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

Temperature-dependent vibrational energy relaxation of hydrogen-bonded and free OD groups at the air-water interface

Water interfaces play a crucial role in regulating interactions and energy flow. Vibrational sum-frequency generation (vSFG) spectroscopy provides structural and dynamic information on water molecules at interfaces. It has revealed, for instance, the presence of the hydrogen-bonded and free OH groups at the air-water interface. Here, using temperature-dependent, time-resolved vSFG, we focus on the vibrational energy relaxation dynamics of interfacial heavy water (D2O). We reveal that while the relaxation timescale for hydrogen-bonded OD stretch modes is temperature-independent, the lifetime of the free OD stretch mode decreases with increasing temperature. Our data, supported by simulations, suggest that both intramolecular energy transfer and rotational reorientation mechanisms jointly contribute to the energy relaxation process of the free OD, with temperature influencing these mechanisms differently.

Revisiting the Thickness of the Air-Water Interface from Two Extremes of Interface Hydrogen Bond Dynamics

The air-water interface plays a crucial role in many aspects of science because of its unique properties, such as a two-dimensional hydrogen bond (HB) network and completely different HB dynamics compared to bulk water. However, accurately determining the boundary of interfacial and bulk water, that is, the thickness of the air-water interface, still challenges experimentalists. Various simulation-based methods have been developed to estimate the thickness, converging on a range of approximately 3-10 (Å). In this study, we introduce a novel approach, grounded in density functional theory-based molecular dynamics and deep potential molecular dynamics simulations, to measure the air-water interface thickness, offering a different perspective based on prior research. To capture realistic HB dynamics in the air-water interface, two extreme scenarios of the interface HB dynamics are obtained: one underestimates the interface HB dynamics, while the other overestimates it. Surprisingly, our results suggest that the interface HB dynamics in both scenarios converges as the thickness of the air-water interface increases to 4 (Å). This convergence point, indicative of the realistic interface thickness, is also validated by our calculation of anisotropic decay of OH stretch and the free OH dynamics at the air-water interface.

Revealing the molecular structures of α-Al2O3(0001)-water interface by machine learning based computational vibrational spectroscopy

Solid-water interfaces are crucial to many physical and chemical processes and are extensively studied using surface-specific sum-frequency generation (SFG) spectroscopy. To establish clear correlations between specific spectral signatures and distinct interfacial water structures, theoretical calculations using molecular dynamics (MD) simulations are required. These MD simulations typically need relatively long trajectories (a few nanoseconds) to achieve reliable SFG response function calculations via the dipole moment-polarizability time correlation function. However, the requirement for long trajectories limits the use of computationally expensive techniques, such as ab initio MD (AIMD) simulations, particularly for complex solid-water interfaces. In this work, we present a pathway for calculating vibrational spectra (IR, Raman, and SFG) of solid-water interfaces using machine learning (ML)-accelerated methods. We employ both the dipole moment-polarizability correlation function and the surface-specific velocity-velocity correlation function approaches to calculate SFG spectra. Our results demonstrate the successful acceleration of AIMD simulations and the calculation of SFG spectra using ML methods. This advancement provides an opportunity to calculate SFG spectra for complicated solid-water systems more rapidly and at a lower computational cost with the aid of ML.

Water-air interface revisited by means of path-integral ab initio molecular dynamics

Although nuclear quantum effects (NQEs) have been considered on bulk liquid water, the impact of these latter on the air-water interface has not yet been reported. Herein, by performing and comparing ab initio molecular dynamics (AIMD) and path integral AIMD (PI-AIMD) simulations, we reveal the impact of NQEs on structural, dynamical and electronic properties as well as IR spectra of the air-water interface at room temperature. NQEs, being able to describe a more accurate proton delocalization in H-bonded system than AIMD, reveal a different structural arrangement and dynamical behaviour of both bulk and interfacial water molecules in comparison to AIMD results. A more de-structured and de-bound water arrangement and coordination are identified when the quantum nature of nuclei are considered for both bulk and interfacial water molecules. Structural properties, such as inter-/intra-molecular bond lengths, coordination numbers and H-bonding angles of bulk and interfacial water molecules here calculated, are affected by NQEs mitigating the overstructured description given by AIMD. Further evidences of an AIMD overstructured description of bulk water are in the computed IR spectra, where an increased absorption peak intensity and an increased strength of the hydrogen-bond network are alleviated by NQEs. In addition, NQEs show a valuable impact on the electronic structure of the air-water interface, reducing the total valence bandwidth and the electronic energy band-gap when passing from bulk to interfacial water. This work proves how NQEs significantly affect properties and features of the air-water interface, that are essential to accurately describe H-bonded interfacial systems.

