Published: September 22, 2010 r2010 American Chemical Society 5774 dx.doi.org/10.1021/jp107595n | J. Phys. Chem. A 2011, 115, 5774–5784 ARTICLE pubs.acs.org/JPCA Calculated Nuclear Magnetic Resonance Parameters for Multiproton- Exchange and Nonbonded-Hydrogen Rotation Processes in Cyclic Water Clusters Hubert Cybulski and Joanna Sadlej* Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland b S Supporting Information ABSTRACT: In this work we report, for the first time, calcula- tions of nuclear magnetic resonance parameters for the processes of multiproton-exchange and nonbonded-proton rotations in small, cyclic water clusters. The simultaneous proton exchange induces a large decrease in the oxygen shielding constants in both clusters, with a mean value of -52.6 ppm for the water trimer and -50.1 ppm for the water tetramer. The 1(h) J OH coupling constant between an oxygen nucleus and exchanging proton decreases (in absolute value) along the path, changes sign, finally reaching a value of 5-7 Hz. The changes in the NMR parameters induced by the nonbonded proton rotations are smaller. The calculated dependencies of the intermolecular spin-spin coupling constants upon rotation reveal that the largest changes are expected for the couplings transmitted through the hydrogen bond between the rotating and neighboring molecule which acts as a proton donor. The symmetry-adapted perturbation theory (SAPT) interaction energy calculations for each dimer forming the water trimer have allowed us to relate a strength of interactions within pairs of water molecules with coupling constant values. The predicted maximal values of the interaction-energy terms (energetically unfavorable orientations of the constituent dimers) along paths correlate with the extremal values of the spin-spin coupling constants, which mostly correspond to the maximal couplings along pathways. I. INTRODUCTION Long-range proton transfer constitutes a key step not only in water but also in many biological reactions. 1,2 In most of these processes, water plays an important role in the transfer of protons. Cyclic water clusters are convenient models to study proton-exchange phenomenon, since they approach the descrip- tion of the environment of an “infinite” molecular chain. They are optimal to investigate concerted proton transfer avoiding the effects of ionic contributions in ionic water clusters. Because of their size, the most frequently investigated systems are the water trimer and tetramer. The literature data for the simplest cyclic (H 2 O) 3 cluster consists of numerous experimental and theoretical studies 3-9 such data for the water tetramer is less abundant. 10-15 The cyclic structures for both clusters, in which the monomers simultaneously act as proton donors and proton acceptors, have been identified as global minima. 16 Several theoretical approaches have been proposed to model and understand the environmental effects in liquid water on the nuclear magnetic resonace (NMR) parameters. Representative clusters of water molecules taken from molecular dynamics 17,18 or the Car-Parrinello method simulations 19-21 were used to calculate the 1 H and 17 O shielding constants, and the results seem to be promising. The calculated oxygen liquid shift is in qualitative agreement with experiment, although the results depend, e.g., on the chosen interatomic potential, method of averaging molecular properties, or on the cluster size. Besides, supermolecular calcula- tions for small water clusters have also been performed. 22-24 The enhancement of the cooperative effects with cluster size and changes in ligand environment results in decreasing 17 O shield- ing constants. A very large shift of -76.2 ppm has been predicted for the oxygen nucleus of the four-coordinated, central water molecule in the largest n = 17 cluster. 24 The indirect nuclear spin-spin coupling constants in water are less widely investi- gated than the shielding constants. Only a few studies have been devoted to the calculations of spin-spin coupling constants for small water clusters. 25,26 In the aforementioned studies, the influence of a proton transfer on the calculated NMR parameters was completely neglected. The methods based on molecular dynamics or Car-Parrinello method, where randomly chosen snapshots of molecules extracted from liquid water simulations were used to pre- dict molecular properties, or rigid water clusters from first- principles computational studies account for the deformation Special Issue: Victoria Buch Memorial Received: August 11, 2010 Revised: August 31, 2010