Quantum Dynamics and Spectroscopy of Ab Initio Liquid Water: The Interplay of Nuclear and Electronic Quantum Effects

Quantum kinetic energy and isotope fractionation in aqueous ionic solutions

At room temperature, the quantum contribution to the kinetic energy of a water molecule exceeds the classical contribution by an order of magnitude. The quantum kinetic energy (QKE) of a water molecule is modulated by its local chemical environment and leads to uneven partitioning of isotopes between different phases in thermal equilibrium, which would not occur if the nuclei behaved classically. In this work, we use ab initio path integral simulations to show that QKEs of the water molecules and the equilibrium isotope fractionation ratios of the oxygen and hydrogen isotopes are sensitive probes of the hydrogen bonding structures in aqueous ionic solutions. In particular, we demonstrate how the QKE of water molecules in path integral simulations can be decomposed into translational, rotational and vibrational degrees of freedom, and use them to determine the impact of solvation on different molecular motions. By analyzing the QKEs and isotope fractionation ratios, we show how the addition of the Na⁺, Cl^- and HPO₄^2- ions perturbs the competition between quantum effects in liquid water and impacts their local solvation structures.

Nuclear Quantum Effects from the Analysis of Smoothed Trajectories: Pilot Study for Water

Nuclear quantum effects have significant contributions to thermodynamic quantities and structural properties; furthermore, very expensive methods are necessary for their accurate computation. In most calculations, these effects, for instance, zero-point energies, are simply neglected or only taken into account within the quantum harmonic oscillator approximation. Herein, we present a new method, Generalized Smoothed Trajectory Analysis, to determine nuclear quantum effects from molecular dynamics simulations. The broad applicability is demonstrated with the examples of a harmonic oscillator and different states of water. Ab initio molecular dynamics simulations have been performed for ideal gas up to the temperature of 5000 K. Classical molecular dynamics have been carried out for hexagonal ice, liquid water, and vapor at atmospheric pressure. With respect to the experimental heat capacity, our method outperforms previous calculations in the literature in a wide temperature range at lower computational cost than other alternatives. Dynamic and structural nuclear quantum effects of water are also discussed.

Self-interaction error overbinds water clusters but cancels in structural energy differences

We gauge the importance of self-interaction errors in density functional approximations (DFAs) for the case of water clusters. To this end, we used the Fermi-Löwdin orbital self-interaction correction method (FLOSIC) to calculate the binding energy of clusters of up to eight water molecules. Three representative DFAs of the local, generalized gradient, and metageneralized gradient families [i.e., local density approximation (LDA), Perdew-Burke-Ernzerhof (PBE), and strongly constrained and appropriately normed (SCAN)] were used. We find that the overbinding of the water clusters in these approximations is not a density-driven error. We show that, while removing self-interaction error does not alter the energetic ordering of the different water isomers with respect to the uncorrected DFAs, the resulting binding energies are corrected toward accurate reference values from higher-level calculations. In particular, self-interaction-corrected SCAN not only retains the correct energetic ordering for water hexamers but also reduces the mean error in the hexamer binding energies to less than 14 meV/[Formula: see text] from about 42 meV/[Formula: see text] for SCAN. By decomposing the total binding energy into many-body components, we find that large errors in the two-body interaction in SCAN are significantly reduced by self-interaction corrections. Higher-order many-body errors are small in both SCAN and self-interaction-corrected SCAN. These results indicate that orbital-by-orbital removal of self-interaction combined with a proper DFA can lead to improved descriptions of water complexes.