Nuclear Quantum Effects on the Electronic Structure of Water and Ice

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of the hydrogen atoms. Despite numerous previous studies, a comprehensive understanding of the nuclear quantum effects (NQEs) on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness efficient machine-learning potentials and many-body perturbation theory to assess how NQEs impact the electronic bands of water and hexagonal ice. By comparing path-integral and classical simulations, we find that NQEs lead to a larger renormalization of the fundamental gap of ice, compared to that of water, ultimately yielding similar bandgaps in the two systems, consistent with experimental estimates. Our calculations suggest that the increased quantum mechanical delocalization of protons in ice, relative to water, is a key factor leading to the enhancement of NQEs on the electronic structure of ice.

Nuclear quantum effects on the vibrational dynamics of the water-air interface

We have applied path-integral molecular dynamics simulations to investigate the impact of nuclear quantum effects on the vibrational dynamics of water molecules at the water-air interface. The instantaneous fluctuations in the frequencies of the O-H stretch modes are calculated using the wavelet method of time series analysis, while the time scales of vibrational spectral diffusion are determined from frequency-time correlation functions and joint probability distributions. We find that the inclusion of nuclear quantum effects leads not only to a redshift in the vibrational frequency distribution by about 120 cm-1 for both the bulk and interfacial water molecules but also to an acceleration of the vibrational dynamics at the water-air interface by as much as 35%. In addition, a blueshift of about 45 cm-1 is seen in the vibrational frequency distribution of interfacial water molecules compared to that of the bulk. Furthermore, the dynamics of water molecules beyond the topmost molecular layer was found to be rather similar to that of bulk water.

Surface stratification determines the interfacial water structure of simple electrolyte solutions

The distribution of ions at the air/water interface plays a decisive role in many natural processes. Several studies have reported that larger ions tend to be surface-active, implying ions are located on top of the water surface, thereby inducing electric fields that determine the interfacial water structure. Here we challenge this view by combining surface-specific heterodyne-detected vibrational sum-frequency generation with neural network-assisted ab initio molecular dynamics simulations. Our results show that ions in typical electrolyte solutions are, in fact, located in a subsurface region, leading to a stratification of such interfaces into two distinctive water layers. The outermost surface is ion-depleted, and the subsurface layer is ion-enriched. This surface stratification is a key element in explaining the ion-induced water reorganization at the outermost air/water interface.

Art, fact and artifact: reflections on the cross-talk between theory and experiment

With the increasing sophistication of each, theory and experiment have become highly specialized endeavors conducted by separate research groups. A result has been a weakening of the coupling between them and occasional hostility. Examples are given and suggestions are offered for strengthening the traditional synergy between theory and experiment.

Neural Network-Based Sum-Frequency Generation Spectra of Pure and Acidified Water Interfaces with Air

The affinity of hydronium ions (H3O+) for the air-water interface is a crucial question in environmental chemistry. While sum-frequency generation (SFG) spectroscopy has been instrumental in indicating the preference of H3O+ for the interface, key questions persist regarding the molecular origin of the SFG spectral changes in acidified water. Here we combine nanosecond long neural network (NN) reactive simulations of pure and acidified water slabs with NN predictions of molecular dipoles and polarizabilities to calculate SFG spectra of long reactive trajectories including proton transfer events. Our simulations show that H3O+ ions cause two distinct changes in phase-resolved SFG spectra: first, a low-frequency tail due to the vibrations of H3O+ and its first hydration shell, analogous to the bulk proton continuum, and second, an enhanced hydrogen-bonded band due to the ion-induced static field polarizing molecules in deeper layers. Our calculations confirm that changes in the SFG spectra of acidic solutions are caused by hydronium ions preferentially residing at the interface.

