Water Tetramer, Pentamer, and Hexamer in Inert Matrices - The

Article pubs.acs.org/JPCA

Water Tetramer, Pentamer, and Hexamer in Inert Matrices J. Ceponkus,†,‡ P. Uvdal,†,§ and B. Nelander*,† †

MAX-IV Laboratory, Lund University, P.O. Box 118, SE-22100 Lund, Sweden Chemical Physics, Department of Chemistry, Lund University, P.O. Box 124, SE-22100 Lund, Sweden

§

ABSTRACT: The infrared spectrum of water, isolated in inert matrices, has been studied in the interval from 60 to 4000 cm−1. Experiments with partially deuterated water combined with DFT (density functional theory) calculations have been used to investigate the structure of matrix-isolated water tetramer. A few, strong intermolecular fundamentals of the water tetramer have been observed. Mid-infrared bands due to deuterated pentamers and hexamers have been observed and are used to discuss the assignments of these water clusters.

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INTRODUCTION The earliest observations of water monomer and small water aggregates were made by Pimentel and co-workers in their pioneering studies of the matrix isolation method.1 Early studies of the water monomer in noble gas matrices showed that it rotates almost freely in these matrices,2−13 suggesting that these matrices interact very weakly with trapped species. In the earliest papers on matrix-isolated water bands were assigned to monomer, dimer, and polymer.1,14 Ayers and Pullin15 assigned bands to trimers and tetramers but with question marks. Bentwood et al.16 removed the question marks on the trimer assignment and claimed that the trimer existed both as an open chain species and as a cyclic species. Engdahl and Nelander published a study of partially deuterated trimers, which showed clearly that the trimer in argon and krypton matrices is cyclic.17 Ab initio calculations find that the minimum energy structure of the trimer is cyclic but with inequivalent components.18 Experiments by Saykally and coworkers have shown that in the gas phase the trimer is a symmetric top.19 The free trimer tunnels so rapidly between the ab initio minima that the three water molecules are equivalent. This tunneling motion is called pseudorotation. The matrix-isolated trimer has recently been shown to undergo pseudorotation similar to what it does in the gas phase.20 Work by Saykally and co-workers in the far-infrared established that in the gas phase the water tetramer21 and pentamer22 are both cyclic while the hexamer has a “three-dimensional” structure (“cage”)23 in supersonic beam expansion experiments. The ab initio minimum of the cyclic pentamer has inequivalent components, but in the gas phase a rapid tunneling between equivalent minima averages out the differences, so the resulting spectrum is that of a symmetric top.22 Ab initio calculations have found at least four isomeric hexamers (cage, book, prism, and cyclic (S6 symmetry)) which differ slightly in energy of formation from six water molecules.18,24−27 The calculations © 2012 American Chemical Society

show that the differences in zero-point vibration energy between the different isomers are important for their relative stabilities. Calculation of the zero-point vibration energy in the harmonic approximation may be insufficient27 to give correct relative stabilities. The work by Lin et al.23 shows that the cage isomer is formed in supersonic beam experiments, at least at a very low temperature. Paul et al.28,29 and Nesbitt et al.30 measured infrared spectra in the OH and OD stretching regions of water clusters containing H2O or D2O in supersonic molecular beams. Bands have been assigned to dimers, trimers, tetramers, and pentamers. There is a band near 3220 cm−1 which Paul et al. assigned to hexamer. The OD stretching region is a scaled version of the OH region, and the 3220 cm−1 band shifts to 2395 cm−1. Nauta and Miller31 measured spectra of water clusters in helium droplets in the OH stretching region and noted the similarity between spectra in helium droplets and in the gas phase. There is a band near 3220 cm−1 which they assigned to the cage form of the hexamer in both cases. However, they found that the helium cluster spectra have an extra peak in the bound OH stretching region at a frequency slightly smaller than the bound OH stretch of the pentamer but at a significantly higher frequency than the bound OH stretch of the gas-phase hexamer. They assigned this peak to a cyclic hexamer, which is trapped in the helium droplets thanks to their very low temperature and sequential formation of water clusters in helium droplet experiments. Further work including ab initio calculations strengthened this assignment considerably.32 Spectra by Steinbach et al.33 of the OH stretching region of water hexamer in molecular beams at temperatures between 40 and 60 K give spectra which differ strongly from Received: February 15, 2012 Revised: April 25, 2012 Published: April 25, 2012 4842

