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The exponents of extra diffuse basis sets (s and p) were used with scaled values of the outermost s and p functions of the given basis set of oxygen atom by the factor of 1/8 (with consecutive scaling for the diffuse 2s and 2p basis functions). Although the exponents at the core/valence levels are generally scaled down by 1/2-1/4, we note that the exponents at the diffuse basis sets can be scaled by a much smaller factor due to the diffuse nature of the excess electron. In particular, when the diffuse basis set with a larger scale factor is employed for all oxygen atoms, serious convergence problems often arise, The diffuse functions are very important for the hydration study of an excited electron. Therefore, we already discussed this issue in our previous work [Ref. 8(d)]. The best test of the diffuse basis set was made with the comparison between a neutral water heptamer and a system comprised of a neutral water heptamer and an excess (practically free, i.e., unbound) electron. Based on the MP2/6-311++G**[3s3p] calculations, the error in the total binding energy is only 0.13 kcal/mol and the error in VDE is only 0.01 eV. Since the aug-cc-pVDZ+diffs(2s2p/2s) basis set is as diffusive as the 6-311 + +G**[3s3p] basis set, our results would be reliable (within 0.01 kcal/mol in energy and 0.01 eV in VDE). Indeed, our results are in good agreement with experimental VDEs and OH vibrational frequencies.
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