First-principles spectroscopy of aqueous interfaces using machine-learned electronic and quantum nuclear effects

Vibrational spectroscopy is a powerful approach to visualising interfacial phenomena. However, extracting structural and dynamical information from vibrational spectra is a challenge that requires first-principles simulations, including non-Condon and quantum nuclear effects. We address this challenge by developing a machine-learning enhanced first-principles framework to speed up predictive modelling of infrared, Raman, and sum-frequency generation spectra. Our approach uses machine learning potentials that encode quantum nuclear effects to generate quantum trajectories using simple molecular dynamics efficiently. In addition, we reformulate bulk and interfacial selection rules to express them unambiguously in terms of the derivatives of polarisation and polarisabilities of the whole system and predict these derivatives efficiently using fully-differentiable machine learning models of dielectric response tensors. We demonstrate our framework's performance by predicting the IR, Raman, and sum-frequency generation spectra of liquid water, ice and the water-air interface by achieving near quantitative agreement with experiments at nearly the same computational efficiency as pure classical methods. Finally, to aid the experimental discovery of new phases of nanoconfined water, we predict the temperature-dependent vibrational spectra of monolayer water across the solid-hexatic-liquid phases transition.

Raman and IR spectra of water under graphene nanoconfinement at ambient and extreme pressure-temperature conditions: a first-principles study

The nanoconfinement of water can result in dramatic differences in its physical and chemical properties compared to bulk water. However, a detailed molecular-level understanding of these properties is still lacking. Vibrational spectroscopy, such as Raman and infrared, is a popular experimental tool for studying the structure and dynamics of water, and is often complemented by atomistic simulations to interpret experimental spectra, but there have been few theoretical spectroscopy studies of nanoconfined water using first-principles methods at ambient conditions, let alone under extreme pressure-temperature conditions. Here, we compute the Raman and IR spectra of water nanoconfined by graphene at ambient and extreme pressure-temperature conditions using ab initio simulations. Our results revealed alterations in the Raman stretching and low-frequency bands due to the graphene confinement. We also found spectroscopic evidence indicating that nanoconfinement considerably changes the tetrahedral hydrogen bond network, which is typically found in bulk water. Furthermore, we observed an unusual bending band in the Raman spectrum at ∼10 GPa and 1000 K, which is attributed to the unique molecular structure of confined ionic water. Additionally, we found that at ∼20 GPa and 1000 K, confined water transformed into a superionic fluid, making it challenging to identify the IR stretching band. Finally, we computed the ionic conductivity of confined water in the ionic and superionic phases. Our results highlight the efficacy of Raman and IR spectroscopy in studying the structure and dynamics of nanoconfined water in a large pressure-temperature range. Our predicted Raman and IR spectra can serve as a valuable guide for future experiments.

Multiscale Modeling of Aqueous Electric Double Layers

From the stability of colloidal suspensions to the charging of electrodes, electric double layers play a pivotal role in aqueous systems. The interactions between interfaces, water molecules, ions and other solutes making up the electrical double layer span length scales from Ångströms to micrometers and are notoriously complex. Therefore, explaining experimental observations in terms of the double layer's molecular structure has been a long-standing challenge in physical chemistry, yet recent advances in simulations techniques and computational power have led to tremendous progress. In particular, the past decades have seen the development of a multiscale theoretical framework based on the combination of quantum density functional theory, force-field based simulations and continuum theory. In this Review, we discuss these theoretical developments and make quantitative comparisons to experimental results from, among other techniques, sum-frequency generation, atomic-force microscopy, and electrokinetics. Starting from the vapor/water interface, we treat a range of qualitatively different types of surfaces, varying from soft to solid, from hydrophilic to hydrophobic, and from charged to uncharged.

