CCSD(T) Complete Basis Set Limit Relative Energies for Low-Lying Water Hexamer Structures

Abstract

MP2 and CCSD(T) complete basis set (CBS) limit relative electronic energies (DeltaE(e)) have been determined for eight low-lying structures of the water hexamer by combining explicitly correlated MP2-R12 computations with higher-order correlation corrections from CCSD(T) calculations. Higher-order correlation effects are quite substantial and increase DeltaE(e) by at least +0.19 kcal mol(-1) and as much as +0.59 kcal mol(-1). The effects from zero-point vibrational energy (ZPVE) have been assessed from unscaled harmonic vibrational frequencies computed at the MP2 level with a correlation consistent triple-zeta basis set (cc-pVTZ for H and aug-cc-pVTZ for O). ZPVE effects are even more significant than higher-order correlation effects and are uniformly negative, decreasing the relative energies by -0.16 kcal mol(-1) to -1.61 kcal mol(-1). Although it has been widely accepted that the cage becomes the lowest-energy structure after ZPVE effects are included [Nature 1996, 381, 501-503], the prism is consistently the most stable structure in this work, lying 0.06 kcal mol(-1) below the nearly isoenergetic cage isomer at the electronic MP2 CBS limit, 0.25 kcal mol(-1) below at the electronic CCSD(T) CBS limit, and 0.09 kcal mol(-1) below at the harmonic ZPVE corrected CCSD(T) CBS limit. Moreover, application of any uniform scaling factor less than unity to correct for anharmonicity further stabilizes the prism and increases the relative energies of the other structures.

Communication: Energy benchmarking with quantum Monte Carlo for water nano-droplets and bulk liquid water

“…1-5). Coupledcluster benchmarks for small water clusters [6][7][8] have been invaluable in calibrating the methods of density functional theory (DFT) and in creating parameterised interaction potentials. However, data on small clusters are not enough for understanding extended water systems, and several groups have recently begun to report benchmarks on clusters as large as (H 2 O) 24 9, 10 and on ice structures.…”

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.…”

“…, 5, as well as the "halfaugmented" triple-zeta basis set (haTZ) that includes augmentation only on the oxygen atom. This basis set was recommended for the water hexamer by Bates and Tschumper 71 as a good compromise between size and performance.…”

“…hexamer interaction energies at the HF and MP2 CBS levels are about 0.4-0.5 kcal/mol, or only 1% of the hexamer interaction energy, but are clearly too large for investigations of subtle effects as the cage-prism energy difference that amounts to 0.25 kcal/mol. 37,71 Interestingly enough, the use of MP2 gives only a negligible improvement over the HF level of theory. In contrast, going up to the CCSD(T) level gives a substantial contribution to the hexamer energy.…”

“…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.…”