. The result-ing energies are tabulated in Table IV. The distorted8clusters derived from the W9(D1) and W9(S1) species areindeed predicted to be about 7 kcal/mol less stable than thderived from the W9(D2), W9(S2), and W9(S3) clusters,for reasons just discussed. However, a compensating eoccurs when the additional H-bonds are formed upon instion of the ninth water molecule. In the W9(D1) and W9(S1)clusters the new H-bonds are AAD→AD and AD→ADD innature; in the other clusters they are ADD→AD andAD→AAD. The AAD→ADD, AD→ADD, and AAD→ADH-bonds are strong and comparable in strength (Ene

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FIG. 8. Calculated @Becke3LYP/6-311G(d)/6-31G(d)# minimum-energy structures for~a! W9(D1)and ~b! W9(S2a) H-bonded clusters. The labels on thoxygen atoms illustrate the numbering scheme usthroughout the text and tables. The signed numbersport the changes in OO distances that occur in the cuin going from the respectiveD2d or S4 symmetry W8

structures to theD1 or S2a W9 structures, respectivelyin angstroms. Only changes of greater than 0.005 Åshown for clarity.


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TABLE IV. Calculateda OH stretch frequencies~cm21!b and frequency shifts~cm21!c for the expanded-cube W9 isomers.

W9(D1) W9(S1) W9(S1a) W9(S2) W9(S2a)Freq. Shift Freq. Shift Freq. Shift Freq. Shift Freq. Shift

3811.5 22.4 3818.1 29.0 3811.5 22.4 3813.9 24.8 3814.7 253810.5 21.4 3815.1 26.0 3811.3 22.2 3809.9 20.8 3810.6 213809.5 20.4 3813.0 23.9 3808.2 19.1 3808.5 19.4 3808.7 193808.5 19.4 3808.9 19.8 3807.9 18.8 3807.4 18.3 3807.1 183805.7 16.6 3808.7 19.6 3804.4 15.3 3799.9 10.8 3802.9 133621.8 2167.3 3617.7 2171.4 3620.7 2168.4 3613.4 2175.7 3614.6 2174.53621.3 2167.8 3598.7 2190.4 3601.0 2188.1 3606.3 2182.8 3604.3 2184.83568.7 2220.4 3594.6 2194.5 3600.0 2189.1 3579.4 2209.7 3576.9 2212.23568.1 2221.0 3563.9 2225.2 3567.5 2221.6 3569.5 2219.6 3564.6 2224.53550.5 2238.6 3541.8 2247.3 3547.4 2241.7 3542.8 2246.3 3545.1 2244.03547.8 2241.3 3531.4 2257.7 3536.1 2253.0 3535.0 2254.1 3534.3 2254.83529.6 2259.5 3526.6 2262.5 3533.3 2255.8 3510.0 2279.1 3512.2 2276.93527.1 2262.0 3519.3 2269.8 3522.5 2266.6 3497.1 2292.0 3500.0 2289.13256.5 2532.6 3242.4 2546.7 3258.3 2530.8 3449.0 2340.1 3453.3 2335.83208.9 2580.2 3158.2 2630.9 3172.6 2616.5 3182.9 2606.2 3184.2 2604.93144.9 2644.2 3147.6 2641.5 3169.4 2619.7 3122.6 2666.5 3122.8 2666.33138.1 2651.0 3120.4 2668.7 3136.2 2652.9 3088.1 2701.0 3092.9 2696.23114.0 2675.1 3091.3 2697.8 3108.5 2680.6 3042.5 2746.6 3039.1 2750.0

