Optimal geometries and harmonic vibrational frequencies of the global minima of water clusters (H2O)n, n = 2–6, and several hexamer local minima at the CCSD(T) level of theory

Understanding the structure and hydrogen bonding network of (H2O)32 and (H2O)33: an improved Monte Carlo temperature basin paving (MCTBP) method and quantum theory of atoms in molecules (QTAIM) analysis

Large water clusters are of particular interest because of their connection to liquid water and the intricate hydrogen bonding networks they possess.

Modeling Molecular Interactions in Water: From Pairwise to Many-Body Potential Energy Functions

Almost 50 years have passed from the first computer simulations of water, and a large number of molecular models have been proposed since then to elucidate the unique behavior of water across different phases. In this article, we review the recent progress in the development of analytical potential energy functions that aim at correctly representing many-body effects. Starting from the many-body expansion of the interaction energy, specific focus is on different classes of potential energy functions built upon a hierarchy of approximations and on their ability to accurately reproduce reference data obtained from state-of-the-art electronic structure calculations and experimental measurements. We show that most recent potential energy functions, which include explicit short-range representations of two-body and three-body effects along with a physically correct description of many-body effects at all distances, predict the properties of water from the gas to the condensed phase with unprecedented accuracy, thus opening the door to the long-sought "universal model" capable of describing the behavior of water under different conditions and in different environments.

Toward an Accurate and Inexpensive Estimation of CCSD(T)/CBS Binding Energies of Large Water Clusters

Owing to the steep scaling behavior, highly accurate CCSD(T) calculations, the contemporary gold standard of quantum chemistry, are prohibitively difficult for moderate- and large-sized water clusters even with the high-end hardware. The molecular tailoring approach (MTA), a fragmentation-based technique is found to be useful for enabling such high-level ab initio calculations. The present work reports the CCSD(T) level binding energies of many low-lying isomers of large (H2O)n (n = 16, 17, and 25) clusters employing aug-cc-pVDZ and aug-cc-pVTZ basis sets within the MTA framework. Accurate estimation of the CCSD(T) level binding energies [within 0.3 kcal/mol of the respective full calculation (FC) results] is achieved after effecting the grafting procedure, a protocol for minimizing the errors in the MTA-derived energies arising due to the approximate nature of MTA. The CCSD(T) level grafting procedure presented here hinges upon the well-known fact that the MP2 method, which scales as O(N(5)), can be a suitable starting point for approximating to the highly accurate CCSD(T) [that scale as O(N(7))] energies. On account of the requirement of only an MP2-level FC on the entire cluster, the current methodology ultimately leads to a cost-effective solution for the CCSD(T) level accurate binding energies of large-sized water clusters even at the complete basis set limit utilizing off-the-shelf hardware.

Dispersion- and Exchange-Corrected Density Functional Theory for Sodium Ion Hydration

A challenge in density functional theory is developing functionals that simultaneously describe intermolecular electron correlation and electron delocalization. Recent exchange-correlation functionals address those two issues by adding corrections important at long ranges: an atom-centered pairwise dispersion term to account for correlation and a modified long-range component of the electron exchange term to correct for delocalization. Here we investigate how those corrections influence the accuracy of binding free energy predictions for sodium-water clusters. We find that the dual-corrected ωB97X-D functional gives cluster binding energies closest to high-level ab initio methods (CCSD(T)). Binding energy decomposition shows that the ωB97X-D functional predicts the smallest ion-water (pairwise) interaction energy and larger multibody contributions for a four-water cluster than most other functionals - a trend consistent with CCSD(T) results. Also, ωB97X-D produces the smallest amounts of charge transfer and the least polarizable waters of the density functionals studied, which mimics the lower polarizability of CCSD. When compared with experimental binding free energies, however, the exchange-corrected CAM-B3LYP functional performs best (error <1 kcal/mol), possibly because of its parametrization to experimental formation enthalpies. For clusters containing more than four waters, "split-shell" coordination must be considered to obtain accurate free energies in comparison with experiment.

Assessing the accuracy of some popular DFT methods for computing harmonic vibrational frequencies of water clusters

A wide range of density functional theory (DFT) methods (37 altogether), including pure, hybrid, range-separated hybrid, double-hybrid, and dispersion-corrected functionals, have been employed to compute the harmonic vibrational frequencies of eight small water clusters ranging in size from the dimer to four different isomers of the hexamer. These computed harmonic frequencies have been carefully compared to recently published benchmark values that are expected to be very close to the CCSD(T) complete basis set limit. Of the DFT methods examined here, ωB97 and ωB97X are the most consistently accurate, deviating from the reference values by less than 20 cm(-1) on average and never more than 60 cm(-1). The performance of double-hybrid methods including B2PLYP and mPW2-PLYP is only slightly better than more economical approaches, such as the M06-L pure functional and the M06-2X hybrid functional. Additionally, dispersion corrections offer very little improvement in computed frequencies.