Molecular Structure and Modeling of Water-Air and Ice-Air Interfaces Monitored by Sum-Frequency Generation

From a glass of water to glaciers in Antarctica, water-air and ice-air interfaces are abundant on Earth. Molecular-level structure and dynamics at these interfaces are key for understanding many chemical/physical/atmospheric processes including the slipperiness of ice surfaces, the surface tension of water, and evaporation/sublimation of water. Sum-frequency generation (SFG) spectroscopy is a powerful tool to probe the molecular-level structure of these interfaces because SFG can specifically probe the topmost interfacial water molecules separately from the bulk and is sensitive to molecular conformation. Nevertheless, experimental SFG has several limitations. For example, SFG cannot provide information on the depth of the interface and how the orientation of the molecules varies with distance from the surface. By combining the SFG spectroscopy with simulation techniques, one can directly compare the experimental data with the simulated SFG spectra, allowing us to unveil the molecular-level structure of water-air and ice-air interfaces. Here, we present an overview of the different simulation protocols available for SFG spectra calculations. We systematically compare the SFG spectra computed with different approaches, revealing the advantages and disadvantages of the different methods. Furthermore, we account for the findings through combined SFG experiments and simulations and provide future challenges for SFG experiments and simulations at different aqueous interfaces.

Inexpensive modeling of quantum dynamics using path integral generalized Langevin equation thermostats

The properties of molecules and materials containing light nuclei are affected by their quantum mechanical nature. Accurate modeling of these quantum nuclear effects requires computationally demanding path integral techniques. Considerable success has been achieved in reducing the cost of such simulations by using generalized Langevin dynamics to induce frequency-dependent fluctuations. Path integral generalized Langevin equation methods, however, have this far been limited to the study of static, thermodynamic properties due to the large perturbation to the system's dynamics induced by the aggressive thermostatting. Here, we introduce a post-processing scheme, based on analytical estimates of the dynamical perturbation induced by the generalized Langevin dynamics, which makes it possible to recover meaningful time correlation properties from a thermostatted trajectory. We show that this approach yields spectroscopic observables for model and realistic systems that have an accuracy comparable to much more demanding approximate quantum dynamics techniques based on full path integral simulations.

Raman spectrum and polarizability of liquid water from deep neural networks

Using deep neural networks to model the polarizability and potential energy surfaces, we compute the Raman spectrum of liquid water at several temperatures with ab initio molecular dynamics accuracy.

Similarities and differences between potassium and ammonium ions in liquid water: a first-principles study

Understanding ion solvation in liquid water is critical in optimizing materials for a wide variety of emerging technologies, including water desalination and purification.

Quantifying the hydration structure of sodium and potassium ions: taking additional steps on Jacob's Ladder

The ability to reproduce the experimental structure of water around the sodium and potassium ions is a key test of the quality of interaction potentials due to the central importance of these ions in a wide range of important phenomena.

Vibrational mode frequency correction of liquid water in density functional theory molecular dynamics simulations with van der Waals correction

We develop a frequency correction scheme for the stretch and bending modes of liquid water, which substantially improves the prediction of the vibrational spectra.

Ab initio spectroscopy of water under electric fields

Whereas a broad range of literature exists on the spectroscopy of water in disparate conditions, infrared (IR) and Raman spectra of water subjected to electric fields have never extensively been investigated so far. Based on ab initio molecular dynamics simulations, here we present IR and Raman spectra of bulk liquid water under the effect of static electric fields. A contraction of the entire frequency range is recorded upon increasing the field intensity both in the IR and in the Raman spectra. Whilst the OH stretching band is progressively shifted toward lower frequencies - indicating a field-induced strengthening of the H-bond network - all the other bands are up-shifted by the field. Furthermore, an evident modification of the librational mode band appears in all the spectra. Finally, the order-maker action of the field emerges also from the increase of the water orientational tetrahedral order. Upon field exposure, the water structure becomes more "ice like".

Accessing the Accuracy of Density Functional Theory through Structure and Dynamics of the Water-Air Interface

Density functional theory-based molecular dynamics simulations are increasingly being used for simulating aqueous interfaces. Nonetheless, the choice of the appropriate density functional, critically affecting the outcome of the simulation, has remained arbitrary. Here, we assess the performance of various exchange-correlation (XC) functionals, based on the metrics relevant to sum-frequency generation spectroscopy. The structure and dynamics of water at the water-air interface are governed by heterogeneous intermolecular interactions, thereby providing a critical benchmark for XC functionals. We find that the XC functionals constrained by exact functional conditions (revPBE and revPBE0) with the dispersion correction show excellent performance. The poor performance of the empirically optimized density functional (M06-L) indicates the importance of satisfying the exact functional condition. Understanding the performance of different XC functionals can aid in resolving the controversial interpretation of the interfacial water structure and direct the design of novel, improved XC functionals better suited to describing the heterogeneous interactions in condensed phases.