W9(D2) W9(D2a) W9(S3) W9(S3a)Freq. Shift Freq. Shift Freq. Shift Freq. Shift

3814.2 25.1 3814.8 25.7 3814.8 25.7 3812.8 23.3813.0 23.9 3812.2 23.1 3811.7 22.6 3812.1 23.3808.2 19.1 3807.7 18.6 3807.5 18.4 3807.1 18.3805.4 16.3 3807.2 18.1 3805.9 16.8 3806.9 17.3799.8 10.7 3803.0 13.9 3803.7 14.6 3800.0 10.3617.7 2171.4 3616.4 2172.7 3610.8 2178.3 3613.2 2175.93610.2 2178.9 3611.3 2177.8 3603.0 2186.1 3603.3 2185.83581.9 2207.2 3578.9 2210.2 3592.9 2196.2 3591.4 2197.73567.1 2222.0 3563.7 2225.4 3568.2 2220.9 3570.5 2218.63540.7 2248.4 3542.5 2246.6 3535.5 2253.6 3538.8 2250.33526.1 2263.0 3528.6 2260.5 3522.0 2267.1 3525.4 2263.73509.0 2280.1 3513.1 2276.1 3511.1 2278.0 3515.3 2273.83495.9 2293.2 3499.4 2287.7 3500.2 2288.9 3495.5 2293.63447.2 2341.9 3451.5 2337.6 3453.2 2335.9 3446.4 2342.73185.2 2603.9 3188.4 2600.7 3141.1 2648.0 3159.8 2629.33124.2 2664.9 3127.9 2661.2 3137.8 2651.3 3152.5 2636.63082.4 2706.7 3086.9 2702.2 3087.7 2701.7 3078.1 2711.03050.3 2738.8 3046.7 2742.4 3062.1 2727.0 3055.0 2734.1

aResults obtained from Becke3LYP/6-311G(d) calculations.bUnscaled, harmonic frequencies.cFrequency shifts reported relative to the mean of the OH stretch symmetric and antisymmetric stretch frequencies at the same level of theory~3789.1 cm21!.

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'S), the ADD→AAD bonds are considerably weaker (E'W), and the AD→AAD and ADD→AD bonds are inter-mediate in strength (E'1). Thus insertion of a water molecule into site 1 of the W8 D2d or S4 cubes leads to anenergy changeDE(1)52S2S5S. The corresponding energy change for inserting a water molecule into the 2 opositions isDE(2 or 3)52I 2W. If I were exactly equal tothe average ofSandW, then the energy changesDE(2) andDE(3) would be equal toDE(1). Although ‘‘I’’ is not pre-cisely 0.5(S1W), this analysis explains why all ninexpanded-cube W9 isomers have similar energies despite tdifferent points of insertion in the W8 cube.

2. Calculated OH stretch infrared spectra of the W 9isomers

The OH stretch spectra of all nine of the expanded-cisomers were calculated with both the 6-311G(d)/


3

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6-31 G(d) and aug-cc-pVDZ basis sets. The two setsspectra are in close agreement, with an average discrepbetween the two sets of frequency shifts being aboutcm21. Consequently only results calculated with the smabasis set are reported here, again to facilitate comparwith the calculated results for the BW9 clusters. The resultsobtained with the larger basis set are available from thethors upon request.

The calculated OH stretch vibrational frequencies aassociated frequency shifts for the nine expanded cube9

isomers are reported in Table IV. The correspondingspectra are shown as stick diagrams in Fig. 9 for easy valization of the spectroscopic consequences of expandingcubes in different ways. The axial isomersS2a, D2a, andS3a have virtually indistinguishable IR spectra from theequatorial counterparts, and so are not included in Fig. 9Table IV explicitly.


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The OH stretch spectra of theD1 andS1 forms of W9

@Figs. 10~a! and 10~c!# closely resemble those of the W8clusters from which they are derived@Figs. 10~b! and 10~d!,respectively#. This reflects the smaller distortions associawith insertion of a ninth water in position ‘1’ rather thaelsewhere in the cube. The major difference betweencorresponding W8 and W9 spectra is the appearance ofadditional transition in the single-donor OH stretch regionthe W9 IR spectrum, marked by an AD in Figs. 10~b! and10~d!. The normal modes responsible for these transitionslocalized mainly on the inserted AD water monomer.