Confining He Atoms in Diverse Ice-Phases: Examining the Stability of He Hydrate Crystals through DFT Approaches

In the realm of solid water hydrostructures, helium atoms have a tendency to occupy the interstitial spaces formed within the crystal lattice of ice structures. The primary objective of this study is to examine the stability of various ice crystals when influenced by the presence of He atoms. Presenting a first attempt at a detailed computational description of the whole energy components (guest-water, water-water, guest-guest) in the complete crystal unit cells contributes to enhancing the knowledge available about these relatively unexplored helium-water systems, which could potentially benefit future experiments. For this purpose, two different ice structures were considered: the previously established He@ice II system, and the predicted (but currently nonexistent) He@ice XVII system. One of the main features of these He-filled structures is the stability conferred by the weak van der Waals dispersion forces that occur between the host lattice and the guest atoms, in addition to the hydrogen bonds established among the water molecules. Hence, it is crucial to accurately describe these interactions. Therefore, the first part of this research is devoted examining the performance and accuracy of various semi-local and non-local DFT/DFT-D functionals, in comparison with previous experimental and/or high-level computational data. Once the best-performing DFT functional has been identified, the stability of these empty and He-filled structures, including different number of He atoms within the lattices, is analysed in terms of their structural (lattice deformation), mechanical (pressure compression effects) and energetic properties (binding and saturation energies). In this manner, the potential formation of these structures under zero temperature and pressure conditions can be evaluated, while their maximum storage capacity is also determined. The obtained results reveal that, despite the weak underlying interactions, the He encapsulation has a rather notable effect on both lattice parameters and energetics, and therefore, the guest-host interactions are far from being negligible. Besides, both ice crystals are predicted to remain stable when filled with He atoms, with ice XVII exhibiting a higher capacity for accommodating a larger number of guest atoms within its interstitial spaces.

Capturing Weak Interactions in Surface Adsorbate Systems at Coupled Cluster Accuracy: A Graph-Theoretic Molecular Fragmentation Approach Improved through Machine Learning

The accurate and efficient study of the interactions of organic matter with the surface of water is critical to a wide range of applications. For example, environmental studies have found that acidic polyfluorinated alkyl substances, especially perfluorooctanoic acid (PFOA), have spread throughout the environment and bioaccumulate into human populations residing near contaminated watersheds, leading to many systemic maladies. Thus, the study of the interactions of PFOA with water surfaces became important for the mitigation of their activity as pollutants and threats to public health. However, theoretical study of the interactions of such organic adsorbates on the surface of water, and their bulk concerted properties, often necessitates the use of ab initio methods to properly incorporate the long-range electronic properties that govern these extended systems. Notable theoretical treatments of "on-water" reactions thus far have employed hybrid DFT and semilocal DFT, but the interactions involved are weak interactions that may be best described using post-Hartree-Fock theory. Here, we aim to demonstrate the utility of a graph-theoretic approach to molecular fragmentation that accurately captures the critical "weak" interactions while maintaining an efficient ab initio treatment of the long-range periodic interactions that underpin the physics of extended systems. We apply this graph-theoretical treatment to study PFOA on the surface of water as a model system for the study of weak interactions seen in the wide range of surface interactions and reactions. The approach divides a system into a set of vertices, that are then connected through edges, faces, and higher order graph theoretic objects known as simplexes, to represent a collection of locally interacting subsystems. These subsystems are then used to construct ab initio molecular dynamics simulations and for computing multidimensional potential energy surfaces. To further improve the computational efficiency of our graph theoretic fragmentation method, we use a recently developed transfer learning protocol to construct the full system potential energy from a family of neural networks each designed to accurately model the behavior of individual simplexes. We use a unique multidimensional clustering algorithm, based on the k-means clustering methodology, to define our training space for each separate simplex. These models are used to extrapolate the energies for molecular dynamics trajectories at PFOA water interfaces, at less than one-tenth the cost as compared to a regular molecular fragmentation-based dynamics calculation with excellent agreement with couple cluster level of full system potential energies.

