Water Hexamer Research Articles

Improvements on the FANTASIO set-up and new spectroscopic results concerning the Ar-H2O van der Waals complex in the 2OH overtone region

We present a series of improvements of the FANTASIO experimental set-up that couples a supersonic expansion to a cavity ring-down spectrometer originally reported by M. Herman, et al., Mol. Phys. 105, 815 (2007). In particular, the implementation of a new pulsed slit valve of 80 mm in length is detailed. The design is based on a powerful piezo stack actuator. Schlieren imaging is used to verify the homogeneity of the molecular beam and the quality of the pulsed slit performance. The ability to form weakly bound van der Waals complexes is assessed using the cavity ring-down spectrometer and a new chirped-pulse Fourier transform microwave spectrometer with the 12–18 GHz operating range. The water hexamer and heptamer were observed using this microwave spectrometer. Following enhancements and an extended laser coverage of the CRDS in the 2OH region, we observed and analyzed seven sub-bands of the Ar-H216O van der Waals complex, along with one sub-band of the much less abundant Ar-H218O isotopologue.

Performant automatic differentiation of local coupled cluster theories: Response properties and ab initio molecular dynamics

In this work, we introduce a differentiable implementation of the local natural orbital coupled cluster (LNO-CC) method within the automatic differentiation framework of the PySCFAD package. The implementation is comprehensively tuned for enhanced performance, which enables the calculation of first-order static response properties on medium-sized molecular systems using coupled cluster theory with single, double, and perturbative triple excitations [CCSD(T)]. We evaluate the accuracy of our method by benchmarking it against the canonical CCSD(T) reference for nuclear gradients, dipole moments, and geometry optimizations. In addition, we demonstrate the possibility of property calculations for chemically interesting systems through the computation of bond orders and Mössbauer spectroscopy parameters for a [NiFe]-hydrogenase active site model, along with the simulation of infrared spectra via ab initio LNO-CC molecular dynamics for a protonated water hexamer.

How Does HF-DFT Achieve Chemical Accuracy for Water Clusters?

Bolstered by recent calculations of exact functional-driven errors (FEs) and density-driven errors (DEs) of semilocal density functionals in the water dimer binding energy [Kanungo, B. J. Phys. Chem. Lett. 2024, 15, 323-328], we investigate approximate FEs and DEs in neutral water clusters containing up to 20 monomers, charged water clusters, and alkali- and halide-water clusters. Our proxy for the exact density is r2SCAN 50, a 50% global hybrid of exact exchange with r2SCAN, which may be less correct than r2SCAN for the compact water monomer but importantly more correct for long-range electron transfers in the noncompact water clusters. We show that SCAN makes substantially larger FEs for neutral water clusters than r2SCAN, while both make essentially the same DEs. Unlike the case for barrier heights, these FEs are small in a relative sense and become large in an absolute sense only due to an increase in cluster size. SCAN@HF, short for SCAN evaluated on the Hartree-Fock (HF) density, produces a cancellation of errors that makes it chemically accurate for predicting the absolute binding energies of water clusters. Likewise, adding a long-range dispersion correction to r2SCAN@HF, as in the composite method HF-r2SCAN-DC4, makes its FE more negative than in r2SCAN@HF, permitting a near-perfect cancellation of FE and DE. r2SCAN by itself (and even more so, r2SCAN evaluated on the r2SCAN 50 density), is almost perfect for the energy differences between water hexamers, and thus probably also for liquid water away from the boiling point. Thus, the accuracy of composite methods like SCAN@HF and HF-r2SCAN-DC4 is not due to the HF density being closer to the exact density, but to a compensation of errors from its greater degree of localization. We also give an argument for the approximate reliability of this unconventional error cancellation for diverse molecular properties. Finally, we confirm this unconventional error cancellation for the SCAN description of the water trimer via Kohn-Sham inversion of the CCSD(T) density.

Seamless integration of GEM, a density based-force field, for QM/MM simulations via LICHEM, Psi4, and Tinker-HP.

Hybrid quantum mechanics/molecular mechanics (QM/MM) simulations have become an essential tool in computational chemistry, particularly for analyzing complex biological and condensed phase systems. Building on this foundation, our work presents a novel implementation of the Gaussian Electrostatic Model (GEM), a polarizable density-based force field, within the QM/MM framework. This advancement provides seamless integration, enabling efficient and optimized QM/GEM calculations in a single step using the LICHEM Code. We have successfully applied our implementation to water dimers and hexamers, demonstrating the ability to handle water systems with varying numbers of water molecules. Moreover, we have extended the application to describe the double proton transfer of the aspartic acid dimer in a box of water, which highlights the method's proficiency in investigating heterogeneous systems. Our implementation offers the flexibility to perform on-the-fly density fitting or to utilize pre-fitted coefficients to estimate exchange and Coulomb contributions. This flexibility enhances efficiency and accuracy in modeling molecular interactions, especially in systems where polarization effects are significant.