As one can see from Fig. 9, inserting the ninth wamolecule into the positions 2 or 3 of the W8 cube ~Fig. 6!produces much larger changes in the OH stretch spectraposition 1. This is consistent with the trends in the structudistortions discussed earlier. The most dramatic consequof insertion in positions 2 or 3 is that the AD single-dontransitions~Fig. 9! move up to near 3450 cm21, almost en-tering the double-donor region. The smaller frequency sof these transitions directly reflects the weaker AD→AADH-bonds formed by the AD molecule when inserted in potions 2 and 3, compared to the AD→ADD H-bond formedwhen inserting in position 1. In addition, the double-donOH stretch fundamentals of the isomers substituted in ptions 2 and 3 have their intensity spread over more trations and cover a wider frequency range than those sututed in position 1. The calculations predict, then, thatH-bonded AD stretch and double-donor regions providmeans of distinction between expanded-cube structuressubstitution occurring in position 1 vs those in 2 or 3.

Finally, the calculated IR spectra for the W9 isomersshow similar frequency and intensity profiles to those otained by Sadlejet al.10,29 using a model potential. This po

FIG. 9. DFT/Becke3LYP/6-311G(d) calculated OH stretch vibrational frequencies and infrared intensities of the nine lowest-energy isomers opanded cube W9.


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tential also predicted the W9(D1) isomer as the global minimum form of W9, and much of the structure in theobserved IR spectrum was assigned to this isomer, althopotential contributions of other conformations to the expemental spectrum was recognized.

3. Structures and binding energies of the BW 9isomers

Three isomers of BW9 have been identified based otheir unique UV and IR spectra. The RIDIR spectra ofthree isomers show the general characteristics of expancube structures. However, there are 45 unique BW9 struc-tures which can be formed by complexing benzene to anthe five free OH groups on nine expanded cube W9 struc-tures, making unique assignments of the observed spectindividual BW9 isomers a daunting task. The nomenclatuadopted for the benzene–~water!9 clusters builds on that usefor the W9 clusters, with the addition of a ‘‘B’’ preface toindicate the presence of the benzene molecule and an ‘‘Om’’suffix to give the numberm of the oxygen on the watemolecule~Fig. 12! that forms thep hydrogen bond to benzene, for example, BW9(S1a~O8!).

Geometry optimizations and vibrational frequency cculations, even with the smaller 6-311G(d)/6-31G(d) basisset, are very time consuming for a molecule the size of BW9,and for this reason only a subset~seven! of the possible 45expanded-cube BW9 isomers were examined theoreticallOne limiting possibility is that the three observed BW9 iso-mers arise from a single W9 isomer to which benzene i

FIG. 10. Stick diagrams of the calculated OH stretch vibrational frequenand intensities for~a! W8(D2d), ~b! W9(D1), ~c! W8(S4), and~d! W9(S1a)clusters. The close correspondence between the corresponding W8 and W9

frequencies and intensities is broken largely by the additional single-dotransition due to the ninth water molecule. The numbers in parenthesethe number of~near-degenerate! free OH stretch transitions in each clusteThe D-a and D-s designations stand for double-donor antisymmetric asymmetric stretch vibrations, respectively.

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attached at various positions. To test this possibility, fivethe seven isomers chosen for study are W9(D1) structureswhich differ only in their point of attachment to benzenThe other two isomers studied theoretically, BW9(S2a~O8!)and BW9(S1a~O8!), are representative examples of BW9

isomers built from the low energyS1a and S2a isomers,sharing a common attachment point to benzene~at C8!.

Table V lists the calculated relative energies and dipmoments for the seven BW9 isomers described above. Thtable also reports the changes in the dipole moments in gfrom W9 to the BW9 clusters. The five BW9(D1) isomershave a computed energy spread of only 0.35 kcal/mol~with-out vibrational ZPE corrections! with the energetically-favored attachment site being the free OH of W8 @Fig. 11~a!#which acts as a H-bond donor to the inserted~9th! watermolecule, and the least favored binding site being at theserted water molecule~O9!. The three positions which arremote from O9~namely, O5, O6, and O7! are intermediatebetween these two extremes. The changes in the dipolements in going from W9 to BW9 range from about20.8 D to11.2 D. This is consistent with a sizable polarization intaction between the benzene molecule and the water clu

The BW9(D1~O8!) and BW9(D1~O5!) species were alsoexamined at the Becke3LYP/aug-cc-pVDZ level of theoThe energy separation calculated between these two isowith this larger basis set is nearly identical to that calculawith the 6-311G(d)/6-31G(d) basis set~0.14 vs 0.17 kcal/mol!, lending further credence to the viability of the sma6-311G(d)/6-31G(d) basis set for accounting for the relative trends for the various expanded cube BW9 isomers.

