Proper Gaussian basis sets for density functional studies of water dimers and trimers

The accuracy of the Perdew-Burke-Ernzerhof and Tao-Perdew-Staroverov-Scuseria density functionals for describing noncovalent interaction energies in small water clusters is studied by testing I I basis sets on a reduced test set proposed by Dahlke and Truhlar (J. Phys. Chem. B 2005, 109, 15677). We have also tested variants of the Perdew-Burke-Ernzerhof functional and the Becke98 hybrid functional. While moderate basis sets give converged density functional theory results for covalent dissociation energies, this is not true for noncovalent interaction energies. Our results show that density functionals give converged interaction energies with aug-cc-pVTZ and aug-cc-pVQZ basis sets. Gradual simplification of the basis set introduces an increasing overbinding effect. The best agreement with the high-level result was obtained by the Perdew-Burke-Ernzerhof functional at the basis set limit. The converged Tao-Perdew-Staroverov-Scuseria interaction energies show a systematic underbinding effect that can be compensated by a somewhat systematic overbinding basis set effect of smaller basis sets such as 6-31 +G(d,2p). The inclusion of the diffuse functions in the oxygen basis set is very important, while the inclusion of the f functions practically does not influence the results. Improvement can be obtained by adding more hydrogen p functions to the 6-31+G basis set.