How the Acidity of Water Droplets and Films Is Controlled by the Air-Water Interface

Acidity is a key determinant of chemical reactivity in atmospheric aqueous aerosols and water microdroplets used for catalysis. However, many fundamental questions about these systems have remained elusive, including how their acidity differs from that of bulk solutions, the degree of heterogeneity between their core and surface, and how the acid-base properties are affected by their size. Here, we perform hybrid density functional theory (DFT)-quality neural network-based molecular simulations with explicit nuclear quantum effects and combine them with an analytic model to describe the pH and self-ion concentrations of droplets and films for sizes ranging from nm to μm. We determine how the acidity of water droplets and thin films is controlled by the properties of the air-water interface and by their surface-to-volume ratio. We show that while the pH is uniform in each system, hydronium and hydroxide ions exhibit concentration gradients that span the two outermost molecular layers, enriching the interface with hydronium cations and depleting it with hydroxide anions. Acidity depends strongly on the surface-to-volume ratio for system sizes below a few tens of nanometers, where the core becomes enriched in hydroxide ions and the pH increases as a result of hydronium stabilization at the interface. These results obtained for pure water systems have important implications for our understanding of chemical reactivity in atmospheric aerosols and for catalysis in aqueous microdroplets.

Fully First-Principles Surface Spectroscopy with Machine Learning

Our current understanding of the structure and dynamics of aqueous interfaces at the molecular level has grown substantially due to the continuous development of surface-specific spectroscopies, such as vibrational sum-frequency generation (VSFG). As in other vibrational spectroscopies, we must turn to atomistic simulations to extract all of the information encoded in the VSFG spectra. The high computational cost associated with existing methods means that they have limitations in representing systems with complex electronic structure or in achieving statistical convergence. In this work, we combine high-dimensional neural network interatomic potentials and symmetry-adapted Gaussian process regression to overcome these constraints. We show that it is possible to model VSFG signals with fully ab initio accuracy using machine learning and illustrate the versatility of our approach on the water/air interface. Our strategy allows us to identify the main sources of theoretical inaccuracy and establish a clear pathway toward the modeling of surface-sensitive spectroscopy of complex interfaces.

Evaluation of the MACE force field architecture: From medicinal chemistry to materials science

The MACE architecture represents the state of the art in the field of machine learning force fields for a variety of in-domain, extrapolation, and low-data regime tasks. In this paper, we further evaluate MACE by fitting models for published benchmark datasets. We show that MACE generally outperforms alternatives for a wide range of systems, from amorphous carbon, universal materials modeling, and general small molecule organic chemistry to large molecules and liquid water. We demonstrate the capabilities of the model on tasks ranging from constrained geometry optimization to molecular dynamics simulations and find excellent performance across all tested domains. We show that MACE is very data efficient and can reproduce experimental molecular vibrational spectra when trained on as few as 50 randomly selected reference configurations. We further demonstrate that the strictly local atom-centered model is sufficient for such tasks even in the case of large molecules and weakly interacting molecular assemblies.

A fully quantum-mechanical treatment for kaolinite

Neural network potentials for kaolinite minerals have been fitted to data extracted from density functional theory calculations that were performed using the revPBE + D3 and revPBE + vdW functionals. These potentials have then been used to calculate the static and dynamic properties of the mineral. We show that revPBE + vdW is better at reproducing the static properties. However, revPBE + D3 does a better job of reproducing the experimental IR spectrum. We also consider what happens to these properties when a fully quantum treatment of the nuclei is employed. We find that nuclear quantum effects (NQEs) do not make a substantial difference to the static properties. However, when NQEs are included, the dynamic properties of the material change substantially.

On the Fresnel factor correction of sum-frequency generation spectra of interfacial water

Insights into the microscopic structure of aqueous interfaces are essential for understanding the chemical and physical processes on the water surface, including chemical synthesis, atmospheric chemistry, and events in biomolecular systems. These aqueous interfaces have been probed by heterodyne-detected sum-frequency generation (HD-SFG) spectroscopy. To obtain the molecular response from the measured HD-SFG spectra, one needs to correct the measured ssp spectra for local electromagnetic field effects at the interface due to a spatially varying dielectric function. This so-called Fresnel factor correction can change the inferred response substantially, and different ways of performing this correction lead to different conclusions about the interfacial water response. Here, we compare the simulated and experimental spectra at the air/water interface. We use three previously developed models to compare the experiment with theory: an advanced approach taking into account the detailed inhomogeneous interfacial dielectric profile and the Lorentz and slab models to approximate the interfacial dielectric function. Using the advanced model, we obtain an excellent quantitative agreement between theory and experiment, in both spectral shape and amplitude. Remarkably, we find that for the Fresnel factor correction of the ssp spectra, the Lorentz model for the interfacial dielectric function is equally accurate in the hydrogen (H)-bonded region of the response, while the slab model underestimates this response significantly. The Lorentz model, thus, provides a straightforward method to obtain the molecular response from the measured spectra of aqueous interfaces in the H-bonded region.

