Structure and Stability of Water Clusters

Structure and Stability of Water Clusters (H₂O)n, n= 8-20: An Ab Initio Investigation

Shruti Maheshwary, Nitin Patel, and Narayanasami Sathyamurthy Department of Chemistry, Indian Institute of Technology, Kanpur, 208 016 India Anant D. Kulkarni and Shridhar R. Gadre Department of Chemistry, UniVersity of Pune, Pune, 411 007 India ReceiVed: August 15, 2001

Extensive ab initio calculations have been performed using the 6-31G(d,p) and 6-311++G(2d,2p) basis sets for several possible structures of water clusters (H2O)n, n ) 8-20. It is found that the most stable geometries arise from a fusion of tetrameric or pentameric rings. As a result, (H2O)n, n ) 8, 12, 16, and 20, are found to be cuboids, while (H2O)10 and (H2O)15 are fused pentameric structures. For the other water clusters (n ) 9, 11, 13, 14, and 17-19) under investigation, the most stable geometries can be thought of as arising from either the cuboid or the fused pentamers or a combination thereof. The stability of some of the clusters, namely, n ) 8-16, has also been studied using density functional theory. An attempt has been made to estimate the basis set superposition error and zero-point energy correction for such clusters at the HartreeFock (HF) level using the 6-311++G(2d,2p) basis set. To ensure that a minimum on the potential-energy surface has been located, frequency calculations have been carried out at the HF level using the 6-31G(d,p) and 6-311++G(2d,2p) basis sets for some of the clusters. Molecular electrostatic potential topography mapping has been employed for understanding the reactivity as well as the binding patterns of some of the structurally interesting clusters.

1. Introduction

“Water clusters”, groups of water molecules held together by hydrogen bonds, have been the subject1 of a number of intense experimental and theoretical investigations because of their importance in understanding cloud and ice formation, solution chemistry, and a large number of biochemical processes. The exploration of the structural and binding properties of water clusters is the first step to understanding the properties of bulk water, the nectar of life. The difficulty in obtaining a rigorous molecular scale description of the structure of liquid and solid water largely is due to the extended hydrogen-bonding network therein and its soft modes. There are numerous local minima on the potential-energy hypersurface of water clusters, the number of which grows rapidly with increasing cluster size, thus making the search for global minima a computationally demanding job.

Substantial progress has been made in recent years in the study of the structure of water clusters. From a theoretical point of view, many different models of water clusters have been studied with the aim of understanding the characteristics of hydrogen bonds. A number of ab initio calculations have also been carried out to investigate the strength of the hydrogen bonds and their cooperativity. Some of the recent reviews on the subject can be found elsewhere.2-4

The water dimer, the smallest water cluster which constitutes the fundamental step in the study of water clusters, has been studied in great detail experimentally5-11 as well as theoretically.12-25 It has been established that the most stable structure of a water dimer is of the Cs symmetry and that it has a single hydrogen bond with a strength of 5.5 ( 0.7 kcal/ mol.5-11

Vibrational spectroscopic studies26 as well as some of the early ab initio studies27 suggested an open-chain conformer with nearly linear hydrogen bonds as the most stable structure of a water trimer. Some of the other experimental28-30 and theoretical31-39 studies show a cyclic structure with C1 symmetry, with two external hydrogen atoms on one side of the O-O-O plane and a third one on the other side of the plane, to be the most stable. In such a structure, each monomer behaves as a donor as well as an acceptor. Perhaps the most interesting feature of the trimer structure deduced by vibration-rotationtunneling (VRT) spectroscopy29 is its chiral nature, with a low barrier to the quantum tunneling motion interconverting the leftand right-handed stereoisomers.

Ab initio calculations12,16,19,21,23,24,38,40,41 have established a homodromic cyclic structure with S4 symmetry to correspond to the global minimum for the tetramer. In this case, the “free” hydrogen atoms alternate in their arrangement above and below the plane of the O-O-O-O ring. Infrared (IR) spectra of benzene-(H2O)411 and VRT spectra of (D2O)442 and (H2O)443 showed an equilibrium structure with S4 symmetry having the concerted flipping motions of the free H atoms for the tetramer. Pentagonal rings of water molecules appear to be ubiquitous in nature, for example, in clathrate hydrates and in the solvation of hydrophobic groups of small molecules as well as in proteins and in DNA molecules. The most stable structure for the pentamer follows the same cyclic ring pattern as that observed for the trimer except that it is puckered.1,11,44-46 It is also chiral. Ab initio calculations12,15,20,23,38,40,47,48 also predicted such a ring structure. Burke et al.,48 for example, examined various Author for correspondence: Honorary Professor Jawaharlal Nehru Centre for Advanced Scientific Research, Jakkur, Bangalore 560 064, India. E-mail: nsath@iitk.ac.in.

E-mail: gadre@chem.unipune.ernet.in. 10525 J. Phys. Chem. A 2001, 105, 10525-10537 10.1021/jp013141b CCC: $20.00 © 2001 American Chemical Society

Published on Web 10/30/2001

structures of pentamers at the Hartree-Fock (HF) level and found that the ring was more stable than the bipyramidal forms by at least 1 kcal/mol. Wales49 pointed out the existence of different ring structures that can be interconverted through lowenergy barrier pathways consisting of the flipping of hydrogen atoms and bifurcation mechanisms.

The structure of (H2O)6 represents a transition from cyclic to three-dimensional geometries, and it has been studied extensively by theory and experiments. Although some of the ab initio calculations15,16,19,50-52 suggested the cyclic and the prismatic structures to be the most stable, it has recently become clear40,53-58 that a large number of alternative three-dimensional structures, such as chair, boat, and cage, are likely to be of comparable energies. Perhaps the first experimental evidence for the cage structure came from the work of Pribble and Zwier11 from their study of the C6H6-(H2O)6 adduct. Liu et al.1,59,60 verified through their FIR-VRT spectroscopy experiments that the isolated water hexamer does have a cage structure. Zeropoint vibrational energy (ZPE) seems to play an important role in deciding the preferred geometry of the hexamer. A detailed study on water hexamer cages at the semiempirical (PM3) level has been carried out recently by Coe et al.58b Diffusion quantum Monte Carlo calculations23,61 predict the cage structure to be the most stable, and the computed properties, such as rotational constants, dipole moment, and so forth, are in agreement with the experimental results.