dx.doi.org/10.1021/jp301521b | J. Phys. Chem. A 2012, 116, 4842−4850

The Journal of Physical Chemistry A

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hydrogens in an up, up, down, down pattern. It is much higher in energy (+3.9 kJ/mol) and is not expected it to be observable in our low-temperature samples. Therefore, only one isomer of water tetramer was considered in the further studies. The same B3LYP 6-311++G(3df,3pd) method was used to calculate harmonic vibrational frequencies of all possible water tetramer isotopologues. The harmonic approach always gives overestimated absolute vibrational frequencies, but for the assignment of the experimental bands it is more important to know relative band positions and their shifts upon isotopic substitution. For water dimers40 and trimers20 these appear to be accurately predicted by the B3LYP calculations. In fact, it seems easier to interpret the results from calculations in the harmonic approximation than to use direct anharmonic calculation, where the deviations between observed and calculated frequencies may have different signs for different isomers. The 30 vibration coordinates of the water tetramer can be divided into 12 intramolecular fundamentals and 18 intermolecular fundamentals. Each of the intramolecular monomer degrees of freedom form one A-symmetric fundamental (forbidden), one B-symmetric fundamental, and one doubly degenerate E-symmetric fundamental. The B-symmetric fundamental has its transition dipole moment orthogonal to the OOOO plane. The intensity of the B-symmetric component is therefore very low for the OHb vibrations, where the motion is approximately in the OOOO plane. For the E-symmetric doubly degenerate vibrations, the transition dipole moments are in the OOOO plane and are intense. In a reasonable approximation, the 18 intermolecular vibrations are combinations of the 12 individual water rotations and of 6 of the individual water translations. The overall translations and rotations of the tetramer are formed from the 6 remaining linearly independent combinations of individual water translations. The highest frequency intermolecular fundamentals are linear combinations of the librations of the water molecules around their free OH bonds. They have high frequencies since only a single hydrogen per molecule is involved in the motion and the hydrogen bonds are deformed. They give one Bsymmetric and one E-symmetric band, both strong since the hydrogens in part move orthogonal to the OOOO plane. In addition, there is a forbidden A-symmetric component. These vibrations are denoted OPB in Table 4. The next lowest fundamentals are formed from the water librations around the c axis (the inertia axis orthogonal to the HOO plane). They deform the hydrogen bonds and involve two hydrogens per water molecule. They are denoted IPB. The librations around the bound OH bonds give rise to four fundamentals, which we denote as torsions. Finally, 6 of the 12 translations give one outof-plane deformation of the OOOO ring (forbidden), one breathing motion of the ring (forbidden), one vibration where the OO distances between neighbors in the ring alternately stretch and compress (very weak), and a doubly degenerate vibration where the OO distances on opposite sides of the ring stretch and compress (allowed). The last one is likely to be the observed ring deformation.

those of Paul et al. and of Nesbitt et al. Steinbach et al. point out that the observed spectra are very similar to the calculated spectrum of the book isomer by Losada and Leutwyler.24 The latter authors24 also predicted that the book isomer should be the dominating hexamer above 26 K. Another water hexamer spectrum obtained with a different method by Diken et al.34 is very similar to that of Steinbach et al. Steinbach et al. therefore suggest that the temperature of the hexamer clusters of Diken et al. is in the same interval as they have used. Fajardo and Tam35 noted that the spectrum of water in parahydrogen (p-H2) at high water concentrations is very similar to the spectrum of water in helium droplets and has the same extra peak as the helium cluster spectra and concluded that cyclic water hexamer is present also in this matrix. The matrix spectra are in fact very similar to the gas-phase spectra obtained at very low temperatures. Losada and Leutwyler24 calculated infrared spectra of cyclic and three-dimensional water clusters and suggested that even weak bands not assigned previously may be assigned by a combination of experimental spectroscopy and ab initio calculations. Hirabayashi and Yamada continued this approach and measured spectra of water in argon, krypton, and xenon matrices.36,37 They recently observed a peak which they assign to a cyclic water hexamer in a neon matrix.38 There is one problem with this approach, which may be important. The water clusters with an odd number of water molecules are known to undergo a fast pseudorotation in the gas phase.19,22 There is evidence that also the matrix-isolated water trimer has this type of motion.20 In our opinion it is likely that the matrix does not stop the pentamer pseudorotation. Noble gas and parahydrogen matrices interact weakly with their guest molecules, and for instance, ammonia inversion39 and water dimer acceptor switching40 still go on in matrices. The calculated spectra have splittings corresponding to the low symmetry of the ab initio minima, which are averaged out by the pseudorotation. Therefore, the calculated spectra have splittings which are expected to be absent in the gas phase and probably also in matrix spectra. It is at present not easy to make calculations for the positions of the OHb stretches of the odd numbered water clusters, which takes into consideration the pseudorotation of the cluster. The best one can do is probably to calculate for structures constrained to be planar. For the water trimer it proved very useful to study partially or fully deuterated trimers in addition to the normal (H2O)3 and use comparisons with ab initio17 and DFT20 calculated spectra to assign the resulting spectra. Here we used this approach to explore larger water clusters, in particular, the tetramer. In addition, we measured far-infrared spectra, which make it possible to assign four or five intermolecular tetramer bands.

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CALCULATIONS The Gaussian 03 package and density functional method B3LYP41 were used for calculations of the water tetramer. The basis set 6-311++G(3df,3pd) was used along with the tight convergence criteria and an ultrafine grid for optimization of the ground state. In the calculated ground state the water tetramer is cyclic with the four oxygens almost in the same plane. Each water molecule has one bonded and one free hydrogen. The bonded hydrogens lie in the plane defined by the oxygen atoms. The most stable isomer of the water tetramer is the one with two of the free hydrogens above the OOOO plane and two below in an up, down, up, down pattern. The next isomer has the free

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EXPERIMENTAL SECTION The cryostat used in this work is a small immersion helium cryostat (IHC-3) from the Estonian Academy of Sciences (Dr. Ants Lômus), modified for matrix work. The cryostat can operate from approximately 2.5 to 300 K. The matrix is deposited on a gold-plated OFHC copper mirror (oxygen-free 4843