On the Propensity of Excess Hydroxide Ions at the Alcohol Monolayer-Water Interface

Atomistic molecular dynamics simulations have been employed to study the self-ion (H⁺ and OH^-) distribution at the interface between long-chain C₁₆-OH alcohol (cetyl alcohol) monolayer and water. It is well known that the free air-water interface is acidic due to accumulation of the hydronium (H₃O⁺) ions at the interface. In the present study, we have observed that contrary to the air-water interface, at the long-chain alcohol monolayer-water interface, it is the hydroxide (OH^-) ion, not the hydronium ion (H₃O⁺) that gets accumulated. By calculating the potential of mean forces, it is confirmed that there is extra stabilization for the OH^- ions at the interface relative to the bulk, but no such stabilization is observed for the H₃O⁺ ions. By analyzing the interaction of the self-ions with other constituents in the medium, it is clearly shown that the favorable interaction of the OH^- ions with the alcoholic -OH groups stabilizes this ion at the interface. By calculating coordination numbers of the self-ions it is observed that around 50% water neighbors are substituted by alcoholic -OH in case of the hydroxide ion at the interface, whereas in the case of hydronium ions, only 15% water neighbors are substituted by the alcoholic -OH. The most interesting observation about the local structure and H-bonding pattern is that the hydroxide ion acts solely as the H-bond acceptor, but the hydronium ion acts only as the H-bond donor.

Polarization-Dependent Heterodyne-Detected Sum-Frequency Generation Spectroscopy as a Tool to Explore Surface Molecular Orientation and Ångström-Scale Depth Profiling

Sum-frequency generation (SFG) spectroscopy provides a unique optical probe for interfacial molecules with interface-specificity and molecular specificity. SFG measurements can be further carried out at different polarization combinations, but the target of the polarization-dependent SFG is conventionally limited to investigating the molecular orientation. Here, we explore the possibility of polarization-dependent SFG (PD-SFG) measurements with heterodyne detection (HD-PD-SFG). We stress that HD-PD-SFG enables accurate determination of the peak amplitude, a key factor of the PD-SFG data. Subsequently, we outline that HD-PD-SFG can be used not only for estimating the molecular orientation but also for investigating the interfacial dielectric profile and studying the depth profile of molecules. We further illustrate the variety of combined simulation and PD-SFG studies.

Accurate molecular orientation at interfaces determined by multimode polarization-dependent heterodyne-detected sum-frequency generation spectroscopy via multidimensional orientational distribution function

Many essential processes occur at soft interfaces, from chemical reactions on aqueous aerosols in the atmosphere to biochemical recognition and binding at the surface of cell membranes. The spatial arrangement of molecules specifically at these interfaces is crucial for many of such processes. The accurate determination of the interfacial molecular orientation has been challenging due to the low number of molecules at interfaces and the ambiguity of their orientational distribution. Here, we combine phase- and polarization-resolved sum-frequency generation (SFG) spectroscopy to obtain the molecular orientation at the interface. We extend an exponentially decaying orientational distribution to multiple dimensions, which, in conjunction with multiple SFG datasets obtained from the different vibrational modes, allows us to determine the molecular orientation. We apply this new approach to formic acid molecules at the air–water interface. The inferred orientation of formic acid agrees very well with ab initio molecular dynamics data. The phase-resolved SFG multimode analysis scheme using the multidimensional orientational distribution thus provides a universal approach for obtaining the interfacial molecular orientation.

Effects of Stearyl Alcohol Monolayer on the Structure, Dynamics and Vibrational Sum Frequency Generation Spectroscopy of Interfacial Water

The structure, dynamics and vibrational spectroscopy of water surface covered by a monolayer of stearyl alcohol (STA) are investigated by means of molecular dynamics simulations and vibrational sum frequency generation...