Calculations on the BW9(S2a~O8!) and BW9(S1a~O8!)isomers probe the effect of benzene onS4-derived W9 struc-tures with the ninth water inserted in the two lowest-eneinsertion points~1 and 2! of W8(S4). The BW9(S2a) andBW9(S1a) structures predicted to be 0.24 and 0.37 kcal/mrespectively, less stable~again without vibrational ZPE corrections! than BW9(D1~O8!). Inclusion of ZPE correctionsdestabilizes these two isomers relative to BW9(D1~O8!) byan additional 0.1–0.2 kcal/mol.

The interaction of a benzene ring with the W9 clusterleads to significant changes in the oxygen–oxygen~and alsoOH! distances of the cluster. Figures 11~a! and 11~b! reportthe oxygen–oxygen distances that are changed by more

TABLE V. Calculated relative stabilities~kcal/mol! and dipole moments~D! of the seven expanded cube BW9 isomers studied theoretically.a

Structure Relative energya,bDipole

momentDipole moment

changec

BW9(D1~O8!) 0.00 ~0.04! 2.88 1.16BW9(D1~O5!) 0.17 ~0.17! 2.11 0.39BW9(D1~O7!) 0.17 ~0.17! 1.99 0.27BW9(D1~O6!) 0.17 ~0.18! 0.94 20.78BW9(S2a~O8!) 0.24 ~0.38! 2.92 1.02BW9(D1~O9!) 0.35 ~0.47! 2.70 0.98BW9(S1a~O8!) 0.37 ~0.47! 2.82 1.12

aAll results calculated at the Becke3LYP/6-311G(d) level. Numbers inparentheses include effects of vibrational zero-point energies.

bThe absolute binding energy of BW9(D1~O8!) is 2103.40 kcal/mol.cChange in dipole moment in going from W9 to BW9.


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0.005 Å in forming the BW9(D1~O8!) and BW9(S2a~O8!)isomers, respectively. Note that these changes are similamagnitude to those induced in the W8 cube by insertion of aninth water molecule. As was found in our studies of smaBWn clusters, the largest structural changes occur in thecinity of the water molecule to which benzene is attachThe nature of the distortions is similar to that in BW8,

27

shortening the donor H-bond, and lengthening the acceH-bonds to the water attached to benzene.

4. Calculated OH stretch infrared spectra of the BW 9isomers

The Becke3LYP/6-311G(d)/6-31G(d) OH stretch har-monic vibrational frequencies, frequency shifts, and IRtensities of the seven BW9 isomers described above are summarized in Table VI. The corresponding vibrational stispectra of these isomers are presented in Fig. 12 for compson with the experimental RIDIR spectra of Fig. 4. For tBW9(D1~O8!) and BW9(D1~O5!) isomers the vibrationaspectra were also calculated at the Becke3LYP/aug-cc-pV

FIG. 11. Calculated@Becke3LYP/6-311G(d)/6-31G(d)# minimum-energystructures for~a! BW9(D1(O8)) and ~b! BW9(S2a(O8)) clusters. Thesigned numbers report the changes in OO distance that occur upon comation of the W9 cluster to benzene in angstroms. Only changes of grethan 0.005 Å are shown for clarity.


3388


TABLE VI. Calculated OH stretch frequencies~cm21!, frequency shifts~cm21!, and intensitiesa of selected BW9 isomers.b

BW9(D1~O8!) BW9(D1~O9!) BW9(D1~O5!) BW9(D1~O6!) BW9(D1~O7!)