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A 6 μm beam splitter and a He-cooled bolometer were used to record spectra in the far-infrared region below 650 cm−1. Spectra of p-H2 matrices were recorded at 2.8 K. Neon matrix spectra were recorded at temperatures from 2.8 to 10 K. Spectra of argon matrices were recorded at temperatures between 4.5 and 30 K. When neon matrices were brought to 9−10 K or argon matrices were brought to 30 K the concentrations of trimers and, in particular, higher water aggregates increased significantly. This aided the assignment of their bands very significantly. We were less successful with diffusion experiments in p-H2, and therefore, fewer bands due to higher aggregates have been observed in p-H2.

high-conductivity copper). In order to allow the study of thick matrices, a 3 mm deep, 10 mm diameter cavity with a flat bottom is drilled in the center of the mirror. The mirror temperature is measured with a Lake Shore silicon diode. The temperature of the matrix mirror is stable within less than 0.1 K using feedback electronics. The outer shroud has a valve through which the depositions are performed. In order to reduce the heat load on the cryostat, the matrix gas is precooled with liquid nitrogen before entering the cryostat. The water is deposited from a separate volume and kept at 0 °C with ice− water, through a needle valve and a separate stainless steel tube parallel to the inlet tube for matrix gas. Two substance inlets are present; this makes it possible to perform experiments with H2O and D2O with only traces of HDO present. Before deposition, the valve on the shroud is opened and the deposition tubes are slid into the cryostat to a well-defined position ∼10 mm from the cavity in the mirror. After deposition, the tubes are withdrawn and the valve is closed. The outer shroud is rotated to place the appropriate IR window in front of the mirror. The cryostat is used here to study almost 3 mm thick p-H2 matrices with no particular difficulties. This set up makes it possible to record spectra over the entire infrared region for one deposition using interchangeable CsI and TPX windows (TPX is a transparent polymer used for far-infrared spectroscopy). The neon and p-H2 matrices were deposited at 3.6 K and the argon matrices at 17 K. The temperature of the matrix mirror was kept constant by adjusting the matrix gas flow. In this way the rate of deposition was kept constant. Approximately 100 mbar of matrix gas from a 10 L volume was deposited in about 1 h. The same deposition geometry was used for all experiments. Water was doubly distilled and degassed, and D2O (Norsk hydro 99.5%D) was degassed. Ne (L’Air Liquide 99.5%) was used as received. Equilibrium mixtures of H2O and D2O were used to obtain HDO. Argon (L’Air Liquid 99.9995%) was used as received. Hydrogen (AGA) was used as received. Infrared spectra of pure matrices showed the presence of traces of carbon dioxide and water. The para/ortho-hydrogen conversion was performed in a stainless steel tube. The bottom of the tube was filled with a paramagnetic catalyst (iron(III) oxide, catalyst grade, Aldrich Chemical Co.). The tube inlet was connected to a 10 L volume filled with the desired amount of normal hydrogen. The inlet and outlet of the tube are connected in such a way that the gas coming from the inlet has to pass the catalyst to reach the outlet. The tube was immersed in a liquid helium dewar, and the gas from the inlet volume was condensed on the catalyst. Hydrogen was kept condensed on the catalyst for close to 20 min. Then the catalyst was warmed to approximately 15 K by taking the tube just above the surface of the liquid He. The outlet from the conversion tube was collected in a separate volume. Spectra were recorded with a Bruker HR120 FTIR spectrometer at 0.1 cm−1 resolution in the mid-infrared spectrum and 1 cm−1 below 600 cm−1. The region between 60 and 150 cm−1 has several intense water monomer, dimer, and trimer bands, which may well hide bands due to larger water clusters. No such bands have been observed in the intervals between the monomer, the dimer, and the trimer bands. A Ge/KBr beam splitter and an MCT detector operating above 650 cm−1 (Judson) was used in the mid-infrared region.

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NOMENCLATURE The bound OH (OD) frequency of a water cluster is denoted by OHb (ODb) and the free OH (OD) frequencies by OHf (ODf). A tetramer formed from two different isotopomeric water molecules X and Y is denoted t-X2Y2 if both X form hydrogen bonds to Y and conversely both Y form hydrogen bonds with X. A tetramer built up from one X2 dimer and one Y2 dimer is denoted c-X2Y2.

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RESULTS AND DISCUSSION Our assignment of the OHb region in Ne, Ar, and p-H2 agrees with one exception (see below) with previous authors15,17,35−38 (Figure 1). The overall appearance of the ODb region in D2O

Figure 1. OHb region of a neon matrix at high water concentration. Lower blue “dotted” curve, initial spectrum at 2.8 K. Upper, red, full curve recorded at 2.8K after warming to 8K. (abs cm−1): Tr, trimer; Te, tetramer; P, pentamer; c-H, cyclic hexamer. H: hexamer.

experiments is a scaled version of the OHb region similar to what was seen by Paul et al.29 and by Nesbitt et al.30 in gasphase experiments (Figure 2). H2O and D2O assignments are collected in Table 1. The water clusters with three, four, and five water molecules are known to have cyclic equilibrium structures, and a cyclic hexamer is also known.31 Ab initio calculations for the clusters with an odd number of water molecules give asymmetric minima separated by low barriers, but in the gas phase, spectra show that both the trimer42 and the penatamer42 are symmetric tops, which means that the tunneling between the ab initio minima is fast. The tetramer has two symmetric minima separated by a significant barrier. The structure has S4 symmetry, and all four water molecules are equivalent. The chair form of the cyclic hexamer has a S6 symmetric minimum with equivalent water molecules.43 We have shown that the water trimer in inert matrices at low temperature has equivalent components,20 which means that the tunneling between the 4844



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Figure 3. Equilibrium structure of the water tetramer determined by DFT calculations.

