First Principles Simulations of the Infrared Spectrum of Liquid Water Using Hybrid Density Functionals

Modelling chemical processes in explicit solvents with machine learning potentials

Solvent effects influence all stages of the chemical processes, modulating the stability of intermediates and transition states, as well as altering reaction rates and product ratios. However, accurately modelling these effects remains challenging. Here, we present a general strategy for generating reactive machine learning potentials to model chemical processes in solution. Our approach combines active learning with descriptor-based selectors and automation, enabling the construction of data-efficient training sets that span the relevant chemical and conformational space. We apply this strategy to investigate a Diels-Alder reaction in water and methanol. The generated machine learning potentials enable us to obtain reaction rates that are in agreement with experimental data and analyse the influence of these solvents on the reaction mechanism. Our strategy offers an efficient approach to the routine modelling of chemical reactions in solution, opening up avenues for studying complex chemical processes in an efficient manner.

Nonlinear Effects of Hydrophobic Confinement on the Electronic Structure and Dielectric Response of Water

Fundamental studies of the dielectrics of confined water are critical to understand the ion transport across biological and synthetic nanochannels. The relevance of these fundamental studies, however, surmounts the difficulty of probing water's dielectric constant as a function of a fine variation in confinement. In this work, we explore the computational efficiency of machine learning potentials to derive the confinement effects on the dielectric constant, polarization, and dipole moment of water. Our simulations predict an enhancement of the axial dielectric constant of water under extreme confinement, arising from either the formation of ferroelectric structures of ordered water or larger dipole fluctuations facilitated by the disruption of water's H-bond network. Our study highlights the impact of hydrophobic nanoconfinement on the dielectric constant and on the ionic and electronic structure of water molecules, pointing to the importance of geometric flexibility and electronic polarizability to properly model confinement effects on water.

Born-Oppenheimer Molecular Dynamics with a Linear Combination of Atomic Orbitals and Hybrid Functionals for Condensed Matter Simulations Made Possible. Theory and Performance for the Microcanonical and Canonical Ensembles

The implementation of an original Born-Oppenheimer molecular dynamics module is presented, which is able to perform simulations of large and complex condensed phase systems for sufficiently long time scales at the level of density functional theory with hybrid functionals, in the microcanonical (NVE) and canonical (NVT) ensembles. The algorithm is fully integrated in the Crystal code, a program for quantum mechanical simulations of materials, whose peculiarity stems from the use of atom-centered basis functions within a linear combination of atomic orbitals to describe the wave function. The corresponding efficiency in the evaluation of the exact Fock exchange series has led to the implementation of a rich variety of hybrid density functionals at a low computational cost. In addition, the molecular dynamics implementation benefits also from the effective MPI parallelization of the code, suited to exploit high-performance computing resources available on current generation supercomputer architectures. Furthermore, the information contained in the trajectory of the dynamics is extracted through a series of postprocessing algorithms that provide the radial distribution function, the diffusion coefficient and the vibrational density of states. In this work, we present a detailed description of the theoretical framework and the algorithmic implementation, followed by a critical evaluation of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach, when ice and liquid water simulations are performed in the microcanonical and canonical ensembles.

Long-range proton and hydroxide ion transfer dynamics at the water/CeO2 interface in the nanosecond regime: reactive molecular dynamics simulations and kinetic analysis

