On the accuracy of density-functional theory exchange-correlation functionals for H bonds in small water clusters. II. The water hexamer and van der Waals interactions.

Second order Møller-Plesset perturbation theory at the complete basis set limit and diffusion quantum Monte Carlo are used to examine several low energy isomers of the water hexamer. Both approaches predict the so-called prism to be the lowest energy isomer, followed by cage, book, and cyclic isomers. The energies of the four isomers are very similar, all being within 10-15 meV/H(2)O. These reference data are then used to evaluate the performance of several density-functional theory exchange-correlation (xc) functionals. A subset of the xc functionals tested for smaller water clusters [I. Santra et al., J. Chem. Phys. 127, 184104 (2007)] has been considered. While certain functionals do a reasonable job at predicting the absolute dissociation energies of the various isomers (coming within 10-20 meV/H(2)O), none predict the correct energetic ordering of the four isomers nor does any predict the correct low total energy isomer. All xc functionals tested either predict the book or cyclic isomers to have the largest dissociation energies. A many-body decomposition of the total interaction energies within the hexamers leads to the conclusion that the failure lies in the poor description of van der Waals (dispersion) forces in the xc functionals considered. It is shown that the addition of an empirical pairwise (attractive) C(6)R(-6) correction to certain functionals allows for an improved energetic ordering of the hexamers. The relevance of these results to density-functional simulations of liquid water is also briefly discussed.