Table 2. Calculated Fundamentals for (H216O)4 and (H218O)4a

Figure 2. The ODb region of a Ne matrix with a high D2O concentration. Lower blue, dashed curve, Initial spectrum. Upper red full curve, recorded at 2.8 K, after warming to 9 K. (abs, cm−1): Tr, trimer; Te, tetramer; P, pentamer; c-H, cyclic hexamer; H, hexamer.

minima is fast also for the trapped trimer. We have also shown that this is true also for trimers where an OHb stretch is excited. The excitation energy is delocalized over the three trimer components, and only a small rearrangement is needed when the trimer tunnels between its minima. As seen below, also the matrix-isolated pentamer appears to tunnel rapidly between its minima both in the ground state and in the OHb excited state. The ab initio minimum structure of the water tetramer has S4 symmetry (Figure 3). The intramolecular fundamentals then have one A-symmetric component which is inactive in the infrared spectrum, a B-symmetric component with a transition dipole moment orthogonal to the OOOO plane, and a pair of E-symmetric components with transition dipoles in the OOOO plane. Table 2 illustrates this for the calculated fundamentals of (H216O)4 and (H218O)4. The A-symmetric components are identified by their complete lack of intensity. The E-symmetric fundamentals appear in pairs and have substantial intensities. The B-symmetric fundamentals have very variable intensities. Note the very small intensity of the allowed B-symmetric component of the OHb stretches (3300−3500 cm−1); this is expected since the OHb bonds lie approximately in the OOOO plane. Experimentally we observe the OHb fundamental as a symmetric, smooth peak at 3383 cm−1 in Ne. The ODb

(H216O)4

(H218O)4

(H216O)4

(H218O)4

(H216O)4

(H218O)4

53.5 0.0 89.5 2.2 207.2 0.0 230.7 47.5 242.8 10.4 242.9 10.8 258.7 2.1 267.9 248.8 268.4 248.8 308.0 0.0

50.9 0.0 84.7 2.0 196.5 0.0 229.6 43.1 231.3 18.7 231.3 19.2 246.3 6.3 265.8 231.5 266.3 231.5 305.8 0.0

421.9 0.0 455.4 17.4 469.0 41.7 469.1 41.9 770.4 170.9 843.2 172.9 843.3 172.9 1009.9 0.0 1643.1 91.1 1656.0 51.2

420.4 0.0 455.2 17.6 466.9 45.2 466.9 45.3 767.6 168.7 841.5 171.1 841.6 171.1 1008.2 0.0 1636.3 90.1 1649.9 50.5

1656.0 51.2 1683.9 0.0 3345.3 0.0 3444.8 1478.0 3444.8 1478.0 3484.3 19.1 3874.5 83.3 3875.2 88.1 3875.2 87.8 3876.3 0.3

1649.9 50.5 1678.4 0.0 3334.5 0.0 3434.1 1474.2 3434.1 1474.2 3473.8 20.0 3861.9 80.6 3862.4 80.9 3862.4 80.6 3863.4 0.4

The upper entry gives the frequency in cm−1, and just below each frequency is given the intensity in km/mol in italics.

a

Table 1. Observed Mid-Infrared Bands of Tetramer (n = 4), Pentamer (n = 5), and Hexamer (n = 6; c-6 denotes cyclic hexamer)a (H2O)n Ne

Ar

3718.5 3467

3694.8 3471

3400(i) 3383

3445 3410 3392(sh) 3372

3345 3330(sh) 3224 3140

3330 3325 3290 3211 3140

(D2O)n p-H2

3415 3394(i) 3378

Ne

Ar

2745 2548 2542

2733 2543

2516

2509 2495 2488 2487 2486(i) 2461 2456 2426 2372 2326

3337 3320

2494.1 2492.1 2489.2 2470 2460

3219

2380.5

p-H2 2737

2492(i) 2491.2 2489(sh) 2465 2454 2377

1191.5 a

n

assignment

4 >4 >4 >4 >3 >4 4 4 4 5 c-6 >5 6 >6 4

OHf, ODf a a a a a OHb, ODb ODb ODb OHb, ODb OHb, ODb OHb, ODb OHb, ODb DOD bend

Code: i, inflection point; sh, shoulder; a, weak lines which grow rapidly in diffusion experiments. 4845



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fundamental of (D2O)4 is found at 2492 cm−1. It has the structure shown in Figure 4. This may be connected to the fact

(H216O)4 and (H218O)4 are small. Experimentally we observe an intense pair of bands at 689 c and 669 cm−1 (Figure 5 and

Figure 4. Bound OD stretch of (D2O)4: lower (blue) curve after deposition; upper (red) curve after warming to 9 K (neon matrix, 2.8 K, abs, cm−1).

