Faraduy Discuss. Chem. Soc., 1982, 73, 387-397 Vibrational Predissociation Spectra and Dynamics of SmalI Molecular Clusters of H20 and HF BY MATTHEW F. VERNON," JAMES M. LISY,? DOUGLAS J. KRAJNOVICH," ANDRZEJ TRAMER, $HU€-SING KWUK,S Y. RUN SHES 7 AND YUAN T. LEE * Materials and Molecular Research Division, Lawrence Berkeley Laboratory, University of California, Berkeley, California 94720, U.S.A. Receitvd 9th December, 1381 Experimental results are presented for the vibrational predissociation spectra in the frequency range 3000-4000 cm-I for the species (HF), and (H,O),, n = 2-6, using moIecuIar-beam techniques and a tunable infrared laser. The observed spectra show a dramatic change between the dimer and larger clusters which is thought to be a result of the cyclic structure of the trimer and larger clusters.The spectra are compared with calculated harmonic force constants of available intermolecular potentials to understand how these small, gas-phase dusters relate to the liquid and solid phases of HF and H,O. Additionally, the angular distributions of the predissociation products show that little energy appears as translational motion of the fragment molecules. This conclusion is consistent with recent theoretical rnodeIs of the predissociation process. An upper limit of ca. 2 p s is observed for the lifetime of the vibrationally excited clusters. Van der Waals (VDW) molecules have long been suggested as a well defined, accessible model for studying the spectroscopic and dynamicaI properties of condensed phases. Hydrogen-bonded liquids, in particular, have received much attention because of the noticeable spectroscopic changes which occur in the Iiquid and solid phases.' Despite the extensive study, little is known about the detailed electronic restructuring (potential-energy surface) which is responsible for the large red shifts and intensity changes associated with hydrogen bonding.' Until the physical mechanisms for these changes are known, it will be difficult to parameterize analytical model potentials in an accurate and economical way.Tndeed, most potential models proposed to date consist of simpIe atom-atom interactions which rarely predict more than one property correctly over a substantial range of conditions.2 The experimental results presented below were obtained in an attempt to understand the rate at which the bulk-phase spectroscopic behaviour is approached for these two molecules.* Also associated with the Department of Chemistry, University of California, Berkeley, Cali- t Permanent address: School of Chemical Sciences, University of Illinois, 505 South Mathews 1 Permanent address : Laboratory of Molecular Photophysics, CNRS, Universite Paris-Sud, 5 Permanent address: Department of Electrical Engineering, State University of New York, 'r Also associated with the Department of Physics, University of California, Berkeley, California, fornia, U.S.A. Avenue, Urbana, Illinois 61801, U.S.A. 91405 Orsay, France. Buffalo, New York 14226, USA. U S A .388 DYNAMICS OF SMALL MOLECULAR CLUSTERS EXPERIMENTAL The (HzO), and (HF),, clusters are formed in an adiabatic expansion using neat or rare- gas mixtures of HF and HIO.The infrared radiation is obtained from a Nd : YAG pumped LiNb03 optical parametric oscillator (OPO) based on the L-shaped cavity design of B ~ e r . ~ For the frequency range 3000-4000 cm-’, the pulse energy is 1-4 mS with a pump energy fluence of 1 J cm’z, and the linewidth (f.w.h.m.) varies from 3 to 4 cm-I. The predissociation of the clusters is detected in two different configurations using a mass spectrometer. PERP END I C U LAR LASER- MOL E C U LA R - B EA M ARRANGEMENT Fig. 1 shows an in-plane view of this experimental configuration. The vibrational pre- dissociation is observed by monitoring the appearance of the predissociation fragments. FIG. 1 .--In-plane view of perpendicular laser-molecular-beam apparatus.Labelled components are: (1) 0.007 in, diameter quartz nozzle heated to 125 C, (2) first skimmer, (3) second skimmer, (4) third skimmer, ( 5 ) power meter, (6) germanium filter, (7) ionizer assembly, (8) quadrupoIe mass spectro- meter. 0 measures the angle of rotation of the detector from the molecular beam. The electron bombardment ionizer-mass spectrometer assembly rotates on a 20 cm radius circle about the intersection point of the laser and molecular beams. The defining apertures in the mass spectiometer limit the detector’s line of sight to a 3 mm x 3 rnm region at the intersection point. Clusters that predissociate before travelling beyond this viewing region (nominal residence time is 2 ps) and whose fragments recoil into the detector are detected as an increase in the ion signal at the masses characteristic of the cluster predissociation fragments.The predissociation signals are collected by a muItichanne1 scaler triggered by the laser pulse and accumulated for 2000-10000 laser pulses. The laser power is monitored by a power meter placed after the intersection region. The power dependence of the signal is measured to ensure that the predissociation yield is linear with photon number. The angular distri- bution of the predissociation fragments is used to determine the translational energy distribu- tion of the product molecule^.