We report a database consisting of the putative minima and ∼3.2 × 106 local minima lying within 5 kcal/mol from the putative minima for water clusters of sizes n = 3–25 using an improved version of the Monte Carlo temperature basin paving (MCTBP) global optimization procedure in conjunction with the ab initio based, flexible, polarizable Thole-Type Model (TTM2.1-F, version 2.1) interaction potential for water. Several of the low-lying structures, as well as low-lying penta-coordinated water networks obtained with the TTM2.1-F potential, were further refined at the Møller-Plesset second order perturbation (MP2)/aug-cc-pVTZ level of theory. In total, we have identified 3 138 303 networks corresponding to local minima of the clusters n = 3–25, whose Cartesian coordinates and relative energies can be obtained from the webpage https://sites.uw.edu/wdbase/. Networks containing penta-coordinated water molecules start to appear at n = 11 and, quite surprisingly, are energetically close (within 1–3 kcal/mol) to the putative minima, a fact that has been confirmed from the MP2 calculations. This large database of water cluster minima spanning quite dissimilar hydrogen bonding networks is expected to influence the development and assessment of the accuracy of interaction potentials for water as well as lower scaling electronic structure methods (such as different density functionals). Furthermore, it can also be used in conjunction with data science approaches (including but not limited to neural networks and machine and deep learning) to understand the properties of water, nature’s most important substance.

We report new global minimum candidate structures for the (H2O)25 cluster that are lower in energy than the ones reported previously and correspond to hydrogen bonded networks with 42 hydrogen bonds and an interior, fully coordinated water molecule. These were obtained as a result of a hierarchical approach based on initial Monte Carlo Temperature Basin Paving sampling of the cluster's Potential Energy Surface with the Effective Fragment Potential, subsequent geometry optimization using the Molecular Tailoring Approach with the fragments treated at the second order Møller-Plesset (MP2) perturbation (MTA-MP2) and final refinement of the entire cluster at the MP2 level of theory. The MTA-MP2 optimized cluster geometries, constructed from the fragments, were found to be within <0.5 kcal/mol from the minimum geometries obtained from the MP2 optimization of the entire (H2O)25 cluster. In addition, the grafting of the MTA-MP2 energies yields electronic energies that are within <0.3 kcal/mol from the MP2 energies of the entire cluster while preserving their energy rank order. Finally, the MTA-MP2 approach was found to reproduce the MP2 harmonic vibrational frequencies, constructed from the fragments, quite accurately when compared to the MP2 ones of the entire cluster in both the HOH bending and the OH stretching regions of the spectra.

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Large water clusters are of particular interest because of their connection to liquid water and the intricate hydrogen bonding networks they possess. Generally, clusters above (H 2 O) 25 are cage-like; however, the diversity of their hydrogen bonding can be enormous and is related to the stability of the cluster. Two main challenges for understanding hydrogen bonding networks are how to determine a few low energy minima in the extremely rugged energy surface of large water clusters and how to rationalize the relative stability of different structures of a cluster based on simple chemical concepts, particularly when they are very close in energy. In the current work, an improved version of the Monte Carlo Temperature Basin Paving (MCTBP) method has been used to find low energy structures of (H 2 O) 32 and (H 2 O) 33 as an answer to the first challenge. Previously, the MCTBP method has been applied to large water clusters with reasonable success.In this work, we have changed the Monte Carlo acceptance/rejection condition to make the calculation more efficient. After finding several structures at either the same or lower energy of previously known structures, the quantum theory of atoms in molecules (QTAIM) method has been applied to analyze the relationship between the stability and polarized charges on each water molecule in a cluster. Overall, an increase of the polarized charge on the oxygen atom was found to stabilize the energy of a water molecule in a cluster.

The knowledge of degree of completeness of energy landscape search by stochastic algorithms is often lacking. A graph theory based method is used to investigate the completeness of search performed by Monte Carlo Temperature Basin Paving (MCTBP) algorithm for (H 2 O) n , (n=6, 7, and 20). In the second part of the work, a combination of MCTBP and graph theory was used to devise a new algorithm for finding low energy structures of (H 2 O) n , (n=21-25), where input structures for (H 2 O) n comes from the graphs of (H 2 O) n−1. The new algorithm can be a complementary tool to the MCTBP method.