Figure 5. Out-of-plane bend of (H2O)4. Neon matrix. Lower, blue dashed curve recorded at 2.8 K immediately after deposition. Upper, full red curve recorded after warming to 9 K and cooling back to 2.8 K. Increase in absorption in the interval from 740 to 770 cm−1 may be due to (H2O)5 and different isomers of (H2O)6 (abs, cm−1).

that the two degenerate components of the allowed ODb band are located in OD bonds across the ring. One component involves the ODb of one pair of D2O not bound to each other and the other component the ODb of the other pair of D2O. Even a very slight anisotropy of the trapping cage will therefore split the degeneracy. We note that the width of the ODb band of the tetramer is approximately as wide as the ODb stretches of (D2O)5 and c-(D2O)6 if we include the structure. The OHb band of (H2O)4 is 1.5 times wider than the OHb bands of (H2O)5 and c-(H2O)6. It is therefore possible that also OHb of (H2O)4 has a structure whose components are broader, so they coalesce into a single band. We note that the tunneling between the two equivalent minima in the vibrational ground state of the free tetramer is slow on the time scale of the matrix infrared measurements.21 We therefore do not expect any split due to this motion. The intermolecular fundamentals are formed from the librations (frustrated rotations) and translations of the cluster-forming water molecules. An intermolecular fundamental formed from librations will have approximately equal value in (H216O)4 and (H218O)4, while a fundamental with a significant translation component will shift depending on the weight of the translation component, at most approximately 12 cm−1. From experience with the water dimer and trimer, we expect the highest intermolecular fundamentals to be water librations. The four highest fundamentals are expected to be combinations of the four out-of-plane bends, where the water molecules librate around their free OH bonds; therefore, the motion is confined to the hydrogen atoms of the hydrogen bonds. The S4 symmetry dictates that they appear as one inactive A-symmetric component, one nondegenerate B component, and a doubly degenerate E-symmetric fundamental. Both the E-symmetric and the B-symmetric fundamentals are expected to have significant intensities since they involve motions of the permanent dipole moment of water and the hydrogen motion is expected to have components both in the OOOO plane and orthogonal to this plane. The relative intensities of the B- and E-symmetric fundamentals are determined by the angle between the free OH bonds and the OOOO plane. These frequencies are clearly seen in Table 2. The highest intermolecular fundamental at 1010 cm−1 is inactive. The next highest are the intense degenerate pair at 843 cm−1, and the lowest in this group is the intense nondegenerate 768 cm−1 frequency. The calculated isotope shifts between

Table 3. Intermolecular Bands of the Tetramera (H2O)4

(D2O)4

NeQ

Ne

Ar

p-H2

calcd

Ne

calcd

assignment

689 668 255 211.3 205

689 669 255 222.1 215.9

679 655 245 216.3

680 658 254 214 211

843 770 268 243

515 498 213.0

606 563 233 191

OPB OPB torsion O···O str.

148.2

165

Calcd: strong bands from DFT calculations (cm−1). Assignment see text. NeQ: (H218O in a neon matrix).

a

Table 3) with small 16O to 18O isotope shifts. The separation is significantly less than the calculated separation, and the lowfrequency component is more intense than the high-frequency component. The anharmonicities of these modes are expected to be large. We note that the doubly degenerate vibration involves motions in molecules which are not bound to each other, while in the nondegenerate mode all water molecules participate. This probably gives a larger anharmonic upshift of the nondegenerate mode compared to the degenerate mode. The corresponding bands of (D2O)4 are found at 515 and 498 cm−1 (Table 3). Here the high-frequency band is more intense than the low-frequency band. The change of the intensity ratio probably reflects differences in the vibrational averages of the angles between the OOOO plane and the OHf and ODf bond, respectively. The next lower group of intermolecular fundamentals is probably formed from in-plane bendings, where the water molecules librate around their c axis (the inertial axis orthogonal to their planes). In the calculated spectra these fundamentals are found between 400 and 500 cm−1 and their calculated intensities are small. They are expected in a region where dimer and trimer absorption makes it hard to observe weak tetramer bands. The lowest intermolecular fundamentals are expected to form from the 4 torsions, where the water molecules librate around their OHb and six of the 12 translations of the centers of mass of the water molecules. Six of the translations are expected 4846



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to combine to form the overall rotations and translations of the tetramer. For the intermolecular vibrations, the intensity has to come from the torsions and the isotope shifts between (H216O)4 and (H218O) 4 from the translations. In the calculations we note a fundamental at 308 cm−1 with no intensity and a small isotope shift; this is the totally symmetric torsion. Next is a very intense pair at 268 cm−1 with a small isotope shift. This is the degenerate pair from the torsions. We observe a band at 255 cm−1 without 16O to 18O isotope shift (Table 3), which we assign to this transition. Below this pair we calculate a nondegenerate band with low intensity at 259 cm−1. It has a substantial 16O to 18O shift. Below this we find a degenerate pair at 243 cm−1 with a slightly larger intensity and a 11.3 cm−1 16O to 18O shift. This should be the degenerate O···O stretching vibration mentioned above. We observe weak bands at 222.1 and 215.9 cm−1, which shift to 211.3 cm−1 and 205 cm−1 with 18O, which we assign to this fundamental (Table 3 and Figure 6). We believe that the calculated band has a smaller

Table 4. Calculated Isomerization Energies of Isotopomeric Tetramers (cm−1)a t-(H2O)2(D2O)2 → c-(H2O)2(D2O)2 t-(H2O)2(HDO)2 → c-(H2O)2(HDO)2 (H2O)3HOD → (H3O)3DOH (D2O)3HOD → (D2O)3DOH

−1.14 −0.28 −54.96 −55.43

a

Zero-point vibration energies were obtained from B3LYP calculations (see text).