^M. F. V E R N O N ~ ~ al. 389 C O A X I A L LASER-MOLECULAR-BEAM ARRANGEMENT A cross-sectional view of this apparatus is shown in fig.2 . Here, the laser and molecular beams are superimposed while the mass spectrometer monitors the molecular beam. Vib- rational predissociation is observed as depletion in the signal of the parent cluster mass. FIG. 2.-Side view of the coaxial laser-molecular-beam apparatus. Labelled components are: (1) BaFz entrance window for the OPO beam, (2) quadrupole mass spectrometer, (3) ionizer assembly, (4) final molecular-beam-defining aperture, ( 5 ) second skimmer, (6) first skimmer, (7) nozzle. Compared with the perpendicular arrangement, this method has thirty times the interaction volume between the laser and molecular beams, and detects all predissociation events, in contrast to the small fraction sampled by the perpendicular arrangement. The increase in the detectable signal (ca.lo6) permits the use of 1 .O-0.1 % seeded beam ratios (HF or H,O in a He or Ar carrier) and faster data acquisition. However, it cannot supply angular distribution information. RESULTS Vibrational predissociation spectra of (H20), and (HF), are displayed in fig. 3-6. The angular dependence of the (H20),, predissociation fragments is shown in fig. 7. Similar results were obtained for (HF),t. The narrow angular range of the products (0 < 10') indicates that little of the excess energy appears as product translation. The steep monotonic decrease in the angular data with increasing laboratory angle can only be fitted by a product translational energy distribution which peaks at or near zero degrees. The excess energy thus remaining after the cluster dissociates must be in the internal degrees of freedom of the fragments.For energetic reasons * the dominant predissociation channel for both (HF), and (H20),, is thought to be (H20)n + Iiv --+ (H20)n--1+ H20 (HF), + hv --f (HF)n-, + HF (1) (2) since this is consistent with the observed independence of the shape of the angular distribution with OPO frequency. The electron bombardment ionization cam- * Calculations of the dissociation energy, D,, of water clusters using a variety of intermolecular Dissociation into non-monomeric potentials indicate that this process [eqn (l)] is always allowed. products is not allowed over the complete frequency range probed for these same potentials.390 D Y N A M I C S OF SMALL MOLECULAR CLUSTERS 1.c 0 * 5 0 .0 1 . a 7 0 . 0 C M ._ ul 1 . 0 0.5 0 . o 1 . o 0.5 . (el 0 .o 3000 3200 3400 36003800 3000 3200 3400 3600 3800 f'requency/cm - FIG. 3.-Water-cluster and condensed-phase spectra. Panels (a)-(e) are spectra observed in the present work. (a) (H20)3, (b) (H20j4, (c.) (H20j5, (4 ( H z ~ ) ~ , ( P ) (HzO)~, ( f ) NZ matrix, ( g ) liquid, ( h ) solid. plicates the assignment of the signal observed at il particular mass peak to a specific cluster. The dominant ionization channel is most probably (H20),, +-- e- -+ (H,O),-,H+ -1 OH $- 2e- (3) (HF), - I - e- 3 (NF),-,H-+ + F -1 2e-. (4) However, the channels (H20), 4- e- -+ (H,O),,-,-H + 1.- . . . (HF),, + e- + (HF),l-,n- Ht + . , .M . F . V E R N O N ~ ~ al. 39 1 with rn > 1 are also observed to occur. Fig. 3 (a) and (e) show two frequency scans at the H30+ mass under two different source conditions.The changes observed for the two different cluster distributions are a result of the larger cluster predissociation fragments from process (1) ionizing by channel (5) with m > 1. In cases where 3 500 3600 3700 frequency /cm - FIG. 4.-Vibrational predissociation spectra of (H20)2 and (H20)3 obtained by the coaxial method. several clusters absorb at the same frequency, varying the source pressure and seeding ratios and recording the spectra at many masses can distinguish the bands belonging to different polymers. DISCUSSION From the data displayed in fig. 3-6 it is obvious that the dimer species (H,O), and (HF), are substantially different compared with the larger clusters. Molecular-beam electric resonance spectroscopy has established the ground vibrational state structures of (H20), and (HF)2.6 The three (HF), bands are assigned to the HF stretch of the hydrogen-bonded proton (3720 cm-'), the HF stretch of the " free " proton (3878 cm-l), and a combination band involving an intra- and inter-molecular vibration (3970 cm-l).The (H,O), bands are similarly assigned to free (3715, 3625 cm-') and hydrogen-bonded (3596, 3524 cm-') protons. The bands at 3715 and 3500 cm-' are also seen in the spectra of larger water clusters. Their presence at the dimer parent mass could be due to the larger neutral cluster ionizing via eqn (5). More detailed studies will be necessary to measure unambiguously the complete (H20), spectra in this region. The (HF), and (H20),*, n = 3-6, clusters exhibit a strong, broad, red-shifted band structure which is assigned to the hydrogen-bonded protons.The lack of any absorption peaks above 3500 cm-l for the (HF),, n = 3-6, clusters indicates the absence of a terminal - - H-F or - * * F-H molecule. Consequently, these larger clusters must be cyclic. Similarly, the absence of a band at 3596 cm-I for the larger392 10 a 6 4 m 2 A Y .