Low Temperature Kinetics of the First Steps of Water Cluster Formation

We present a combined experimental and theoretical low temperature kinetic study of water cluster formation. Water cluster growth takes place in low temperature (23-69 K) supersonic flows. The observed kinetics of formation of water clusters are reproduced with a kinetic model based on theoretical predictions for the first steps of clusterization. The temperature- and pressure-dependent association and dissociation rate coefficients are predicted with an ab initio transition state theory based master equation approach over a wide range of temperatures (20-100 K) and pressures (10^{-6}-10  bar).

Molecular orbital analysis of the hydrogen bonded water dimer

As an essential interaction in nature, hydrogen bonding plays a crucial role in many material formations and biological processes, requiring deeper understanding. Here, using density functional theory and post-Hartree-Fock methods, we reveal two hydrogen bonding molecular orbitals crossing the hydrogen-bond’s O and H atoms in the water dimer. Energy decomposition analysis also shows a non-negligible contribution of the induction term. Our finding sheds light on the essential understanding of hydrogen bonding in ice, liquid water, functional materials and biological systems.

Accurate vibrational spectra via molecular tailoring approach: a case study of water clusters at MP2 level

In spite of the recent advents in parallel algorithms and computer hardware, high-level calculation of vibrational spectra of large molecules is still an uphill task. To overcome this, significant effort has been devoted to the development of new algorithms based on fragmentation methods. The present work provides the details of an efficient and accurate procedure for computing the vibrational spectra of large clusters employing molecular tailoring approach (MTA). The errors in the Hessian matrix elements and dipole derivatives arising due to the approximation nature of MTA are reduced by grafting the corrections from a smaller basis set. The algorithm has been tested out for obtaining vibrational spectra of neutral and charged water clusters at Møller-Plesset second order level of theory, and benchmarking them against the respective full calculation (FC) and/or experimental results. For (H2O)16 clusters, the estimated vibrational frequencies are found to differ by a maximum of 2 cm(-1) with reference to the corresponding FC values. Unlike the FC, the MTA-based calculations including grafting procedure can be performed on a limited hardware, yet take a fraction of the FC time. The present methodology, thus, opens a possibility of the accurate estimation of the vibrational spectra of large molecular systems, which is otherwise impossible or formidable.

A double stranded metal-organic assembly accommodating a pair of water trimers in the host cavity and catalysing Glaser coupling

A supramolecular compound, catena-poly{[Cu2(1,3-μ2-(1a))2(μ2-ter)2(H2O)2]n·(6H2O)n} (1) has been synthesized using (1a) [(1a = N(1),N(3),N(5)-trimethyl-N(1),N(3),N(5)-tris((pyridin-4-yl)methyl)-1,3,5-benzene tricarboxamide] and terephthalate (ter) as the pillaring unit by self-assembly. The terephthalate units are connected by copper(II) ions forming a single strand, while a pair of such strands are then linked by (1a) via two pyridyl terminal arms bound to copper(II) nodes on either side forming a one-dimensional double stranded assembly propagating along the c axis. The compound crystallizes in the Fdd2 space group. The cavity created in the interior of this double strand assembly trap six water molecules and are stabilized by hydrogen bonding with the host. The arrangement of the pair of acyclic water trimers in isolated cavities of (1) is such that it resembles a closed-bracket-like formation. The Hirshfeld surface analysis of (1) reveals the presence of strong intermolecular hydrogen-bonding interactions between one-dimensional ladder-like units and with the water trimer in the host cavity. The copper(II)-containing coordination polymer also acts as an efficient catalyst for the Glaser-Hay homo-coupling reaction.

Low energy isomers of (H2O)25 from a hierarchical method based on Monte Carlo temperature basin paving and molecular tailoring approaches benchmarked by MP2 calculations

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.

Infrared and Raman Spectroscopy of Liquid Water through "First-Principles" Many-Body Molecular Dynamics

Vibrational spectroscopy is a powerful technique to probe the structure and dynamics of water. However, deriving an unambiguous molecular-level interpretation of the experimental spectral features remains a challenge due to the complexity of the underlying hydrogen-bonding network. In this contribution, we present an integrated theoretical and computational framework (named many-body molecular dynamics or MB-MD) that, by systematically removing uncertainties associated with existing approaches, enables a rigorous modeling of vibrational spectra of water from quantum dynamical simulations. Specifically, we extend approaches used to model the many-body expansion of interaction energies to develop many-body representations of the dipole moment and polarizability of water. The combination of these "first-principles" representations with centroid molecular dynamics simulations enables the simulation of infrared and Raman spectra of liquid water under ambient conditions that, without relying on any ad hoc parameters, are in good agreement with the corresponding experimental results. Importantly, since the many-body energy, dipole, and polarizability surfaces employed in the simulations are derived independently from accurate fits to correlated electronic structure data, MB-MD allows for a systematic analysis of the calculated spectra in terms of both electronic and dynamical contributions. The present analysis suggests that, while MB-MD correctly reproduces both the shifts and the shapes of the main spectroscopic features, an improved description of quantum dynamical effects possibly combined with a dissociable water potential may be necessary for a quantitative representation of the OH stretch band.