Freq. Shiftc Intensity Freq. Shiftc Intensity Freq. Shiftc Intensity Freq. Shiftc Intensity Freq. Shiftc Intensity

3814 25 53 3813 24 56 3814 25 58 3813 24 58 3812 23 63813 24 63 3813 24 62 3812 23 57 3811 22 67 3811 22 63810 21 69 3810 21 62 3811 22 67 3810 21 60 3810 21 53810 21 61 3808 19 61 3808 19 68 3807 18 67 3808 19 63736 253 254 3747 242 245 3746 243 242 3746 243 242 3748 241 2303622 2167 1123 3629 2160 1056 3630 2159 1045 3629 2160 1050 3628 2161 10173615 2174 1143 3616 2173 1162 3611 2178 1259 3613 2177 1246 3612 2177 12703570 2220 66 3575 2214 42 3574 2215 50 3575 2214 47 3571 2218 793569 2220 3 3566 2223 52 3564 2226 91 3565 2224 99 3560 2229 703551 2238 10 3558 2232 46 3558 2231 105 3556 2233 90 3557 2232 793531 2258 539 3540 2250 91 3532 2257 450 3532 2257 509 3532 2257 5743525 2264 229 3534 2256 409 3531 2259 134 3528 2262 119 3531 2258 933491 2298 381 3513 2276 418 3498 2291 390 3499 2290 404 3504 2285 3773304 2485 1053 3292 2497 1233 3256 2533 2238 3258 2531 2203 3260 2529 13693218 2571 3250 3193 2596 750d 3248 2541 1236 3548 2541 1188 3247 2542 22573160 2629 664 3192 2597 2343d 3176 2613 1266 3172 2617 1417 3169 2620 13553123 2666 15 3139 2650 8 3126 2663 110 3125 2664 80 3126 2663 133106 2683 86 3116 2673 6 3105 2684 223 3105 2684 185 3117 2672 108

3066 2723 537

BW9(S1a~O8!) BW9(S2a~O8!)

Freq. Shiftc Intensity Freq. Shiftc Intensity

3813 24 45 3815 26 753813 24 70 3813 24 553810 21 57 3811 22 673809 20 70 3809 20 583735 254 241 3737 252 2523619 2170 1103 3615 2174 9523602 2188 577 3601 2188 6923589 2200 908 3581 2208 3863566 2223 50 3563 2227 2653545 2244 311 3538 2251 2393534 2255 351 3522 2267 6573520 2269 175 3520 2269 643490 2299 368 3481 2309 3833304 2486 966 3421 2368 9283204 2585 1437 3181 2609 11873168 2621 1583 3160 2629 18863122 2667 591 3114 2675 1073095 2694 315 3044 2745 802

aIntensities in units of~km/mol!.bResults obtained at the Becke3LYP level of theory with the mixed 6-311G(d)/6-31G(d) basis set.cVibrational frequency shifts reported relative to the mean of symmetric and antisymmetric stretch frequencies at the same level of theory~3789.1 cm21!.dMixed OH/CH stretch mode.

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level. The OH stretch spectra calculated with this basisare very similar to those obtained with the smaller 6-1G(d)/6-31G(d) basis set. Several deductions candrawn from the calculated spectra.

~1! As can be seen from Table VI, the position of benzeattachment producesp H-bonded OH stretch transitionwhich are shifted about 10 cm21 further ~252 to 254cm21! in the O8 isomers than in the others~241 to244cm21 in O5, O6, O7, and O9!. The greater shift suggestthe presence of a somewhat strongerp H-bond in the O8position, consistent with BW9(D1~O8!) being the moststable of the five possible BW9D1 isomers.

~2! The presence of the attached benzene has little effec


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the double-donor transitions~Fig. 12, Table IX!, as onemight expect since benzene attachment necessarilycurs at the free OH of a single-donor molecule.

~3! The characteristic shifts of the AD H-bonded OH stretfrequency with position of water insertion noted earlifor W9 are retained in the presence of benzene. Thesingle-donor harmonic frequency for position 2 insertiin BW9(S2~O8!) @Fig. 12~g!# is over 100 cm21 higher infrequency than any of the six position 1 stick spec@Figs. 12~a!–12~f!#.