Low-order many-body interactions determine the local structure of liquid water

Two-body and three-body energies, modulated by higher-body terms and nuclear quantum effects, determine the structure of liquid water and require sub-chemical accuracy that is achieved by the MB-pol model but not by existing DFT functionals.

Despite its apparent simplicity, water displays unique behavior across the phase diagram which is strictly related to the ability of the water molecules to form dense, yet dynamic, hydrogen-bond networks that continually fluctuate in time and space. The competition between different local hydrogen-bonding environments has been hypothesized as a possible origin of the anomalous properties of liquid water. Through a systematic application of the many-body expansion of the total energy, we demonstrate that the local structure of liquid water at room temperature is determined by a delicate balance between two-body and three-body energies, which is further modulated by higher-order many-body effects. Besides providing fundamental insights into the structure of liquid water, this analysis also emphasizes that a correct representation of two-body and three-body energies requires sub-chemical accuracy that is nowadays only achieved by many-body models rigorously derived from the many-body expansion of the total energy, which thus hold great promise for shedding light on the molecular origin of the anomalous behavior of liquid water.

Hydration-Shell Vibrational Spectroscopy

Hydration-shell vibrational spectroscopy provides an experimental window into solute-induced water structure changes that mediate aqueous folding, binding, and self-assembly. Decomposition of measured Raman and infrared (IR) spectra of aqueous solutions using multivariate curve resolution (MCR) and related methods may be used to obtain solute-correlated spectra revealing solute-induced perturbations of water structure, such as changes in water hydrogen-bond strength, tetrahedral order, and the presence of dangling (non-hydrogen-bonded) OH groups. More generally, vibrational-MCR may be applied to both aqueous and nonaqueous solutions, including multicomponent mixtures, to quantify solvent-mediated interactions between oily, polar, and ionic solutes, in both dilute and crowded fluids. Combining vibrational-MCR with emerging theoretical modeling strategies promises synergetic advances in the predictive understanding of multiscale self-assembly processes of both biological and technological interest.

Beyond Badger's Rule: The Origins and Generality of the Structure-Spectra Relationship of Aqueous Hydrogen Bonds

The structure of hydrogen bonded networks is intimately intertwined with their dynamics. Despite the incredibly wide range of hydrogen bond strengths encountered in water clusters, ion-water clusters, and liquid water, we demonstrate that the previously reported correlation between the change in the equilibrium bond length of the hydrogen bonded OH covalent bond and the corresponding shift in its harmonic frequency in water clusters is much more broadly applicable. Surprisingly, this correlation describes the ratios for both the equilibrium OH bond length/harmonic frequency and the vibrationally averaged bond length/anharmonic frequency in water, hydronium water, and halide water clusters. Consideration of harmonic and anaharmonic data leads to a correlation of -19 ± 1 cm^-1/0.001 Å. The fundamental nature of this correlation is further confirmed through the analysis of ab initio Molecular Dynamics (AIMD) trajectories for liquid water. We demonstrate that this simple correlation for both harmonic and anharmonic systems can be modeled by the response of an OH bond to an external field. Treating the OH bond as a Morse oscillator, we develop analytic expressions, which relate the ratio of the shift in the vibrational frequency of the hydrogen-bonded OH bond to the shift in OH bond length, to parameters in the Morse potential and the ratio of the first and second derivatives of the field-dependent projection of the dipole moment of water onto the hydrogen-bonded OH bond. Based on our analysis, we develop a protocol for reconstructing the AIMD spectra of liquid water from the sampled distribution of the OH bond lengths. Our findings elucidate the origins of the relationship between the molecular structure of the fleeting hydrogen-bonded network and the ensuing dynamics, which can be probed by vibrational spectroscopy.