Water clusters in an argon matrix: infrared spectra from molecular dynamics simulations with a self-consistent charge density functional-based tight binding/force-field potential

The present theoretical study aims at investigating the effects of an argon matrix on the structures, energetics, dynamics, and infrared (IR) spectra of small water clusters (H2O)n (n = 1-6). The potential energy surface is obtained from a hybrid self-consistent charge density functional-based tight binding/force-field approach (SCC-DFTB/FF) in which the water clusters are treated at the SCC-DFTB level and the matrix is modeled at the FF level by a cluster consisting of ∼340 Ar atoms with a face centered cubic (fcc) structure, namely (H2O)n/Ar. With respect to a pure FF scheme, this allows a quantum description of the molecular system embedded in the matrix, along with all-atom geometry optimization and molecular dynamics (MD) simulations of the (H2O)n/Ar system. Finite-temperature IR spectra are derived from the MD simulations. The SCC-DFTB/FF scheme is first benchmarked on (H2O)Arn clusters against correlated wave function results and DFT calculations performed in the present work, and against FF data available in the literature. Regarding (H2O)n/Ar systems, the geometries of the water clusters are found to adapt to the fcc environment, possibly leading to intermolecular distortion and matrix perturbation. Several energetical quantities are estimated to characterize the water clusters in the matrix. In the particular case of the water hexamer, substitution and insertion energies for the prism, bag, and cage are found to be lower than that for the 6-member ring isomer. Finite-temperature MD simulations show that the water monomer has a quasifree rotation motion at 13 K, in agreement with experimental data. In the case of the water dimer, the only large-amplitude motion is a distortion-rotation intermolecular motion, whereas only vibration motions around the nuclei equilibrium positions are observed for clusters with larger sizes. Regarding the IR spectra, we find that the matrix environment leads to redshifts of the stretching modes and almost no shift of the bending modes. This is in agreement with experimental data. Furthermore, in the case of the water monomer and dimer, the magnitudes of the computed shifts are in fair agreement with the experimental values. The complex case of the water hexamer, which presents several low-energy isomers, is discussed.

Structures and relative stabilities of ammonia clusters at different temperatures: DFT vs. ab initio

The global minimum energy structures of (NH₃)_n=2–10are pointed out for the first time at a given temperature.

Distribution of topologically distinct isomers of water clusters and dipole moments of constituent water molecules at finite atmospheric temperatures

Hydrogen-bonding (HB) patterns correspond to topologically distinct isomers of a water cluster and can be expressed by digraphs. We make use of the HB pattern to divide the configuration space of a water cluster ((H2O)n, n = 3-8) at a finite temperature. Each configuration of a water cluster generated in Monte Carlo (MC) simulation is classified into an HB pattern. The number of observed HB patterns increases exponentially with the cluster size, whereas the population of the most abundant HB pattern decreases. The populations of the HB patterns are transformed into the relative Helmholtz energies. At a finite temperature, it can be observed that isomers other than local minimum structures on the potential energy surface are highly populated. The dipole moment of a constituent molecule in a water cluster is enhanced, depending on the molecular circumstance. The change is rationalized by the difference in the local HB type of the water molecule in the HB network.

Comparative study on the properties of hydration water of Na- and K-halide ions by Raman OH/OD-stretching spectroscopy and dielectric relaxation data

Properties of hypermobile water (HMW) were studied by Raman OH-stretching spectroscopy. Hydration water properties measured by Raman OH-stretching spectra of NaX/KX (X: Cl, Br, I) solutions (0.05-0.2 M) were comparatively analyzed with the data by dielectric relaxation spectroscopy (DRS), NMR, and statistical mechanical studies. The Raman OH-stretching spectra were well-fitted with linear combinations of the spectra of pure water both at the same and the higher temperatures. The fitting analysis determined the "structure temperature" Tstr and mole fraction of the high Tstr water region, giving the hydration number Nhyd, for each electrolyte solution. The determined Tstr was much higher than the solution temperature of 293 K for each tested salt and was higher for larger halide ions, consistent with commonly known "structure-breaking" order Cl < Br < I. No significant differences in Nhyd were observed between NaX and KX and among even halide ion species within the experimental errors. Measured Nhyd values of 25-27 were much greater than the reported numbers by NMR chemical shift and (17)O NMR relaxation studies and comparable to the numbers of hypermobile water reported in the previous DRS studies. The results indicated that the hydration region around NaX or KX measured by the present Raman study was nearly overlapped with the region of HMW by DRS. It was also suggested that differences in the ion size effects on Tstr and the DR frequency resulted from the sensitivity difference to long-range many-body interactions among water molecules. High structure-temperature regions were also detected by the analysis of OH-stretching and OD-stretching bands for 0.2 M NaI in H2O/D2O mixed solvent of 50 mol %, and we found that both OH-stretching and OD-stretching bands have almost equivalent Tstr ≈ 330 K and mole fractions with each other.