~4! Even within the position 1 isomers@Figs. 12~a!–12~f!#, itis the AD band that is still most sensitive to the positiof benzene attachment, giving a different look to t


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single-donor region depending on the relationshiptween the benzene molecule and the AD water. In theand O9 BW9 isomers, the AD band appears at somewhigher frequency@Figs. 12~d!–12~f!# than the othersingle-donor modes, thereby separating itself from thewhile for the O5, O6, and O7 isomers the AD band apears amidst the other single-donor modes@Figs. 12~a!–12~c!#. The O9 and O8 isomers have benzene attachmat or adjacent to the ninth water, while the O5, O6, aO7 isomers place benzene in a position remote fromThe similarity of the spectra of the O5–O7 isomersflects this remote position, suggesting that one need oconsider representative ‘‘remote-benzene’’isomerscomparing with experiment.

~5! The calculated OH stretch spectra of BW9(D1~O8!) bearan especially close resemblance to that of BW8(D2d), asillustrated in Figs. 5~c! and 5~d!. The two spectra differprimarily in that BW9(D1~O8!) has an ‘‘extra’’ single-donor transition ascribable to the inserted AD water mecule appearing on the high-frequency edge ofsingle-donor region. Thus, the addition of a ninth wamolecule in position 1 of W8(D2d) ~Fig. 6! has the leasteffect on the rest of the spectrum when benzene istached at the O8 water.

~6! The effect of benzene on the W9(S1) [email protected]~c! and 9~d!# is somewhat more substantial in formin

FIG. 12. Stick diagrams of the DFT calculated OH stretch vibrationalquencies and infrared intensities for~a! BW9(D1(O5)), ~b! BW9(D1(O6)),~c! BW9(D1(O7)), ~d! BW9(D1(O9)), ~e! BW9(D1(O8)), ~f!BW9(S2a(O8)), and~d! BW9(S1a(O8)).


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BW9(S1~O8!) @Fig. 12~e!#. The AD band remains in itscharacteristic position for insertion point 1. However, tpositions of the two strongest single-donor bandssplit further in the presence of benzene, and the weasingle-donor bands gain significantly in strength.

~7! The addition of benzene to W9(S2) retains the positionof the AD band near the double-donor [email protected]~g!#, but induces changes in the single-donor regionW9(S2) @Fig. 9~b!#. It would seem that the greater strutural distortion imposed on the cubic octamer by instion into position 2 is mirrored also in a greater sensitity of this structure to benzene attachment.

F. BW9 clusters: Comparison of theory andexperiment

The representative set of BW9 expanded-cube isomerexplored in the calculations are here used to make tentaassignments of the three BW9 isomers observed experimentally. One would anticipate that the observed structuwould be among those computed to be most stable. Hever, since the energy differences between the BW9 isomersare quite small, improvements in the theoretical treatmcould lead to reordering, warning against placing too gran emphasis on binding energies alone. In addition,could imagine that the kinetics of cluster growth might favcertain structures over others, a point to which we will retuin the discussion section.

As has already been highlighted in Fig. 5, the remaable resemblance of the RIDIR spectrum of isomer I wthat of BW8(D2d) makes a strong case for this BW9 isomerincorporating aD2d-derived expanded-cube W9 structure.With the calculations now in hand, we can more firmly asign isomer I as the BW9(D1~O8!) structure. In particular,the double-donor region of isomer I retains the same sinunresolved transition in the double-donor antisymmestretch region@D-a in Fig. 5~c!# which characterized anddistinguished the BW8(D2d) isomer from itsS4-symmetrycounterpart.27 Second, the single-donor transition of the Amolecule is clearly observed on the high frequency edgethe single donor region, while the rest of the single-dontransitions are similar in spacing and relative intensity tosingle-donor transitions in BW8(D2d). A comparison of thecomputed spectra of the five BW9(D1) isomers indicatesthat only the BW9(D1~O8!) isomer meets these criteria. Aleast for this isomer, then, the spectrum is unique enoughonly to assign the type of expanded-cube W9 structurepresent in isomer I, but also the position of attachmentbenzene.

Much less firm conclusions can be drawn for the strutures of isomers II and III. In both these cases, the RIDspectra are of somewhat poorer quality, hindering a classignment of the weaker transitions in the spectrum. Fthermore, the close proximity of transitions 3 and 4 leavopen the possibility that the 60

1 splittings of the two isomersoverlap in the ultraviolet spectrum, particularly in transitio4 ~isomer II!. However, this overlap would be small,present, and is not clearly evident in the RIDIR spectra oftwo isomers. As a result, we proceed here to make tentaassignments of isomers II and III. However, further expe

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mental and theoretical work is required before firm concsions can be drawn about these isomers.