Water Arrangements upon Interaction with a Rigid Solute: Multiconfigurational Fenchone-(H2O)4-7 Hydrates.

Insight into the arrangements of water molecules around solutes is important to understand how solvation proceeds and to build reliable models to describe water-solute interactions. We report the stepwise solvation of fenchone, a biogenic ketone, with 4-7 water molecules. Multiple hydrates were observed using broadband rotational spectroscopy, and the configurations of four fenchone-(H2O)4, three fenchone-(H2O)5, two fenchone-(H2O)6, and one fenchone-(H2O)7 complexes were characterized from the analysis of their rotational spectra in combination with quantum-chemical calculations. Interactions with fenchone deeply perturb water configurations compared with the pure water tetramer and pentamer. In two fenchone-(H2O)4 complexes, the water tetramer adopts completely new arrangements, and in fenchone-(H2O)5, the water pentamer is no longer close to being planar. The water hexamer interacts with fenchone as the least abundant book isomer, while the water heptamer adopts a distorted prism structure, which forms a water cube when including the fenchone oxygen in the hydrogen bonding network. Differences in hydrogen bonding networks compared with those of pure water clusters show the influence of fenchone's topology. Specifically, all observed hydrates except one show two water molecules binding to fenchone through each oxygen lone pair. The observation of several water arrangements for fenchone-(H2O)4-7 complexes highlights water adaptability and provides insight into the solvation process.

Structure Discovery in Atomic Force Microscopy Imaging of Ice.

The interaction of water with surfaces is crucially important in a wide range of natural and technological settings. In particular, at low temperatures, unveiling the atomistic structure of adsorbed water clusters would provide valuable data for understanding the ice nucleation process. Using high-resolution atomic force microscopy (AFM) and scanning tunneling microscopy, several studies have demonstrated the presence of water pentamers, hexamers, and heptamers (and of their combinations) on a variety of metallic surfaces, as well as the initial stages of 2D ice growth on an insulating surface. However, in all of these cases, the observed structures were completely flat, providing a relatively straightforward path to interpretation. Here, we present high-resolution AFM measurements of several water clusters on Au(111) and Cu(111), whose understanding presents significant challenges due to both their highly 3D configuration and their large size. For each of them, we use a combination of machine learning, atomistic modeling with neural network potentials, and statistical sampling to propose an underlying atomic structure, finally comparing its AFM simulated images to the experimental ones. These results provide insights into the early phases of ice formation, which is a ubiquitous phenomenon ranging from biology to astrophysics.

Edge-sharing water prisms.

Regular-shaped water clusters and nanostructures can be of particular interest for the self-assembly of complex structures and functional materials involving water molecules. Polyhedral water clusters are the most well studied. The low-energy structures of water hexamer, octamer and decamer are shaped like right prisms. The cavities of gas hydrates also have a polyhedral shape. Ice nanotubes are of no less interest both as configurations of global energy minima and in terms of possible applications. This article presents the results of the first systematic study of the structure and properties of a special class of water clusters. It reveals different combinations of three right prisms sharing an edge. According to modern calculations, the configurations of global energy minima of water clusters with the number of molecules being eighteen and twenty have this structure precisely. The topological characteristics of the edge-sharing water prisms are studied and the formulas for estimating the residual entropy are obtained. For these clusters (3-prisms), the usefulness of using a discrete model of intermolecular interaction [strong-weak-effective-bond model], previously developed for polyhedral water clusters, is shown. Calculations of the binding energy were performed using the non-additive Amoeba potential. To understand the relative stability of 3-prisms among other cluster forms, we use the structures recently reported in a published database containing over 3 × 106 unique water cluster networks (H2O)N of size N = 3-25 [Rakshit et al., J. Chem. Phys., 2019, 151(21), 214307, DOI: 10.1063/1.5128378].