positions, some of which are expected at higher frequency than the pure (H2O)5 or (D2O)5 frequency, it is difficult to assign those bands of partially deuterated tetramers, which are shifted to lower frequencies than the main band of (H2O)4 or (D2O)4. The number of isotopomeric tetramers is large, and calculations suggest that their OHb (ODb) frequencies appear in groups, with very small shifts between different members of a given group. It therefore impossible to make a detailed comparison between calculated and observed isotope shifts for the isotopomeric tetramers. We tried to simplify the observations by limiting us to two situations: low concentration of the minority isotope (H or D) and experiments with only H2O and D2O and almost no HDO present. In experiments with D2O contaminated with traces of H2O in equilibrium we observe a band at 3375.0 cm−1 (Ne) (Figure 7). The calculations indicate that a tetramer has to have at least

Figure 6. 16O to 18O shift of a tetramer far-infrared band. Lowest, black dashed curve: initial spectrum of an H218O experiment in a neon matrix at 2.8 K. Next lowest, dash-dotted blue curve: same experiment after warming to 9 K and cooling to 2.8 K. Next highest, dotted green curve: initial spectrum of a H216O experiment (2.8 K). Upper, full red curve: same experiment after warming to 9 K recorded at 2.8 K. Two 16 O curves have been shifted vertically by the same amount for clarity (neon matrix, abs, cm−1). Figure 7. Lower, red curve is the OHb region at low H2O concentration and high D2O concentration. Upper blue curve is a spectrum from an experiment with high H2O concentration, scaled and shifted for comparison. Note the shift of the lower curve (neon matrix, abs, cm−1; Te, tetramer; P, pentamer).

torsion component than the observed band. As is seen from the 268 cm−1 band even a modest contribution from the torsion can make a band quite intense. We also observed a few lowwavenumber (D2O)4 bands (Table 3). The 148.2 cm−1 band may correspond to the 137.8 cm−1 band observed in the gas phase.42 We measured spectra of matrices simultaneously containing H2O, HDO, and D2O. This type of experiment gave very useful data for the water trimer, where OHb and ODb frequencies of most isotopomers could be assigned.17,20 One notes that HDO as a donor in a dimer or in a trimer always forms a D bond. Calculations and (for the dimer) experiment indicate that the zero-point vibration energy of the H-bonded form is approximately 50 cm−1 higher than for the D-bonded isomer.44 We repeated the calculations for the tetramer and found similar results (Table 4). We therefore only have to consider Dbonding HDO in tetramers. The bound OHb (ODb) stretches of the water trimer are well separated from the bound OHb (ODb) of the dimer and the OHb (ODb) stretches of the tetramer. This made it possible to assign almost all bands of the partially deuterated trimers.17,20 The bound OH stretch of the cyclic pentamer (H2O)5 is found only 38 cm−1 below the corresponding band in (H2O)4. Since the pentamer also has a number of partially deuterated isotopomers with different band

one H2O in order to have a bound OH stretch, as HDO will always form a D bond. The calculations also suggest that the position of the bound OH stretch of (H2O)(HDO)p(D2O)3−p (p = 0, 1, 2, 3) does not depend on p; it is expected 13 cm−1 below the OHb stretch of (H2O)4. The band we observe is found 7 cm−1 below this band (Ne), and we therefore assign it to the OHb stretch of (H2O)(HDO)p(D2O)3−p. In experiments with H2O contaminated with traces of D2O in equilibrium we expect that the first ODb stretch to appear is due to (H2O)3HDO. We therefore assign a band at 2492.1 cm−1 (Ne), which we observe under these conditions, to this tetramer. Its position coincides with the ODb of (D2O)4, which is not present at the low D concentration of the matrix. From the calculations the (H2O)3HDO band is expected 5 cm−1 below the (D2O)4 band. A weak band at 2511.1 cm−1 is assigned to c-(HDO)2(H2O)2, 19 cm−1 above ODb of HDO(H2O)3; the calculated shift is 26 cm−1. For t(HDO)2(H2O)2 we calculate a shift of 13 cm−1. The resulting 4847



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of (D2O)5 give two approximately equally intense bands with widths close to 5 cm−1 and separated by 2.6 cm−1. An equally good fit is obtained with a single peak with a width of 6.5 cm−1. The distance between the pair of peaks of the fit is significantly less than expected from the ab initio calculations (9.6 cm−1). The width of the pentamer band is approximately equal to that of the cyclic hexamer, which is expected to have only one band in this region.24,43 These observations are compatible with rapid pentamer pseudorotation but do not completely exclude the existence of two peaks from a slowly pseudorotating pentamer. A rapidly pseudorotating pentamer will have only one OHb band, while if the pseudorotation is slow at least two bands are expected. Hirabayashi and Yamada38 claim that there is no cyclic hexamer in Ar and Kr matrices. We believe that the OHb (ODb) band of the cyclic hexamer may be hidden under the pentamer band in these matrices. At least in argon the pentamer band changes shape when the matrix is brought to a temperature where water diffusion occurs (30 K). Figure 8

peak may therefore be hidden in the slope of the (HDO)(H2O)3 band. We also did experiments with H2O and D2O, added to the matrix from separate nozzles. In this way we could minimize the HDO concentration and study dimers of composition (H2O)p(D2O)4−p. For (H2O)2(D2O)2 there are two isomers: one formed from a H2O−HOH dimer and a D2O−DOD dimer, c-(H2O)2(D2O)2, and another where both D2O bind to H2O and vice versa, t-(H2O)2(D2O)2. The calculations suggest that the zero-point vibration energies of these isomers differ by 1−2 cm−1 (Table 4). We can therefore assume a statistical distribution of mixed H2O−D2O tetramers. The assignments of the H2O−D2O experiments are collected in Table 5, which also Table 5. Observed and Calculated Shifts of OHb and ODb of (H2O)p(D2O)4−pa (H2O)2(D2O)2 H2O(D2O)3

cis

trans

(H2O)3D2O

obs

calcd

obs

calcd

obs

calcd

obs

calcd

3374 −9

3432 −13

3400 17

3465 20 3397 −48

3379 −4

3445 0 3418 (−27)

