The basis set superposition error (BSSE) is quite essential for calculation of such weakly bonded complexes, even for large basis sets, and the corresponding correction has to be taken into account. BSSE was taken into account during geometry optimization, harmonic vibrational frequencies and single-point calculation by the function counterpoise (CP) method according to the approach of Simon, Duran, and Dannenberg. Water cluster geometry optimization was performed using the second-order Møller-Plesset method (MP2) with the aug-CC-pVTZ basis set. More correlation treatment than MP2 level is found to be less important for such hydrogen bond complexes. To obtain more accurate energy estimations the Complete Basis Set (CBS) limit was extrapolated by the Gaussian/exponential formula of Dunning and Woon using MP2 energies calculated for found geometries utilizing the aug-CC-pVDZ, aug-CC-pVTZ and aug-CC-pVQZ basis sets. The harmonic vibrational frequencies were estimated at MP2/aug-CC-pVDZ level of theory with CP correction based on the geometries obtained at the same level. The equilibrium constants of water clusters formation were then determined from the calculated Gibbís free energy values. Calculated interaction energies, free energies, equilibrium rates of formation of clusters, and corresponding partial pressures with concentrations are shown in the table below. Concentration of water is derived from relative humidity and saturated partial water pressure, which can be obtained from the empirical Tetensís formula. The water dimer concentration calculated for 1 atm. pressure, 25 oC temperature and 85% RH is three orders of magnitude lower than unimolecular water concentration. The water trimer is even less abundant, by approximately a factor of 500, and the water tetramer concentration is about 50 times lower than water trimer concentration. Calculations were performed using the GAUSSIAN 98 (revision A11) and GAUSSIAN 03 program packages. Pictures of the geometries of the calculated molecular structures were created by ViewMol3D programs.
Reference: Andrew B. Ryzhkov and Parisa A. Ariya, The importance of water clusters (H2O)n (n = 2,...,4) in the reaction of Criegee intermediate with water in the atmosphere
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