The optimal structures and harmonic vibrational frequencies of cyclic water clusters, (H2O)n, have been determined at the Hartree–Fock (for n=2–6) and second order perturbation theory (for n=2–4) levels of theory with an augmented correlation consistent double zeta basis set. At the MP2 level this basis set yields very accurate results for the structure, dipole moment, and polarizability of the water monomer as well as results of comparable accuracy for the structure, binding energy, and harmonic vibrational frequencies of the water dimer. The optimal structure of (H2O)4 and the harmonic frequencies of (H2O)3,4 are the first ones reported at a correlated level for these species. Analysis of the structural trends reveals that the separation between neighboring oxygen atoms decreases exponentially with increasing cluster size. The predicted R0(O–O) for the ring hexamer is less than 0.02 Å shorter than the interoxygen separation in ice Ih. Furthermore, the trends in the harmonic vibrational frequencies suggest that, for large clusters, the intramolecular bends are blue shifted by ∼70 cm−1 with respect to the monomer frequency. The frequencies corresponding to the ‘‘free’’ OH stretches show little (≤50 cm−1) shift to the blue for n=2–6, whereas the ones corresponding to the ‘‘bridge’’ hydrogens are shifted to the red by ∼500 cm−1 with respect to the average of the harmonic stretching frequencies in water.
The magnitudes of the two- through six-body energy terms and their contribution to the interaction energy of small ring water clusters (n=2–6) are computed at the Hartree–Fock (HF) and second- through fourth-order many-body perturbation (MP2, MP4) levels of theory. The analysis is performed at the minimum energy geometries reported earlier [J. Chem. Phys. 99, 8774 (1993)]. The correlation correction is found to account for a 10%–20% increase in the individual two-body terms and a much larger increase of 75% for the three-body and 200% for the small four-body terms. The MP4 results are found to differ only slightly (<2%) from the corresponding MP2 results. We have found that three-body terms have a significant contribution as high as 30% to the interaction energy of the larger clusters and that four-body and higher order terms are negligible. The total and incremental association energies for the processes n H2O→(H2O)n and (H2O)n−1+H2O→(H2O)n, n=2–6 are also reported.
The inclusion of the fragment relaxation energy terms in the estimation of the basis set superposition error (BSSE) correction to the interaction energy is necessary in order to ensure formal convergence to the uncorrected result at the complete basis set (CBS) limit. The problems associated with their omission are demonstrated for F−(H2O), Cl−(H2O), and (H2O)2 especially when very large basis sets are used. The family of correlation consistent basis sets allows for a heuristic extrapolation of both uncorrected and BSSE-corrected electronic energy differences of the three complexes to the MP2 CBS limits of −27.1, −15.1, and −4.9 kcal/mol respectively.
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