The structural properties, dynamical behaviors, and ion transport phenomena at the interface between water and cerium oxide are investigated by reactive molecular dynamics (MD) simulations employing neural network potentials (NNPs). The NNPs are trained to reproduce density functional theory (DFT) results, and DFT-based MD (DFT-MD) simulations with enhanced sampling techniques and refinement schemes are employed to efficiently and systematically acquire training data that include diverse hydrogen-bonding configurations caused by proton hopping events. The water interfaces with two low-index surfaces of (111) and (110) are explored with these NNPs, and the structure and long-range proton and hydroxide ion transfer dynamics are examined with unprecedented system sizes and long simulation times. Various types of proton hopping events at the interface are categorized and analyzed in detail. Furthermore, in order to decipher the proton and hydroxide ion transport phenomena along the surface, a counting analysis based on the semi-Markov process is formulated and applied to the MD trajectories to obtain reaction rates by considering the transport as stochastic jump processes. Through this model, the coupling between hopping events, vibrational motions, and hydrogen bond networks at the interface are quantitatively examined, and the high activity and ion transport phenomena at the water/CeO2 interface are unequivocally revealed in the nanosecond regime.

Speeding-up Hybrid Functional-Based Ab Initio Molecular Dynamics Using Multiple Time-stepping and Resonance-Free Thermostat

Ab initio molecular dynamics (AIMD) based on density functional theory (DFT) has become a workhorse for studying the structure, dynamics, and reactions in condensed matter systems. Currently, AIMD simulations are primarily carried out at the level of generalized gradient approximation (GGA), which is at the second rung of DFT functionals in terms of accuracy. Hybrid DFT functionals, which form the fourth rung in the accuracy ladder, are not commonly used in AIMD simulations as the computational cost involved is 100 times or higher. To facilitate AIMD simulations with hybrid functionals, we propose here an approach using multiple time stepping with adaptively compressed exchange operator and resonance-free thermostat, that could speed up the calculations by ∼30 times or more for systems with a few hundred of atoms. We demonstrate that by achieving this significant speed up and making the compute time of hybrid functional-based AIMD simulations at par with that of GGA functionals, we are able to study several complex condensed matter systems and model chemical reactions in solution with hybrid functionals that were earlier unthinkable to be performed.

Developing machine-learned potentials to simultaneously capture the dynamics of excess protons and hydroxide ions in classical and path integral simulations

The transport of excess protons and hydroxide ions in water underlies numerous important chemical and biological processes. Accurately simulating the associated transport mechanisms ideally requires utilizing ab initio molecular dynamics simulations to model the bond breaking and formation involved in proton transfer and path-integral simulations to model the nuclear quantum effects relevant to light hydrogen atoms. These requirements result in a prohibitive computational cost, especially at the time and length scales needed to converge proton transport properties. Here, we present machine-learned potentials (MLPs) that can model both excess protons and hydroxide ions at the generalized gradient approximation and hybrid density functional theory levels of accuracy and use them to perform multiple nanoseconds of both classical and path-integral proton defect simulations at a fraction of the cost of the corresponding ab initio simulations. We show that the MLPs are able to reproduce ab initio trends and converge properties such as the diffusion coefficients of both excess protons and hydroxide ions. We use our multi-nanosecond simulations, which allow us to monitor large numbers of proton transfer events, to analyze the role of hypercoordination in the transport mechanism of the hydroxide ion and provide further evidence for the asymmetry in diffusion between excess protons and hydroxide ions.

Probing Confinement Effects on the Infrared Spectra of Water with Deep Potential Molecular Dynamics Simulations

The hydrogen-bond network of confined water is expected to deviate from that of the bulk liquid, yet probing these deviations remains a significant challenge. In this work, we combine large-scale molecular dynamics simulations with machine learning potential derived from first-principles calculations to examine the hydrogen bonding of water confined in carbon nanotubes (CNTs). We computed and compared the infrared spectrum (IR) of confined water to existing experiments to elucidate confinement effects. For CNTs with diameters >1.2 nm, we find that confinement imposes a monotonic effect on the hydrogen-bond network and on the IR spectrum of water. In contrast, confinement below 1.2 nm CNT diameter affects the water structure in a complex fashion, leading to a strong directional dependence of hydrogen bonding that varies nonlinearly with the CNT diameter. When integrated with existing IR measurements, our simulations provide a new interpretation for the IR spectrum of water confined in CNTs, pointing to previously unreported aspects of hydrogen bonding in this system. This work also offers a general platform for simulating water in CNTs with quantum accuracy on time and length scales beyond the reach of conventional first-principles approaches.