- 5 .E 0 c 10 8 6 4 2 0 DYNAMICS OF SMALL MOLECULAR CLUSTERS 3100 3200 3300 3400 3500 water clusters is consistent with a cyclic geometry for these clusters. The sharp, narrow peak at 37 I5 cm-' is assigned to the " free " hydrogens which point away from the ring. Typical minimum energy water polymer structures predicted by available intermolecular potentials are shown in fig.8 and agree with this assignment of the observed spectra. Molecular-beam deflection experiments for the larger (HF), and (H20),t clusters indicate small to undetectable dipole moments for these species, as wouId be expected for cyclic structures. The band structure of the hydrogen-bonded absorption seems to be best described as a progression of combination bands. The equation 4- t d n t e r ? m = 0,lJ (7) V ~ b s - Vintra where vintra is the fundamental frequency of the hydrogen-bonded intramolecular H-F(H0) stretching motion, Per is a frequency of the intermolecular F * - - HFM . F. VERNON et al. 393 H 10- I 8- -I I-Av tr 4 - 2 - 0 I 3700 3800 3900 .4( frequcncy/cni - 1 O l 1 30 FIG. 6.--Vibrational predissociation spectrum of (HF)2 corrected and normalized for the photon number, with the structure of (HF)2 as determined by tnolecular*-beatn electric resonance spectroscopy.10 9 8 7 6 5 4 3 s 2 -% E: on .& vl .N, 10 2 9 5 6 5 5 4 3 2 5 ; 1 \ \ I 0 1 3 4 5 6 7 8 9 labor at ory angle /" FIG. 7.--Laboratory angular distributions for the detected mass: 0, H,O' ; I-, (HzO)ZH+ ; u, ( H ~ w ; a, ( H ~ ~ ) ~ H + .394 DYNAMICS OF SMALL MOLECULAR CLUSTERS FIG. 8.-Minimum energy cluster geometries for the Watts potential energy function (a,b,d,e,f), for the polarization model trimer (c), and for the configuration characterizing a transition state for the tetramer aissociating into a trimer and a monomer (g). (0 - HO) hydrogen bond, and vobs is the frequency of the observed bands, is con- sistent with the more advanced treatments of hydrogen bonding.For the (HF)n series, the decrease of vintra and increase of vinter with increasing cluster size is in accordance with progressively weaker intramolecular bonds and stronger inter- molecular bonds in the larger clusters. The question arises as to why the hydrogen-bonded protons of the cyclic structure are so red-shifted compared with the dimer species. Since the dimer absorptions are characteristic of the pair-interaction potential, it might be a consequence of the changeM. F . VERNON etal. 395 in the reduced mass of the proton motions in the cyclic as opposed to the open dimer configuration. To investigate this possibility, the harmonic vibrational frequencies at the minimum energy configurations of the (H20)n polymers were calculated using 3 widely used potentials.? -9 The harmonic frequencies of the polymer vibrations were multiplied by a constant chosen to bring the calculated monomer vibrational frequencies into close agreement with the known vibrational frequencies of H,O.This was meant to serve as a crude correction factor for anharmonicity. The best agreement in all cases was from the Watts potential,' which uses the known gas-phase H,O anharmonic vibrational potential to describe the intramolecular forces. The polarization * and central force9 models of Stillinger do not predict the appropriate tight grouping of the free OH peaks, and also indicate blue shifts relative to the monomer. These discrepancies are expected since no particular attention was paid to predicting the high-frequency proton vibrations.The Watts potential predicts the observed dimer spectra quite accurately given the approximations of the normal-mode treatment and the type of data used to derive the intramolecular potential, namely second virial coefficients and solid-state nearest-neighbour distances. When this pair potential is applied to larger clusters, the calculated spectra show two band groups : the free and hydrogen-bonded protons. The calculated frequencies of the larger clusters are more commensurate with the observed and calculated dimer bands than the red shifts observed in the larger clusters. We conclude that the pair potential cannot account for the red shifts, which must then be a result of non-additive interactions.When an OH group is involved in both donating and accepting a hydrogen atom for hydrogen bonding, the electronic structure of that OH bond is significantly perturbed beyond that accountabIe for by pair interactions. An interesting implication of our assignments is how they suggest that past explanations for the infrared structure of liquid water are in error." The basic con- clusion of these previous studies was to assign each observed (or deduced) band