Structures of the four isomers of the water hexamer considered here (obtained with MP2 and an aug-cc-pVTZ basis). The dashed lines indicate H bonds, with the conventional number of H bonds each cluster is assumed to have (; ; ; and ) (Ref. 92). Some of the structural parameters discussed in the text are included alongside the cyclic structure.
Difference in the dissociation energy in (a) and (b) meV/H bond between the various DFT xc functionals and MP2. In (b) the generally accepted number of H bonds in the prism, cage, book, and cyclic isomers of nine, eight, seven, and six, respectively, have been used (Ref. 92). Positive values correspond to an overestimation of the dissociation energy by a given DFT xc functional. We note that the reference MP2 dissociation energies are at the CBS limit, whereas for the DFT xc functionals an aug-cc-pV5Z basis set has been employed. Lines are drawn to guide the eye only.
Structures of the prism isomer optimized with MP2 and the PBE1W and TPSS xc functionals. Dashed lines indicate H bonds. For PBE1W one H bond is broken and for TPSS two H bonds are broken, each broken H bond being associated with a double donor (dd) water molecule. The other H bonds which get stronger as a result of the bond breaking are also indicated. A very bent H bond angle of is also shown in the upper triangle of the PBE1W structure.
(a) Variation in the dispersion contribution with distance from different atom pairs with parameters for BLYP. (b) Intermolecular dispersion interaction for the four isomers as a function of the average interatomic distances of different atom pairs (on optimized structures). Here black, red, green, and blue refer to prism, cage, book, and cyclic isomers, respectively.
Dissociation energies of the four water hexamers obtained from various electronic structure approaches: MP2/CBS; DMC; CCSD(T) with a triple- basis set (Ref. 40); 12 different DFT xc functionals computed, unless indicated otherwise, with an aug-cc-pV5Z basis set; and HF at the CBS limit. The most stable isomer from each method is indicated in bold and the relative energies of the other isomers are given in parenthesis. MEs and MAEs in dissociation energies, averaged over the four hexamers in comparison with MP2 and DMC, are also given. All structures were optimized consistently with MP2, HF, and each DFT functional with an aug-cc-pVTZ basis set except for the DMC calculations which used the MP2 structures. DFT xc functionals are arranged here with increasing value of MAE from MP2. All values are in .
MAE of the various DFT functionals from MP2 for five different structural parameters, averaged over the four water hexamers examined here. The numbers in bold all have MAE for bond lengths and for bond angles. MEs are given in parenthesis. MP2 and DFT (and HF) structures were optimized consistently with MP2 and with each DFT functional (and HF) with an aug-cc-pVTZ basis set. The structures were optimized with a numerical atom-centered basis set (FHI-AIMS code). The order of the DFT xc functionals is the same as in Table I.
Many-body contributions to the total dissociation energies of the cyclic and prism isomers as obtained from MP2, X3LYP, PBE0, BLYP, and . For the MP2 many-body decomposition an aug-cc-pV5Z basis set is employed and so the total MP2 dissociation energies differ slightly from the MP2/CBS values given in Table I. Likewise, to avoid complications from the slightly different optimized structures obtained from MP2 and the DFT xc functionals, the DFT many-body decompositions are performed on the optimized MP2 structures (with an aug-cc-pV5Z basis set for the DFT energies). Values in the parenthesis are the difference between each functional and the MP2 results. Negative values indicate a gain in energy, i.e., a net attraction when all the -body interactions of a given class are summed up, and positive values a net repulsion. All values are in .
Absolute values of vdW interaction energies and vdW corrected total dissociation energies for the four water hexamers for three different xc functionals. The DFT structures employed are fully relaxed geometries calculated with the FHI-AIMS code [the CPMD code gives very similar numbers (Ref. 120)]. For comparison the MP2/CBS results are also displayed. The energies of the most stable isomers are indicated in bold and the relative energies of the other structures with respect to the prism are given in parenthesis. MAEs in total dissociation energies are calculated from the MP2/CBS values averaging over the four hexamers. All numbers are in .
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