Thermal dependence of the hydrated proton and optimal proton transfer in the protonated water hexamer

Water is a key ingredient for life and plays a central role as solvent in many biochemical reactions. However, the intrinsically quantum nature of the hydrogen nucleus, revealing itself in a large variety of physical manifestations, including proton transfer, gives rise to unexpected phenomena whose description is still elusive. Here we study, by a combination of state-of-the-art quantum Monte Carlo methods and path-integral molecular dynamics, the structure and hydrogen-bond dynamics of the protonated water hexamer, the fundamental unit for the hydrated proton. We report a remarkably low thermal expansion of the hydrogen bond from zero temperature up to 300 K, owing to the presence of short-Zundel configurations, characterised by proton delocalisation and favoured by the synergy of nuclear quantum effects and thermal activation. The hydrogen bond strength progressively weakens above 300 K, when localised Eigen-like configurations become relevant. Our analysis, supported by the instanton statistics of shuttling protons, reveals that the near-room-temperature range from 250 K to 300 K is optimal for proton transfer in the protonated water hexamer.

Coupled-Cluster Density-Based Many-Body Expansion.

While CCSD(T) is often considered the "gold standard" of computational chemistry, the scaling of its computational cost as N7 limits its applicability for large and complex molecular systems. In this work, we apply the density-based many-body expansion [ Int. J. Quantum Chem. 2020, 120, e26228] in combination with CCSD(T). The accuracy of this approach is assessed for neutral, protonated, and deprotonated water hexamers, as well as (H2O)16 and (H2O)17 clusters. For the neutral water clusters, we find that already with a density-based two-body expansion, we are able to approximate the supermolecular CCSD(T) energies within chemical accuracy (4 kJ/mol). This surpasses the accuracy that is achieved with a conventional, energy-based three-body expansion. We show that this accuracy can be maintained even when approximating the electron densities using Hartree-Fock instead of using coupled-cluster densities. The density-based many-body expansion thus offers a simple, resource-efficient, and highly parallelizable approach that makes CCSD(T)-quality calculations feasible where they would otherwise be prohibitively expensive.

Implementation of the meta-GGA exchange-correlation functional in numerical atomic orbital basis: With systematic testing on SCAN, rSCAN, and r2SCAN functionals.

Kohn-Sham density functional theory (DFT) is nowadays widely used for electronic structure theory simulations, and the accuracy and efficiency of DFT rely on approximations of the exchange-correlation functional. By including the kinetic energy density τ, the meta-generalized-gradient approximation (meta-GGA) family of functionals achieves better accuracy and flexibility while retaining the efficiency of semi-local functionals. For example, the strongly constrained and appropriately normed (SCAN) meta-GGA functional has been proven to yield accurate results for solid and molecular systems. We implement meta-GGA functionals with both numerical atomic orbitals and plane wave bases in the ABACUS package. Apart from the exchange-correlation potential, we also discuss the evaluation of force and stress. To validate our implementation, we perform finite-difference tests and convergence tests with the SCAN, rSCAN, and r2SCAN meta-GGA functionals. We further test water hexamers, weakly interacting molecules from the S22 dataset, as well as 13 semiconductors using the three functionals. The results show satisfactory agreement with previous calculations and available experimental values.

Equation-of-Motion Block-Correlated Coupled Cluster Method for Excited Electronic States of Strongly Correlated Systems.

An equation-of-motion block-correlated coupled cluster method based on the generalized valence bond wave function (EOM-GVB-BCCC) is proposed to describe low-lying excited states for strongly correlated systems. The EOM-GVB-BCCC2b method with up to two-pair correlation has been implemented and tested for a few strongly correlated systems. For a water hexamer with stretched O-H bonds, which is beyond the capability of the CASSCF method, EOM-GVB-BCCC2b provides very close results as the density matrix renormalization group (DMRG). For four conjugated diradical species with triplet ground states, we found that their vertical S-T gaps from EOM-GVB-BCCC2b are also quite consistent with the DMRG results. This new method is expected to be a promising theoretical tool for describing the low-lying excited states of strongly correlated systems with large active spaces.

A fitting program for structural determination of molecular clusters from rotational spectroscopy

The characterization of the structures of molecular clusters, which serve as building blocks for bulk substances, provides crucial insight into the interactions between constituent units. Chirped-pulse Fourier transform microwave (CP-FTMW) spectroscopy, combined with state-of-the-art quantum chemical calculations, is a powerful tool for characterizing the structures of molecular clusters, as the rotational spectra are directly related to the mass distribution of a molecule or cluster. However, determining the structures of large or complex clusters from experimental rotational spectra remains challenging due to their structural flexibility. Ab initio and density functional theory calculations for searching their stable structures could be significantly time-consuming and method-dependent. To address these challenges, we have developed an approach that relies on the experimental rotational constants to search for potential molecular structures without quantum chemical optimization. Our approach involves creating an initial set of conformers through either a semi-empirical sampling program or the quasi-Monte Carlo method. After-ward, the trust region reflective algorithm is utilized for structure fitting. This procedure enables us to quickly generate potential conformers and gain access to precise structural information. We apply our fitting program to water hexamer and benzaldehyde-water clusters, and the resulting topological structures align extremely well with the experimental results.

