Dynamics of Structural Rearrangements in the Water Trimer

The internal dynamics of the hydrogen bonding network of the water trimer are investigated by tunable far-infrared laser spectroscopy. New intermolecular vibrations have been measured at 87.1 [(HzO),] and 98.1 cm-’ [(DzO),]. Symmetry restrictions produce an exact oblate symmetric rotor pattern in the spectrum, even though theory predicts the trimer structure to be an asymmetric near-planar ring. In addition, each rovibrational transition is split into a quartet. A group theoretical treatment identifies two classes of structural rearrangements to account for these effects. There is considerable current interest in the spectroscopy and dynamics of small water clusters. Experimental and theoretical investigations of these species are motivated by the quest for a detailed understanding of the intermolecular forces and dynamics of the hydrogen bonding networks that operate in the condensed phases of water and in many biological systems. ’ Numerous spectroscopic? ab initio,3 and empirical studies4 have addressed the intermolecular dynamics and potential energy surface of the water dimer. A similarly detailed characterization of the water trimer will enable a quantitative comparison with the dimer that could contribute significantly to the understanding of macroscopic systems. For instance, comparison of the water dimer and trimer ab initio intermolecular potential energy surfaces (IPS) predicts that non-pairwise additive forces (“three-body” interactions that can occur in the trimer but not the dimer) contribute 10% of the total binding energy of the trimer. Other predicted “three-body” effects are shorter 0-0 distances and higher average intermolecular vibrational frequencies in the trimer than in the dimer. Similarities in internal dynamics of the dimer and trimer can suggest mechanisms for important processes, such as proton transfer, that occur in the condensed phases of water. Tunable far-infrared laser vibration-rotation-tunneling spectroscopy (FIRVRTS) has emerged as a powerful new tool for addressing such subjects. ’ Pugliano and Saykally’ (PLS) recently reported the first detailed experimental study of the cyclic water trimer. In that work, an intermolecular vibration of (DzO), was measured near 89.6 cm-1. This band displayed a strongly perturbed nearsymmetric top rotational pattern with each rovibrational transition split into a quartet. Crude estimates of the 0-0 distances were made by assuming three point masses of 20 amu and adjusting their separations for optimal agreement with the reported rotational constants. The spectral splittings were interpreted as resulting from isomerization tunneling among 96 identical frameworks (48 pairs of enatiomers) via three pathways: (1) “flipping” Aktract published in Aduance ACS Abstracts, March 1, 1994. (1) Saykally, R. J.; Blake, G. A. Science 1993, 259, 1570 and references therein. (2) Fraecr,G.T. Int.Reu. Phys. Chem. 1991,10,189andreferencestberein. ( 3 ) Smith, B. J.; Swanton, D. J.; Pople, J. A,; Scbaefer, H. F. , III; Radom, L. J. Chem. Phys. 1990, 92, 1240. Niesor, U. ; Corongin, G. ; Clementi, E. ; Kneller, G. ; Bbattacbaraya, D. J. Phys. Chem. 1990,94, 7949. (4) Reimen, J. R. ; Watts, R. 0. ; Klein, M. L. Chem. Phys. 1982,64,95 and references therein. Cieplak, P.; Kollman, P.; Lybrand, T. J. Chem. Phys. 1990,92,6755. Jorgensen, W. L. ; Chandrasekhar, J.; Madura, J.; Impey, R. ; Klein, M. J. Chem. Phys. 1983, 79, 926. Townsend, M. ; Morse, M. ; Rice, S . A. J. Chem. Phys. 1983, 79, 2496. ( 5 ) F’ugliano, N. ; Saykally, R. J. Science 1992, 257, 1937. OOO2-7863/94/1516-3507$04.50/0 of a single free hydrogen from one side of the ring to the other; (2) a motion that effectively results in a Cz rotation of a single monomer about its symmetry axis; and (3) a concerted motion that reverses the sense (yclockwise” or “counterclockwise” [cwH.s.0~) of the hydrogen bonding network around the ring. That work precipitated a number of sophisticated theoretical calculations of the trimer structure, vibrational frequencies, and interconversion tunneling dynamics.611 Of these, the calculations by Fowler and SchaefeI.6 are done at the highest level. All highlevel ab initio calculations agree that the lowest energy structure is that shown in Figure 1, and that the flipping motion is nearly free; moreover, all disagree with the crudely estimated 0-0 distances. Wales’’‘’ elegant treatment of the tunneling dynamics identified three low-energy reaction paths on the twelvedimensional IPS and estimated and associated splittings within a high barrier approximation. Schiitz et al.” carried out a detailed treatment of just the three flipping coordinates, giving special attention to the implications of the very low barrier to flipping. The highest-level ab initio calculations performed to date are those of Fowler and Schaefer.6 In this paper, we report the measurement of two new intermolecular vibrations of FIRVRTS. The Berkeley tunable far infrared spectrometer systems employed in this work have been described in detail elsewhere.13 A total of 284 VRT transitions rotationally assigned to a C-type band of (H2O)o and 57 transitionsassigned toan a-type bandof (DzO)3 weremeasured. The transitions of each isotopomer were fit to a symmetric top hamiltonian and the determined molecular constants are listed in Table 1. Portions of the (H2O)s and (D2O)s data are displayed in Figure 2.