Suitable acid groups and density in electrolytes to facilitate proton conduction

Proton conducting materials suffer from low proton conductivity under low-relative humidity (RH) conditions. Previously, it was reported that acid-acid interactions, where acids interact with each other at close distances, can facilitate proton conduction without water movement and are promising for overcoming this drawback [T. Ogawa, H. Ohashi, T. Tamaki and T. Yamaguchi, Chem. Phys. Lett., 2019, 731, 136627]. However, acid groups have not been compared to find a suitable acid group and density for the interaction, which is important to experimentally synthesize the material. Here, we performed ab initio calculations to identify acid groups and acid densities as a polymer design that effectively causes acid-acid interactions. The evaluation method employed parameters based on several different optimized coordination interactions of acids and water molecules. The results show that the order of the abilities of polymer electrolytes to readily induce acid-acid interactions is hydrocarbon-based phosphonated polymers > phosphonated aromatic hydrocarbon polymers > perfluorosulfonic acid polymers ≈ perfluorophosphonic acid polymers > sulfonated aromatic hydrocarbon polymers. The acid-acid interaction becomes stronger as the distance between acids decreases. The preferable distance between phosphonate moieties is within 13 Å.

Efficient Quantum Vibrational Spectroscopy of Water with High-Order Path Integrals: From Bulk to Interfaces

Vibrational spectroscopy is key in probing the interplay between the structure and dynamics of aqueous systems. To map different regions of experimental spectra to the microscopic structure of a system, it is important to combine them with first-principles atomistic simulations that incorporate the quantum nature of nuclei. Here we show that the large cost of calculating the quantum vibrational spectra of aqueous systems can be dramatically reduced compared with standard path integral methods by using approximate quantum dynamics based on high-order path integrals. Together with state-of-the-art machine-learned electronic properties, our approach gives an excellent description not only of the infrared and Raman spectra of bulk water but also of the 2D correlation and the more challenging sum-frequency generation spectra of the water-air interface. This paves the way for understanding complex interfaces such as water encapsulated between or in contact with hydrophobic and hydrophilic materials through robust and inexpensive surface-sensitive and multidimensional spectra with first-principles accuracy.

Predicting the substituent effects in the optical and electrochemical properties of N,N'-substituted isoindigos

Isoindigo, the structural isomer of the well-known dye indigo, has seen a major revival recently because of the increasing interest of its use as a potential drug core structure and for the development of organic photovoltaic materials. Highly beneficial for diverse applications are its facile synthesis, straightforward functionalisation and the broad absorption band in the visible range. Moreover, its intrinsic electron deficiency renders isoindigo a promising acceptor structure in bulk heterojunction architectures. Here we present new insights into the substituent effects of N-functionalised isoindigos, developing a reliable and fast in silico screening approach of a library of compounds. Using experimental UV-Vis and electrochemical data increased the accuracy of the TD-DFT method employed. This procedure allowed us to accurately predict the optical and electrochemical properties of N-functionalised isoindigos and the elucidation of the relationship between substituent effects and electronic properties.

Hydrogen bond dynamics of interfacial water molecules revealed from two-dimensional vibrational sum-frequency generation spectroscopy

Vibrational sum-frequency generation (vSFG) spectroscopy allows the study of the structure and dynamics of interfacial systems. In the present work, we provide a simple recipe, based on a narrowband IR pump and broadband vSFG probe technique, to computationally obtain the two-dimensional vSFG spectrum of water molecules at the air-water interface. Using this technique, to study the time-dependent spectral evolution of hydrogen-bonded and free water molecules, we demonstrate that at the interface, the vibrational spectral dynamics of the free OH bond is faster than that of the bonded OH mode.

"On-The-Fly" Calculation of the Vibrational Sum-Frequency Generation Spectrum at the Air-Water Interface

In the present work, we provide an electronic structure based method for the "on-the-fly" determination of vibrational sum frequency generation (v-SFG) spectra. The predictive power of this scheme is demonstrated at the air-water interface. While the instantaneous fluctuations in dipole moment are obtained using the maximally localized Wannier functions, the fluctuations in polarizability are approximated to be proportional to the second moment of Wannier functions. The spectrum henceforth obtained captures the signatures of hydrogen bond stretching, bending, as well as low-frequency librational modes.