Interfacing q-AQUA with a Polarizable Force Field: The Best of Both Worlds.

Polarizable force fields are pervasive in the fields of computational chemistry and biochemistry; however, their empirical or semiempirical nature gives them both weaknesses and strengths. Here, we have developed a hybrid water potential, named q-AQUA-pol, by combining our recent ab initio q-AQUA potential with the TTM3-F water potential. The new potential demonstrates unprecedented accuracy ranging from gas-phase clusters, e.g., the eight low-lying isomers of the water hexamer, to the condensed phase, e.g., radial distribution functions, the self-diffusion coefficient, triplet OOO distribution, and the temperature dependence of the density. This represents a significant advancement in the field of polarizable machine learning potential and computational modeling.

Isotope Effects in the Zundel-Eigen Isomerization of H+(H2O)6.

The isomerization pathway between the energetically low-lying Zundel and Eigen isomers of the protonated water hexamer was investigated using high-level ab initio calculations including a treatment of zero-point corrections. On the basis of these calculations, the Zundel-Eigen isomerization was found to proceed through a stable intermediate isomer, which consists of a four-membered ring with two single acceptor water molecules. The inclusion of vibrational zero-point energy is shown to be important for accurately establishing the relative energies of the three relevant isomers involved in the Zundel-Eigen isomerization. Diffusion Monte Carlo calculations including anharmonic vibrational effects show that all three isomers of H+(H2O)6 and D+(D2O)6 have well-defined structures. The energetic ordering of the three isomers changes upon deuteration. The implications of these results for the vibrational spectra of H+(H2O)6 and D+(D2O)6 are also discussed.

Evolution of Solute-Water Interactions in the Benzaldehyde-(H2O)1-6 Clusters by Rotational Spectroscopy.

The investigation on the preferred arrangement and intermolecular interactions of gas phase solute-water clusters gives insights into the intermolecular potentials that govern the structure and dynamics of the aqueous solutions. Here, we report the investigation of hydrated coordination networks of benzaldehyde-(water)n (n = 1-6) clusters in a pulsed supersonic expansion using broadband rotational spectroscopy. Benzaldehyde (PhCHO) is the simplest aromatic aldehyde that involves both hydrophilic (CHO) and hydrophobic (phenyl ring) functional groups, which can mimic molecules of biological significance. For the n = 1-3 clusters, the water molecules are connected around the hydrophilic CHO moiety of benzaldehyde through a strong CO···HO hydrogen bond and weak CH···OH hydrogen bond(s). For the larger clusters, the spectra are consistent with the structures in which the water clusters are coordinated on the surface of PhCHO with both the hydrophilic CHO and hydrophobic phenyl ring groups being involved in the bonding interactions. The presence of benzaldehyde does not strongly interfere with the cyclic water tetramer and pentamer, which retain the same structure as in the pure water cluster. The book isomer instead of cage or prism isomers of the water hexamer is incorporated into the microsolvated cluster. The PhCHO molecule deviates from the planar structure upon sequential addition of water molecules. The PhCHO-(H2O)1-6 clusters may serve as a simple model system in understanding the solute-water interactions of biologically relevant molecules in an aqueous environment.

Effect of Orientational Isomerism in Neutral Water Hexamers on Their Thermodynamic Properties and Concentrations in the Gas Phase

Effect of Orientational Isomerism in Neutral Water Hexamers on Their Thermodynamic Properties and Concentrations in the Gas Phase

Infrared Spectra at Coupled Cluster Accuracy from Neural Network Representations.

