The Water Trimer Frank N. Keutsch, † Jeffery D. Cruzan, † and Richard J. Saykally* Department of Chemistry, University of California, Berkeley, California 94720 Received November 25, 2002 Contents I. Introduction 2533 II. Theoretical Studies 2535 A. Bulk-Phase Simulations 2535 B. Structure and Energetics of Water Clusters 2535 1. Empirical Potentials 2536 2. Ab Initio/Empirical Potential Hybrid Calculations 2542 3. Ab Initio Calculations 2543 C. Dynamics 2550 1. Group Theory 2551 2. H-Bond Network Rearrangement (HBNR) 2552 3. Intramolecular Vibrations 2557 4. Intermolecular Vibrations 2558 III. Experimental Data 2558 A. Condensed-Phase Environments 2560 1. Matrix-Isolation Spectroscopy 2560 2. Inorganic Host Complexes 2561 3. Water Trimer in Liquid Helium Droplets 2561 B. Gas-Phase Spectroscopy of the Free Water Trimer 2561 1. Far-Infrared Vibration-Rotation-Tunneling (VRT) Spectroscopy 2561 2. IR Spectroscopy of the Free Water Trimer 2570 C. Gas-Phase Spectroscopy of Coordinated Water Trimers and Water Trimer Derivatives 2570 1. X‚W 3 : Coordinated Water Trimers 2571 2. W 2 X: Chemically Substituted Water Trimers 2572 3. Water Trimer Chains 2572 IV. Conclusions 2573 V. Abbreviations 2573 VI. Acknowledgments 2573 VII. Appendix: Summary of Tables 2573 VIII. References 2574 I. Introduction Non-pairwise-additive or cooperative intermolecu- lar forces may account for up to 25% of the cohesive energy of bulk-phase water, most of which result from three-body effects. 1 Because the isolated water trimer is not affected by higher-order nonadditive interac- tions, it is the obvious prototype for a detailed examination of the three-body forces operative in liquid water and ice, even though cyclic structures resembling the water trimer are not themselves an important constituent of liquid water and ice. Many sophisticated simulation efforts have shown that inclusion of non-pairwise-additive intermolecular forces is crucial in order to faithfully reproduce all of the enigmatic properties of water. Efforts to properly incorporate cooperativity into the model potential functions have recently been aided by a profusion of experimental data on gas-phase water clusters. 2 Ultimately, a major goal of this water cluster research is the determination of a “universal” intermolecular potential energy surface (IPS) that is both sufficiently accurate to reproduce the high- resolution cluster spectra and sufficiently general to yield reliable bulk-phase water simulations, wherein computational time constraints restrict the complex- ity that can be tolerated in a potential function. The early theoretical work of Frank and Wen 3 predicted that formation of a single hydrogen bond (H-bond) in liquid water should facilitate formation of additional adjacent H-bonds, and that the cohesive energy gained from H-bonding should be proportional to the number of adjacent H-bonds in a network. Although the detailed picture presented by those early authors has evolved substantially, there is modern consensus that liquid water exists as a continuously rearranging H-bonded network and that inclusion of many-body forces into the model poten- tials is necessary to arrive at a realistic simula- tion. 1,4-15 Indeed, it has recently been shown that energy ordering of the various possible equilibrium structures of water clusters larger than the pentamer (a quasiplanar ring) is strongly dependent upon inclusion of three-body forces in the model poten- tials. 16 The water trimer IPS can be broken down into a sum of two- and three-body interactions: where A, B, and C label the monomers, and V XY and V ABC are two- and three-body terms, respectively. More recent efforts have approached the problem of determining the water dimer IPS (V XY ) by comparing a variety of parametrized trial IPS’s to the dimer spectra and iteratively adjusting those parameters to achieve a faithful reproduction of the experimental data. Ultimately, convergence to the full experimen- tal precision (<0.001 cm -1 in some experiments) is * Corresponding author. Phone: (510) 642-8269. E-mail: saykally@uclink4.berkeley.edu. † Present address: Department of Chemistry and Chemical Biol- ogy, Harvard University, Cambridge, MA 02138. V trimer ) V AB + V BC + V AC + V ABC (1) 2533 Chem. Rev. 2003, 103, 2533-2577 10.1021/cr980125a CCC: $44.00 © 2003 American Chemical Society Published on Web 06/10/2003