Assessment of the Accuracy of Density Functionals for Prediction of Relative Energies and Geometries of Low-Lying Isomers of Water Hexamers

Abstract

Water hexamers provide a critical testing ground for validating potential energy surface predictions because they contain structural motifs not present in smaller clusters. We tested the ability of 11 density functionals (four of which are local and seven of which are nonlocal) to accurately predict the relative energies of a series of low-lying water hexamers, relative to the CCSD(T)/aug′-cc-pVTZ level of theory, where CCSD(T) denotes coupled cluster theory with an interative treatment of single and double excitations and a quasiperturbative treatment of connected triple excitations. Five of the density functionals were tested with two different basis sets, making a total of 16 levels of density functional theory (DFT) tested. When single-point energy calculations are carried out on geometries obtained with second-order Møller-Plesset perturbation theory (MP2), only three density functionals, M06-L, M05-2X, and M06-2X, are able to correctly predict the relative energy ordering of the hexamers. These three functionals predict that the range of energies spanned by the six isomers is 3.2-5.6 kcal/mol, whereas the other eight functionals predict ranges of 1.0-2.4 kcal/ mol; the benchmark value for this range is 3.1 kcal/mol. When the hexamers are optimized at each level of theory, all methods are able to reproduce the MP2 geometries well for all isomers except the boat and bag isomers, and DFT optimization changes the energy ordering for seven of the 16 methods tested. The addition of zero-point energy changes the energy ordering for all of the density functionals studied except for M05-2X and M06-2X. The variation in relative energies predicted by the different methods highlights the necessity for exercising caution in the choice of density functionals used in future studies. Of the 11 density functionals tested, the most accurate results for energies were obtained with the PWB6K, MPWB1K, and M05-2X functionals.

Predictions for water clusters from a first-principles two- and three-body force field

“…3 is self-contained, i.e., was obtained completely within the given approach (except for the benchmark results which were computed at geometries optimized in smaller bases and not including the δE CCSD(T) int contribution). Figure 3 shows that the interaction energies from CCpol23+ and both benchmarks are very close in all cases, although CCpol23+ is noticeably closer to the CBS-level benchmarks of Bates and Tschumper 71 (0.01-0.03 kcal/mol) than to the haTZ results of Dahlke et al 66 (0.03-0.06 kcal/ mol). This is not accidental, as both the two-body and the three-body parts of CCpol23+ were fitted to energies obtained with basis sets much larger than haTZ.…”

“…First, we optimized the geometries of the cage, prism, book, boat, bag, and ring isomers using the CCpol-8s+NB potential, starting from the configurations taken from Ref. 66. Since the latter configurations included flexible monomers, we "projected" our monomers similarly as in the case of the TIP5P potential, except that our rigid-monomer bisector now coincides with the line connecting the position of the oxygen atom with the midpoint of the segment connecting the two hydrogens.…”

“…We investigated six of the lowest structures (prism, cage, book, bag, ring, boat) often considered in the literature, as high-quality comparative benchmarks are available for these configurations. Dahlke et al 66 optimized the geometries at the MP2 level in the haTZ basis set and evaluated the hexamer energies using CCSD(T) in the same basis. Bates contributions, but their MP2 energies were calculated using the MP2-R12 method 89 which should give results close to the MP2 CBS limit.…”

“…We follow the convention adopted in Ref. 66, while in Ref. 71 the names "book-1," "cyclic-boat-1," and "cyclic-chair" are used for book, boat, and ring, respectively, and two more structures are considered ("book-2" and "cyclic-boat-2") differing just by the orientation of the free hydrogen atoms at some monomers.…”

Density functional theory calculation of interaction between bisphosphate and farnesyl pyrophosphate synthase

“…Our findings indicated that the following interactions may be important in the potency of N-BPs: hydrogen bonding with Thr 201 and/or Lys 200, where a bifurcated bond is more potent than a single bond; CH-O hydrogen bonding with the backbone carbonyl oxygen atom of Phe 99; andinteraction with the sidechain of Phe 99. Truhlars group recently developed the global hybrid meta functionals M05-2X [5] and M06-2X [6] and demonstrated that these methods can be effectively applied to many problematic systems [7,8]. Here, we conducted quatum mechanical calculations for several BPs (minodronate, risedronate, alendronate) and their surrounding residues using the M06-2X method.…”