Several features of the RIDIR spectrum of isomer@Fig. 4~b!# suggest an assignment as anS4-derivedexpanded-cube isomer, either BW9(S1) or BW9(S2). Thebroader, more highly structured double-donor region ofspectrum in Fig. 4~b! is consistent with anS4-derived ex-panded cube. In our previous studies of BW8,

3,27 the RIDIRspectra of the BW8(D2d) and BW8(S4) isomers were distin-guished largely on the basis of a splitting of the doubdonor antisymmetric stretch transitions in the latter spectr@see, for example, Fig. 10~c!# which appeared as a singleunresolved transition in BW8(D2d) @Fig. 10~a!#. In the spec-trum of isomer II of BW9 @Fig. 4~b!#, this portion of thespectrum is not a clear doublet, but is nevertheless distinbroader and contains more substructure thanBW9(D1(O8)) spectrum above it. Furthermore, thepH-bonded OH stretch appears at 3644 cm21, identical to thatin isomer I(BW9(D1(O8))), consistent with an O8 attachment point~Table IX!. Beyond this, two features of the spetrum argue more specifically for an assignment as BW9(S2).First, the band at 3422 cm21 is either a combination banbuilt off the single-donor region or the AD single-donstretch. If it is the latter, its location so close to the doubdonor region points toward a BW9(S2) structure @Fig.12~g!#. Second, the presence of a single-donor transitionlow as 2989 cm21 is also suggestive of BW9(S2), whosecalculated single-donor transitions are distinctly lower in fquency than for itsS1 or D1 counterparts~Fig. 12!. On theother hand, the single-donor region spans a wider rangea greater number of similar-intensity transitions than inBW9(D1) isomer, seemingly more consistent withBW9(S1) isomer@Figs. 12~f! and 12~g!#.

Isomer III is the minor isomer associated with transiti3 in the R2PI spectrum. While the RIDIR spectrum of thisomer lacks the clear identifying markers which could leto a firm assignment, several of its characteristics are mconsistent with a BW9(D1) isomer in which benzeneis attached at a remote position, such as BW9(D1(O5,O6, or O7)). First, the double-donor region of the RIDspectrum @Fig. 4~c!# is similar in appearance to thBW9(D1(O8)) isomer’s spectrum@Fig. 4~a!#, consistentwith a D1 isomer. Second, isomer III has a much largorigin-to-60

1 intensity ratio in the ultraviolet than the othetwo isomers~compare the intensity of transition 3, 4, andin Fig. 1 to those in Fig. 3!. This ratio has been used iprevious studies26 as an indication of the degree to which thsixfold degeneracy of the benzene ring has been brokencomplexation to Wn . A change in this ratio suggestsunique attachment point for benzene for isomer III. Thithe RIDIR spectrum shows ap H-bonded OH stretch at 364cm21, corresponding to a frequency shift 4 cm21 less thanfor isomers I and II~Table VII!. According to the calcula-tions, thep H-bonded OH stretch transitions of the remobenzene isomers are characteristically smaller than theresponding transitions for the O8 or O9 isomers. Finally,single-donor region is more compact in isomer III thanisomers I and II, suggesting that the AD water moleculsingle-donor stretch is moved down into the region where


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other single-donor bands exist, as calculated for the O5–isomers@Figs. 12~a!–12~c!#.

IV. DISCUSSION AND CONCLUSIONS

The present paper on the structural isomers of B9

builds directly on our recent assignment of UV and IR sptra of two BW8 isomers to theS4 andD2d symmetry, cubicW8 structures to which benzene is surface-attached viapH-bond.3,27 Given the unique structural stability of thescubes, their potential as building blocks for expanded-custructures is obvious. The ultraviolet transitions due to thBW9 isomers have been identified through R2PI-TOFMand UV-UV hole-burning spectroscopy with two being reshifted and the other being blue-shifted with respect toBW8 UV transitions. A comparison between experiment atheory has led to a firm assignment of isomer IBW9(D1(O8)); that is, as aD2d-derived BW9 structure inwhich the ninth water is inserted in position 1 with benzep H-bonded to the O8 water@Fig. 11~a!#. The two otherisomers are less easily assigned from their infrared speThe second major isomer~isomer II! shows many of thespectral characteristics expected for a BW9 (S1 or S2) struc-ture, while the minor isomer~isomer III! has some featurewhich suggest a BW9(D1) structure in which benzene iattached at a position remote from the ninth water molec~O5–O7!.