Infrared spectroscopy is key to elucidating molecular structures, monitoring reactions, and observing conformational changes, while providing information on both structural and dynamical properties. This makes the accurate prediction of infrared spectra based on first-principle theories a highly desirable pursuit. Molecular dynamics simulations have proven to be a particularly powerful approach for this task, albeit requiring the computation of energies, forces and dipole moments for a large number of molecular configurations as a function of time. This explains why highly accurate first-principles methods, such as coupled cluster theory, have so far been inapplicable for the prediction of fully anharmonic vibrational spectra of large systems at finite temperatures. Here, we push cutting-edge machine learning techniques forward by using neural network representations of energies, forces, and in particular dipoles to predict such infrared spectra fully at "gold standard" coupled cluster accuracy as demonstrated for protonated water clusters as large as the protonated water hexamer, in its extended Zundel configuration. Furthermore, we show that this methodology can be used beyond the scope of the data considered during the development of the neural network models, allowing for the computation of finite-temperature infrared spectra of large systems inaccessible to explicit coupled cluster calculations. This substantially expands the hitherto existing limits of accuracy, speed, and system size for theoretical spectroscopy and opens up a multitude of avenues for the prediction of vibrational spectra and the understanding of complex intra- and intermolecular couplings.

Multicomponent Orbital-Optimized Perturbation Theory with Density Fitting: Anharmonic Zero-Point Energies in Protonated Water Clusters.

Nuclear quantum effects such as zero-point energy are important in a wide range of chemical and biological processes. The nuclear-electronic orbital (NEO) framework intrinsically includes such effects by treating electrons and specified nuclei quantum mechanically on the same level. Herein, we implement the NEO scaled-opposite-spin orbital-optimized second-order Møller-Plesset perturbation theory with electron-proton correlation scaling (NEO-SOS'-OOMP2) using density fitting. This efficient implementation allows applications to larger systems with multiple quantum protons. Both the NEO-SOS'-OOMP2 method and its counterpart without orbital optimization predict proton affinities to within experimental precision and relative energies of protonated water tetramer isomers in agreement with previous NEO coupled cluster calculations. Applications to protonated water hexamers and heptamers illustrate that anharmonicity is critical for computing accurate relative energies. The NEO-SOS'-OOMP2 approach captures anharmonic zero-point energies at any geometry in a computationally efficient manner and hence will be useful for investigating reaction paths and dynamics in chemical systems.

Q-AQUA: A Many-Body CCSD(T) Water Potential, Including Four-Body Interactions, Demonstrates the Quantum Nature of Water from Clusters to the Liquid Phase.

Many model potential energy surfaces (PESs) have been reported for water; however, none are strictly from "first-principles". Here we report such a potential, based on a many-body representation at the CCSD(T) level of theory up to the four-body interaction. The new PES is benchmarked for the isomers of the water hexamer for dissociation energies, harmonic frequencies, and unrestricted diffusion Monte Carlo (DMC) calculations of the zero-point energies of the Prism, Book, and Cage isomers. Dissociation energies of several isomers of the 20-mer agree well with recent benchmark energies. Exploratory DMC calculations on this cluster verify the robustness of the new PES for quantum simulations. The accuracy and speed of the new PES are demonstrated for standard condensed phase properties, i.e., the radial distribution function and the self-diffusion constant. Quantum effects are shown to be substantial for these observables and also needed to bring theory into excellent agreement with experiment.

Water Network Shape-Dependence of Local Interactions with the Microhydrated -NO2- and -CO2- Anionic Head Groups by Cold Ion Vibrational Spectroscopy.

We report the structural evolutions of water networks and solvatochromic response of the CH3NO2- radical anion in the OH and CH stretching regions by analysis of the vibrational spectra displayed by cryogenically cooled CH3NO2-·(H2O)n=1-6 clusters. The OH stretching bands evolve with a surprisingly large discontinuity at n = 6, which features the emergence of an intense, strongly red-shifted band along with a weaker feature that appears in the region assigned to a free OH fundamental. Very similar behavior is displayed by the perdeuterated carboxylate clusters, RCO2-·(H2O)n=5-7 (R = CD3CD2), indicating that this behavior is a general feature in the microhydration of the triatomic anionic domain and not associated with CH oscillators. Electronic structure calculations trace this behavior to the formation of a "book" isomer of the water hexamer that adopts a configuration in which one of the water molecules resides in an acceptor-acceptor-donor (AAD) (A = acceptor, D = donor) H-bonding site. Excitation of the bound OH in the AAD site explores the local network topology best suited to stabilize an incipient -XO2H-OH-(H2O)2 intracluster proton-transfer reaction. These systems thus provide particularly clear examples where the network shape controls the potential energy landscape that governs water network-mediated, intracluster proton transfer. The CH stretching bands of the CH3NO2-·(H2O)n=1-6 clusters also exhibit strong solvatochromic shifts, but in this case, they smoothly blue-shift with increasing hydration with no discontinuity at n = 6. This behavior is analyzed in the context of the solute-ion polarizability response and partial charge transfer to the water networks.