3402 19 3381 −2

2508 16 2494 2

2521 19 2502 0 2450 −52

2506 14

2515 13 2466 −36

2490 −2

2502 0 2478 (−24)

3472 27 3445 0 3374 −71 2490 −12

a The observed frequencies OHb and ODb are given under obs and the calculated frequencies under calcd. Directly below a frequency, the observed or calculated shift from OHb of (H2O)4 or ODb of (D2O)b is given. Values given in parentheses are shifts of forbidden transitions (neon matrix, cm−1).

Figure 8. ODb region in argon and neon matrices before and after diffusion. Neon matrix spectra are recorded at 2.8 K and argon matrix spectra at 4.5 K. Neon matrix was brought to 9 K and argon matrix to 30 K (abs, cm−1). Upper, black full curve: Ar matrix after diffusion. Second from top, green dashed curve: Ar matrix before diffusion. Third from top, red dash dotted curve: Ne matrix after diffusion. Lowest, blue dotted curve: Ne matrix before diffusion. T, tetramer; P, pentamer; c-H, cyclic hexamer; H, hexamer.

gives the calculated shifts for different isotopomeric tetramers. In mixed experiments, the pure (H 2 O) 4 and (D 2 O) 4 isotopomers are relatively rare and we observe small shifts of the dominating tetramer band. The observed position of the main peak in a given experiment is assigned to the mixed isotopomer, which is expected to give the largest contribution in this region. As is seen from the table, the observed shifts are in reasonable agreement with the shifts calculated for a cyclic tetramer. The isotope shift results clearly support the assumption that the matrix-isolated water tetramer is cyclic. The high values of the out-of-plane bendings of the hydrogen bonds, 689 and 669 cm−1 compared to 569.4 cm−1 for the trimer45 and 522.4 cm−1 for the dimer,46 show that the ring is significantly stiffer than the trimer ring. This gets further support from the high value of the ring deformation at 222 cm−1 compared to 170 cm−1 for the trimer.45 Only one, approximately symmetric OHb stretch is observed for the pentamer, (H2O)5. Ab initio calculations predict the existence of two approximately equally intense OHb separated by 9.6 cm−1;47 the remaining three OHb are expected to be very weak. The width of the pentamer band is 12 cm−1 (9.0 cm−1) in neon matrices and 10 cm−1 (6.6 cm−1) in p-H2 matrices ((D2O)5 in parentheses). In addition, the OHb band of the cyclic hexamer overlaps the low-frequency side of the pentamer band. Attempts to fit two Lorentz peaks to the pentamer peak

illustrates the change in the ODb region of an argon matrix. The corresponding change of a neon matrix brought to 9 K and back to 2.8 K is included for comparison. The shift of the pentamer peak suggests that it hides a peak of a higher cluster, which grows faster upon diffusion. The changes in the OHb region in Ar are similar. The assignment is collected in Table 1. The ratio of the OHb and ODb frequencies of a given cluster change from a relatively high value for the dimer to lower values for the trimer and tetramer. The pentamer, cyclic, and cage hexamer have closely similar ratios, Figure 9. This reflects the decreasing coupling between OHf and OHb as the hydrogen bond gets stronger. Gas-phase experiments have shown that the hexamer at 40 K predominantly exits as book isomer,33 with an absorption spectrum in the OHb region which differs significantly from the cage isomer (or prism isomer). We measured spectra of H2O in argon matrices at 30 K and then at 4.5 K, and they show no sign of isomerization. Possibly the barrier for isomerization is too high in the matrix. 4848