The present study highlights both the power and limitions of the RIDIR technique. In the cluster size regimeinterest here, an increasing number of different water clustructures exist with similar H-bonding topologies and tobinding energies. Techniques which are size-selective,not conformation-selective, produce infrared spectra whare the population-weighted sum of those from the contuting conformational isomers.10,29 In RIDIR spectroscopy,on the other hand, the dual mass- and wavelength-selectprovided by R2PI detection, selects out single conformatifor study so long as unique vibronic features for each specan be found and monitored in the R2PI spectrum. Howethe necessity for an ultraviolet chromophore in the clus~e.g., benzene! further increases the number of isomewhich can be formed, in the present case through the numof different ways by which benzene can attach to eachnstructure.

In a sense, it is quite remarkable that only three BW9

isomers are identified in the R2PI spectrum, given the fthat there are 45 expanded-cube BW9 minima which are ex-pected to be very close in energy. Clearly the expansioremarkably efficient at selecting for a few of these structurpresumably based largely on energetics. The factexpanded-cube BW9 structures are observed~and not thoseincorporating other three-dimensional W9 networks!, couldreflect not only the stability of these structures but alsodominance of cubic W8 structures in the expansion whiccan serve as precursors to the expanded-cube water noers. In this viewpoint, the tentative assignments of the tdominant isomers asD2d-derived~isomer I! andS4-derived~isomer II! expanded cubes is a logical extension of troughly equal populations of the W8(D2d) and W8(S4) clus-ters noted in our earlier studies of BW8.

27


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Benzene attaches to the W9 subcluster on its surface via p H-bond with a free OH group on W9. The fact that thebenzene molecule binds to W9 selectively at certain sitesuggests that benzene either samples these different sitesing cluster formation/cooling or is annealed into the loweenergy sites by subsequent two-body displacement collisfollowing initial attachment at a less strongly bound site.

Finally, it is worth commenting briefly on the potentiafor extending RIDIR studies to even larger BWn clusters.The incorporation of benzene into the cluster as an ultralet chromophore has been a useful device for studyingH-bonding topologies of the Wn subclusters with only mini-mal interference from the aromatic molecule used for sand conformation selection. However, binding of benzeneWn is via a weak, nonspecificp H-bond which can occur aessentially any free OH group in the cluster with little engetic differentiation. For such systems, even the dual mand wavelength-selectivity of the RIDIR technique is nearits limits at the present cluster size for recording IR specof single conformational isomers free from interference froone another. Aromatic molecules with H-bonding sites wreduce the number of structures by selecting for thosevolving the H-bonding site~s!, but the perturbations on thWn subcluster will be heightened as well. As a result, expmental studies of even larger BWn clusters will need to focuson broader-brush issues such as the types of cluster stures which are formed in a given size regime at the expeof a sure knowledge that the IR spectra are from a singleand conformation of cluster.

At the same time, the task of computing the structuand IR spectra of all possible isomers usingab initio or DFTmethods is also an increasingly daunting one. Recent deopments in semiempirical potentials~e.g., the EMP potentiaof Buch and co-workers10,29!, fast-multipole methods fordensity functional calculations,45 and linear scalinglocalized-orbital MP2 methods46 hold promise for extendingthe size range of the structures which can be studied thretically.

ACKNOWLEDGMENTS

We gratefully acknowledge the NSF for support of thresearch under Grants Nos. CHE-9728636 and CH9422210. C.J.G. gratefully acknowledges Lubrizol Corp.a graduate fellowship. The calculations were carried outthe HP Exemplar at NCSA and on the IBM 43P 260 coputers in the Laboratory for Molecular and Materials Simlations at the University of Pittsburgh and which wefunded by the NSF and IBM.

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