(Color online) Structures of the four water clusters examined here in their global minimum energy configurations. The dashed lines indicate H bonds. Some of the structural parameters of the H bond are indicated alongside the dimer. We note that in the trimer, tetramer, and pentamer there is one H bond per water molecule.
(a) Variation in the MP2 dissociation energy for the dimer without a counterpoise correction for basis set superposition error (BSSE) (labeled MP2) and with a counterpoise correction for BSSE [labeled MP2(CP)] as a function of basis set size. The extrapolated complete basis set (CBS) dissociation energy for the dimer with MP2 is also indicated. (b) Variation in the dissociation energy for the dimer with and without a counterpoise BSSE correction as a function of basis set size for three different DFT functionals. The basis set labels on the axis of (a) and (b) indicate aug-cc-pVXZ basis sets, where , 4, and 5. Lines are drawn to guide the eyes only. All structures were optimized with an aug-cc-pVTZ basis set consistently with MP2 and with each DFT functional.
(a) Difference in the dissociation energy in meV/H bond of the various DFT functionals compared to MP2, plotted as a function of cluster size. Positive values correspond to an overestimate of the dissociation energy by a given DFT functional. (b) Average value of the MP2 and DFT O–O distances as a function of cluster size. The inset zooms in on the dimer region. (c) Difference in the average O–O distance between MP2 and DFT. Positive values correspond to an overestimate of the average O–O distances by a given DFT functional. [(a)–(c)] All DFT energies are calculated with an aug-cc-pV5Z basis set on geometries optimized consistently with each functional with an aug-cc-pVTZ basis set. Lines are drawn to guide the eyes only.
Mean error (ME) in the dissociation energies obtained with aug-cc-pV5Z (solid bars) and MG3S (dashed bars) basis sets for five selected functionals for the four clusters examined here. Positive values correspond to an average overestimate of the dissociation energy compared to MP2 for the clusters. All errors are measured relative to our reference CBS MP2 values.
Comparison of the MP2 complete basis set dissociation energies to those obtained with various DFT functionals computed with an aug-cc-pV5Z basis set for four different water clusters. DFT dissociation energies that come within of the corresponding MP2 value are indicated in bold. The numbers in parentheses indicate the percentage cooperative enhancement in the H bond strength compared to the dissociation energy of the dimer. Averages of the signed and unsigned errors in the dissociation energies of all DFT functionals from the corresponding MP2 numbers over all four clusters are also provided as mean error (ME) and mean absolute error (MAE). The DFT functionals are ordered in terms of increasing MAE. All structures were optimized consistently with MP2 and with each DFT functional with an aug-cc-pVTZ basis set, and all values are in meV/H bond .
Mean absolute error (MAE) of various DFT functionals from MP2 for five different structural parameters, averaged over the four water clusters examined here. The numbers in bold all have MAE for bond lengths and for bond angles. Mean errors (MEs) are given in parentheses. All structures were optimized consistently with MP2 and with each DFT functional with an aug-cc-pVTZ basis set. The order of the functionals is the same as in Table I.
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