Isotope effect on hydrogen bond symmetrization in hydrogen and deuterium fluoride crystals by molecular dynamics simulation

The isotope effect on the collective proton/deuteron transfer in hydrogen and deuterium fluoride crystals has been investigated at 100 K by ab initio quantum-thermal-bath path-integral molecular dynamics (QTB-PIMD) simulation. The deuterons within a planar zigzag chain of the orthorhombic structure simultaneously flip between covalent and hydrogen bonds due to the barrier crossing through tunnelling. The height of the corresponding static barrier normalized for one deuteron is 29.2 meV. In the HF crystal, all the protons are located at the center of the heavy-atom distance. This evidences the symmetrization of the H-bonds, and indicates that the proton zero-point energy is above the barrier top. The decrease of the heavy-atom distance due to quantum fluctuations in both HF and DF crystals corresponds to a large decrease and an increase of the hydrogen and covalent bond lengths, respectively. Upon deuteration, the increase of the heavy-atom distance (Ubbelohde effect) is in agreement with experimental data.

Ab initio thermodynamics of liquid and solid water

Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations, and proton disorder. This is made possible by combining advanced free-energy methods and state-of-the-art machine-learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments and reliable estimates of the melting points of light and heavy water. We observe that nuclear-quantum effects contribute a crucial [Formula: see text] to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine-learning potentials as an intermediate step.

The Quest for Accurate Liquid Water Properties from First Principles

Developing accurate ab initio molecular dynamics (AIMD) models that capture both electronic reorganization and nuclear quantum effects associated with hydrogen bonding is key to quantitative understanding of bulk water and its anomalies as well as its role as a universal solvent. For condensed phase simulations, AIMD has typically relied on the generalized gradient approximation (GGA) of density functional theory (DFT) as the underlying model chemistry for the potential energy surface, with nuclear quantum effects (NQEs) sometimes modeled by performing classical molecular dynamics simulations at elevated temperatures. Here we show that the properties of liquid water obtained from the meta-GGA B97M-rV functional, when evaluated using accelerated path integral molecular dynamics simulations, display accuracy comparable to a computationally expensive dispersion-corrected hybrid functional, revPBE0-D3. We show that the meta-GGA DFT functional reproduces bulk water properties including radial distribution functions, self-diffusion coefficients, and infrared spectra with comparable accuracy of a much more expensive hybrid functional. This work demonstrates that the underlying quality of a good DFT functional requires evaluation with quantum nuclei and that high-temperature simulations are a poor proxy for properly treating NQEs.

Decoding the spectroscopic features and time scales of aqueous proton defects

Acid solutions exhibit a variety of complex structural and dynamical features arising from the presence of multiple interacting reactive proton defects and counterions. However, disentangling the transient structural motifs of proton defects in the water hydrogen bond network and the mechanisms for their interconversion remains a formidable challenge. Here, we use simulations treating the quantum nature of both the electrons and nuclei to show how the experimentally observed spectroscopic features and relaxation time scales can be elucidated using a physically transparent coordinate that encodes the overall asymmetry of the solvation environment of the proton defect. We demonstrate that this coordinate can be used both to discriminate the extremities of the features observed in the linear vibrational spectrum and to explain the molecular motions that give rise to the interconversion time scales observed in recent nonlinear experiments. This analysis provides a unified condensed-phase picture of the proton structure and dynamics that, at its extrema, encompasses proton sharing and spectroscopic features resembling the limiting Eigen [H₃O(H₂O)₃]⁺ and Zundel [H(H₂O)₂]⁺ gas-phase structures, while also describing the rich variety of interconverting environments in the liquid phase.

First-Principles Simulations of Liquid Water Using a Dielectric-Dependent Hybrid Functional

We carried out first-principles simulations of liquid water under ambient conditions using a dielectric-dependent hybrid functional, where the fraction of exact exchange is set equal to the inverse of the high-frequency dielectric constant of the liquid. We found excellent agreement with experiment for the oxygen-oxygen partial correlation function at the experimental equilibrium density and 311 ± 3 K. Other structural and dynamical properties, such as the diffusion coefficient, molecular dipole moments, and vibrational spectra, are also in good agreement with experiment. Our results, together with previous findings on electronic properties of the liquid with the same functional, show that the dielectric-dependent hybrid functional accurately describes both the structural and electronic properties of liquid water.