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(3) Glasel, J. A. Near-infrared absorption spectra of ortho- and paraH2O in solid xenon and argon. J. Chem. Phys. 1959, 33, 252. (4) Redington, R. L.; Milligan, D. E. Infrared spectroscopic evidence for the rotation of the water molecule in solid argon. J. Chem. Phys. 1962, 37, 2162. (5) Redington, R. L.; Milligan, D. E. Molecular rotation and orthopara nuclear spin conversion of water suspended in solid Ar, Kr, and Xe. J. Chem. Phys. 1963, 39, 1276. (6) Robinson, D. W. Spectra of matrix-isolated water in the “pure rotation” region. J. Chem. Phys. 1963, 39, 3430. (7) Knözinger, E.; Hoffmann, P.; Huth, M.; Kollhoff, H.; Langel, W.; Schrems, O.; Schuller, W. Intermolecular interactions in condensed matter. Microchim. Acta (Wien) 1987, III, 123. (8) Forney, D.; Jacox, M. E.; Thompson, W. E. The mid- and nearinfrared spectra of water and water dimer in solid neon. J. Mol. Spectrosc. 1993, 157, 479. (9) Fajardo, M. E.; Tam, S.; DeRose, M. E. Matrix isolation spectroscopy of H2O, D2O, and HDO in solid parahydrogen. J. Mol. Struct. 2004, 695−696, 111. (10) Michaut, X.; Vasserot, A.-M.; Abouaf-Marguin, L. Temperature and time effects on the rovibrational structure of fundamentals of H2O trapped in solid argon: hindered rotation and RTC satellite. Vib. Spectrosc. 2004, 34, 83. (11) Pardanaud, C.; Vasserot, A.-M.; Michaut, X.; Abouaf-Marguin, L. Observation of nuclear spin species conversion inside the 1593 cm−1 structure of H2O trapped in argon matrices: Nitrogen impurities and the H2O:N2 complex. J. Mol. Struct. 2008, 873, 181. (12) Abouaf-Marguin, L.; Vasserot, A.-M.; Pardanaut, C.; Michaut, X. Nuclear spin conversion of water diluted in solid argon at 4.2K: Environment and atmospheric impurities effects. Chem. Phys. Lett. 2007, 447, 232. (13) Abouaf-Marguin, L.; Vasserot, A.-M.; Pardanaut, C.; Michaut, X. Nuclear spin conversion in solid xenon at 4.2 K: A new assignment of ν2 rovibrational lines. Chem. Phys. Lett. 2009, 480, 82. (14) Tursi, A. J.; Nixon, E. R. Matrix isolation study of the water dimer in solid nitrogen. J. Chem. Phys. 1970, 52, 1521. (15) Ayers, G. P.; Pullin, A. D. E. The i. r. spectra of matrix isolated water species-I. Assignment of bands to (H2O)2, (D2O)2, and HDO dimer species in argon matrices. Spectrochim. Acta 1976, 32A, 1629. (16) Bentwood, R. M.; Barnes, A. J.; Orville-Thomas, W. J. Studies of intermolecular interactions by matrix isolation vibrational spectroscopy. J. Mol. Spectrosc. 1980, 84, 391. (17) Engdah, A.; Nelander, B. On the structure of the water trimer. A matrix isolation study. J. Chem. Phys. 1987, 86, 4831. (18) Xantheas, S. S.; Dunning, T. H., Jr. Ab initio studies of cyclic water clusters(H2O)n, n=1−6. I. Optimal structures and vibrational spectra. J. Chem. Phys. 1993, 99, 8774. (19) Keutsch, F. N.; Cruzan, J. D.; Saykally., R. J. The water trimer. Chem. Rev. 2003, 103, 2533. (20) Ceponkus, J.; Uvdal, P.; Nelander, B. On the structure of the matrix isolated water trimer. J. Chem. Phys. 2011, 134, 064309. (21) Cruzan, J. D.; Viant, M. R.; Brown, M. G.; Saykally, R. J. Teraherz laser vibrationrotation tunneling spectroscopy of the water tetramer. J. Phys. Chem. A 1997, 101, 9022. (22) Liu, K.; Brown, M. G.; Cruzan, J. D.; Saykally, R. J. Terahertz laser spectroscopy of the water pentamer: structure and hydrogen bond dynamics. J. Phys. Chem. A 1997, 101, 9011. (23) Liu, K.; Brown, M. G.; Saykally, R. J. Terahertz laser vibrationrotation tunneling spectroscopy and dipole moment of a cage form of the water hexamer. J. Phys. Chem. A 1997, 101, 8995. (24) Losada, M.; Leutwyler, S. Water hexamer clusters: structures, energies, and predicted mid-infrared spectra. J. Chem. Phys. 2002, 117, 2003. (25) Bates, D. M.; Tschumper, G. S. CCSD(T) complete basis set limit relative energies for the low-lying water hexamer structures. J. Phys. Chem. A 2009, 113, 3555. (26) Hincapie, G.; Acelas, N.; Castano, M.; David, J.; Restrepo, A. Structural studies of the water hexamer. J. Phys.Chem. A 2010, 114, 7809.

Figure 9. Frequency ratio OHb/ODb versus cluster size: (2) dimer,48 (3) trimer,20 (4) tetramer (this work), (5) pentamer (this work), (6) cyclic hexamer (this work), (7) cage hexamer (this work), (red circles) He matrix, (green squares) Ar matrix, (blue diamonds) p-H2.

■

CONCLUSION The H to D shifts of partially deuterated water tetramers support the assumption that the matrix-isolated tetramer is cyclic. The large upshift of the out-of-plane bend of the hydrogen bonds of the tetramer compared to the analogous band of the trimer indicates that the tetramer has a much stiffer structure. The hydrogen-bond stretching deformation of the tetramer ring is found close to 200 cm−1. The width of the bound OH stretch of the pentamer indicates that pseudorotation is rapid in the matrix-isolated pentamer, similar to the gas phase. Diffusion experiments indicate that the cyclic hexamer is present also in argon matrices as it is in parahydrogen and neon matrices.

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AUTHOR INFORMATION

Corresponding Author

*E-mail: [email protected]. Present Address ‡

Department of General Physics and Spectroscopy, University of Vilnius, Universiteto str 3, LT-01513, Vilnius, Lithuania. Notes

The authors declare no competing financial interest.

■

ACKNOWLEDGMENTS This work was made possible by a grant from the Trygger Foundation and the Swedish Research Council (VR). This work was carried out at the infrared beamline at Max I. The running cost of the beamline was paid for by a grant from VR. The generous help from the Max Lab staff is gratefully acknowledged.

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REFERENCES

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Water Tetramer, Pentamer, and Hexamer in Inert Matrices - The

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