to a different local environment. The present work, along with theoretical treatments by Rice and Sceats,l' Marechal and o t h e r ~ , ' ~ suggests that the broad-band structure is intrinsic to the hydrogen bond. Recent studies by Byer et aI.l4 on the depolariza- tion CARS spectra of liquid water have shown similar structure in the wavelength region of this study.Two aspects of the predissociation dynamics were also observed in our experi- ments, an upper limit to the vibrational predissociation lifetime of the cluster, and the partitioning of energy between translational and internal degrees of freedom of the predissociation products. The lifetime was determined by our observations of pre- dissociation (in collision-free conditions) in the perpendicular beam arrangement, and the agreement obtained between spectra measured by the two experimental configurations. Although the information from the product angular distribution is limited, it is possible to understand why little energy appears as translation and why the shape of the angular distributions are independent of the photon energy for the range probed (9- 10.5 kcal).Calculations were performed of the locally adiabatic predissociation (LDP) paths using the Watts potential for the dirner, trimer and tetrarner, as shown in fig. 9. The dimer path is straightforward, and simiIar to a diatomic molecuIe dissociation. The trimer path indicates a two step process. First, the separation of two oxygen atoms from ca. 2.75-5.50 A breaks the cyclic structure to form an open chain, then a terminal monomer molecule dissociates with a curve similar to the dimer. The tetramer indicates more exotic behaviour depending on the order with which the water mole- cules are separated. This is a result of numerous local minima on the potential396 D Y N A M I C S OF SMALL MOLECULAR CLUSTERS 0 .0 -5 -1 0 3 2 2 -15 t! C -20 -25 -30 1 1 1 1 1 1 1 1 1 1 , 2 4 6 8 10 12 14 0-0 separation/A FIG. 9.-Locally adiabatic dissociation energy curves for (A) (H20)2-+2H20, (B) (H20)3+(H20)2 + H20, (C) (H20)4+(H,0)3 + H 2 0 when adjacent hydrogen-bonded waters are separated, (D) (HzO)4t (H20), 4- H20 when it is formed from a monomer adding to a cyclic trimer, (E) (H20)r-+(H20)3 + H20 when opposing non-hydrogen-bonded water molecules of the cyclic tetramer are separated. surface. (The LDP were generated by small sequential displacements of ca. 0.2 8, of the oxygen-oxygen distance, so the curves do not represent global minima.) These paths indicate that the geometry of the cluster when it dissociates is far removed from the equilibrium configuration of the separated products.Many low- frequency vibrational motions will be excited in the cluster fragments left in these extended orientations. This would explain why little energy appears in translation, and why the product energy distribution should not depend dramatically on which motions are excited by the photon. CONCLUSIONS A preliminary study of the fundamental hydrogen-atom vibrations in small clusters of HF and H,O has indicated that the key to understanding the origins of the spectral changes induced by hydrogen bonding is in the differences between the dimer and larger clusters. Accurate quantum-mechanical calculations of the electronic structure should be possible for these systems. These new results will then enable more accurate analytical potential functions suitable for modelling solution behaviour.The predissociation lifetime (c: 2 j i s ) and energy partitioning among the product degrees of freedom were also obtained. The large geometry changes that the trimer and larger clusters must undergo during dissociation appear to explain the small amount of energy released in translation and the insensitivity of this product energy to the photon energy in these experiments, Future experiments on isotopically substituted clusters should further the under- standing of the dynamic coupling present in these clusters. A study of the behaviourM . F . V E R N O N ~ ~ ~ ~ . 397 of large clusters should also indicate whether it is possible to increase the cluster’s heat capacity t o the range where the predissociation can be measured in real time, if indeed the energy is substantially redistributed within the cluster before dissociation.This work was supported by the Assistant Secretary for Nuclear Energy, Ofice of Advanced Systems and Nuclear Projects, Advanced Isotope Separation Division, U .S. Department of Energy under contract no. W-7405-Eng-48. For a recent review, see The Hydrogen Bond, ed. P. Schuster, G. ZundeI and C. Sandorfy (North Holland, Amsterdam, 1976). 1. R. McDonald and M. Klein, Faraday Discuss. Chem. Soc., 1978, 66, 48. S. Rrosrian and R. Byer, fEEE J. Quantum Electron., 1979, QE-15, 415. M. F. Vernon, J. M. Lisy, H. S. Kwok, D. J. Krajnovich, A. Tramer, Y . R. Shen and Y . T. Lee, J. Phys. Chem., 1981, 85, 3327. (a) T. Dyke, K. Mack and J. S. Muenter, J. Chenr. Phys., 1977, 66, 498; (b) T. Dyke and J. S. 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