Unusual Influence of Fluorinated Anions on the Stretching Vibrations of Liquid Water

Infrared (IR) spectroscopy is a commonly used and invaluable tool in the studies of solvation phenomena in aqueous solutions. Concurrently, ab initio molecular dynamics (AIMD) simulations deliver the solvation shell picture at a molecular detail level and allow for a consistent decomposition of the theoretical IR spectrum into underlying spatial correlations. Here, we demonstrate how the novel spectral decomposition techniques can extract important information from the computed IR spectra of aqueous solutions of BF₄^- and PF₆^-, interesting weakly coordinating anions that have been known for a long time to alter the IR spectrum of water in an unusual manner. The distance-dependent spectra of both ions are analyzed using the spectral similarity method that provides a quantitative picture of both the spectrum of the solute-affected solvent and the number of solvent molecules thus altered. We find, in accordance with previous experiments, a considerable blue shift of the ν_OH stretching band of liquid water by 264 cm^-1 for BF₄^- and 306 cm^-1 for PF₆^-, with the affected numbers being 3.7 and 4.2, respectively. Considering also the additional information on solute-solvent dipolar couplings delivered by radially and spatially resolved IR spectra, the computational IR spectroscopy based on AIMD simulations is shown to be a viable predictive tool with strong interpretative power.

The Interplay of Structure and Dynamics in the Raman Spectrum of Liquid Water over the Full Frequency and Temperature Range

While many vibrational Raman spectroscopy studies of liquid water have investigated the temperature dependence of the high-frequency O-H stretching region, few have analyzed the changes in the Raman spectrum as a function of temperature over the entire spectral range. Here, we obtain the Raman spectra of water from its melting to boiling point, both experimentally and from simulations using an ab initio-trained machine learning potential. We use these to assign the Raman bands and show that the entire spectrum can be well described as a combination of two temperature-independent spectra. We then assess which spectral regions exhibit strong dependence on the local tetrahedral order in the liquid. Further, this work demonstrates that changes in this structural parameter can be used to elucidate the temperature dependence of the Raman spectrum of liquid water and provides a guide to the Raman features that signal water ordering in more complex aqueous systems.

Real single ion solvation free energies with quantum mechanical simulation

Single ion solvation free energies are one of the most important properties of electrolyte solutions and yet there is ongoing debate about what these values are. Only the values for neutral ion pairs are known. Here, we use DFT interaction potentials with molecular dynamics simulation (DFT-MD) combined with a modified version of the quasi-chemical theory (QCT) to calculate these energies for the lithium and fluoride ions. A method to correct for the error in the DFT functional is developed and very good agreement with the experimental value for the lithium fluoride pair is obtained. Moreover, this method partitions the energies into physically intuitive terms such as surface potential, cavity and charging energies which are amenable to descriptions with reduced models. Our research suggests that lithium's solvation free energy is dominated by the free energetics of a charged hard sphere, whereas fluoride exhibits significant quantum mechanical behavior that cannot be simply described with a reduced model.

CO2 Hydration Shell Structure and Transformation

The hydration-shell of CO₂ is characterized using Raman multivariate curve resolution (Raman-MCR) spectroscopy combined with ab initio molecular dynamics (AIMD) vibrational density of states simulations, to validate our assignment of the experimentally observed high-frequency OH band to a weak hydrogen bond between water and CO₂. Our results reveal that while the hydration-shell of CO₂ is highly tetrahedral, it is also occasionally disrupted by the presence of entropically stabilized defects associated with the CO₂-water hydrogen bond. Moreover, we find that the hydration-shell of CO₂ undergoes a temperature-dependent structural transformation to a highly disordered (less tetrahedral) structure, reminiscent of the transformation that takes place at higher temperatures around much larger oily molecules. The biological significance of the CO₂ hydration shell structural transformation is suggested by the fact that it takes place near physiological temperatures.