CP2K: An electronic structure and molecular dynamics software package - Quickstep: Efficient and accurate electronic structure calculations

CP2K is an open source electronic structure and molecular dynamics software package to perform atomistic simulations of solid-state, liquid, molecular, and biological systems. It is especially aimed at massively parallel and linear-scaling electronic structure methods and state-of-the-art ab initio molecular dynamics simulations. Excellent performance for electronic structure calculations is achieved using novel algorithms implemented for modern high-performance computing systems. This review revisits the main capabilities of CP2K to perform efficient and accurate electronic structure simulations. The emphasis is put on density functional theory and multiple post-Hartree-Fock methods using the Gaussian and plane wave approach and its augmented all-electron extension.

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.

Decoding the molecular water structure at complex interfaces through surface-specific spectroscopy of the water bending mode

The structure of interfacial water determines atmospheric chemistry, wetting properties of materials, and protein folding. The challenge of investigating the properties of specific interfacial water molecules has frequently been confronted using surface-specific sum-frequency generation (SFG) vibrational spectroscopy using the O-H stretch mode. While perfectly suited for the water-air interface, for complex interfaces, a potential complication arises from the contribution of hydroxyl or amine groups of non-water species present at the surface, such as surface hydroxyls on minerals, or O-H and N-H groups contained in proteins. Here, we present a protocol to extract the hydrogen bond strength selectively of interfacial water, through the water bending mode. The bending mode vibrational frequency distribution provides a new avenue for unveiling the hydrogen bonding structure of interfacial water at complex aqueous interfaces. We demonstrate this method for the water-CaF₂ and water-protein interfaces. For the former, we show that this method can indeed single out water O-H groups from surface hydroxyls, and that with increasing pH, the hydrogen-bonded network of interfacial water strengthens. Furthermore, we unveil enhanced hydrogen bonding of water, compared to bulk water, at the interface with human serum albumin proteins, a prototypical bio-interface.

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.

Nature of Excess Hydrated Proton at the Water-Air Interface

Understanding the interfacial molecular structure of acidic aqueous solutions is important in the context of, e.g., atmospheric chemistry, biophysics, and electrochemistry. The hydration of the interfacial proton is necessarily different from that in the bulk, given the lower effective density of water at the interface, but has not yet been elucidated. Here, using surface-specific vibrational spectroscopy, we probe the response of interfacial protons at the water-air interface and reveal the interfacial proton continuum. Combined with spectral calculations based on ab initio molecular dynamics simulations, the proton at the water-air interface is shown to be well-hydrated, despite the limited availability of hydration water, with both Eigen and Zundel structures coexisting at the interface. Notwithstanding the interfacial hydrated proton exhibiting bulk-like structures, a substantial interfacial stabilization by -1.3 ± 0.2 kcal/mol is observed experimentally, in good agreement with our free energy calculations. The surface propensity of the proton can be attributed to the interaction between the hydrated proton and its counterion.

First-Principles Calculation of Water pKa Using the Newly Developed SCAN Functional

Acid/base chemistry is an intriguing topic that still constitutes a challenge for computational chemistry. While estimating the acid dissociation constant (or pK_a) could shed light on many chemistry processes, especially in the fields of biochemistry and geochemistry, evaluating the relative stability between protonated and nonprotonated species is often very difficult. Indeed, a prerequisite for calculating the pK_a of any molecule is an accurate description of the energetics of water dissociation. Here, we applied constrained molecular dynamics simulations, a noncanonical sampling technique, to investigate the water deprotonation process by selecting the OH distance as the reaction coordinate. The calculation is based on density functional theory and the newly developed SCAN functional, which has shown excellent performance in describing water structure. This first benchmark of SCAN on a chemical reaction shows that this functional accurately models the energetics of proton transfer reactions in an aqueous environment. After taking Coulomb long-range corrections and nuclear quantum effects into account, the estimated water pK_a is only 1.0 pK_a unit different from the target experimental value. Our results show that the combination of SCAN and constrained MD successfully reproduces the chemistry of water and constitutes a good framework for calculating the free energy of chemical reactions of interest.

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.