Nanosecond solvation dynamics of the hematite/liquid water interface at hybrid DFT accuracy using committee neural network potentials

Metal oxide/water interfaces play an important role in biology, catalysis, energy storage and photocatalytic water splitting. The atomistic structure at these interfaces is often difficult to characterize by experimental techniques, whilst results from ab initio molecular dynamics simulations tend to be uncertain due to the limited length and time scales accessible. In this work, we train a committee neural network potential to simulate the hematite/water interface at the hybrid DFT level of theory to reach the nanosecond timescale and systems containing more than 3000 atoms. The NNP enables us to converge dynamical properties, not possible with brute-force ab initio molecular dynamics. Our simulations uncover a rich solvation dynamics at the hematite/water interface spanning three different time scales: picosecond H-bond dynamics between surface hydroxyls and the first water layer, in-plane/out-of-plane tilt motion of surface hydroxyls on the 10 ps time scale, and diffusion of water molecules from the oxide surface characterized by a mean residence lifetime of about 60 ps. Calculation of vibrational spectra confirm that H-bonds between surface hydroxyls and first layer water molecules are stronger than H-bonds in bulk water. Our study showcases how state of the art machine learning approaches can routinely be utilized to explore the structural dynamics at transition metal oxide interfaces with complex electronic structure. It foreshadows that c-NNPs are a promising tool to tackle the sampling problem in ab initio electrochemistry with explicit solvent molecules.

Improving the scaling and performance of multiple time stepping-based molecular dynamics with hybrid density functionals

Density functionals at the level of the generalized gradient approximation (GGA) and a plane-wave basis set are widely used today to perform ab initio molecular dynamics (AIMD) simulations. Going up in the ladder of accuracy of density functionals from GGA (second rung) to hybrid density functionals (fourth rung) is much desired pertaining to the accuracy of the latter in describing structure, dynamics, and energetics of molecular and condensed matter systems. On the other hand, hybrid density functional based AIMD simulations are about two orders of magnitude slower than GGA based AIMD for systems containing ~100 atoms using ~100 compute cores. Two methods, namely MTACE and s-MTACE, based on a multiple time step integrator and adaptively compressed exchange operator formalism are able to provide a speed-up of about 7-9 in performing hybrid density functional based AIMD. In this work, we report an implementation of these methods using a task-group based parallelization within the CPMD program package, with the intention to take advantage of the large number of compute cores available on modern high-performance computing platforms. We present here the boost in performance achieved through this algorithm. This work also identifies the computational bottleneck in the s-MTACE method and proposes a way to overcome it.

Electrocatalysis in Alkaline Media and Alkaline Membrane-Based Energy Technologies

Hydrogen energy-based electrochemical energy conversion technologies offer the promise of enabling a transition of the global energy landscape from fossil fuels to renewable energy. Here, we present a comprehensive review of the fundamentals of electrocatalysis in alkaline media and applications in alkaline-based energy technologies, particularly alkaline fuel cells and water electrolyzers. Anion exchange (alkaline) membrane fuel cells (AEMFCs) enable the use of nonprecious electrocatalysts for the sluggish oxygen reduction reaction (ORR), relative to proton exchange membrane fuel cells (PEMFCs), which require Pt-based electrocatalysts. However, the hydrogen oxidation reaction (HOR) kinetics is significantly slower in alkaline media than in acidic media. Understanding these phenomena requires applying theoretical and experimental methods to unravel molecular-level thermodynamics and kinetics of hydrogen and oxygen electrocatalysis and, particularly, the proton-coupled electron transfer (PCET) process that takes place in a proton-deficient alkaline media. Extensive electrochemical and spectroscopic studies, on single-crystal Pt and metal oxides, have contributed to the development of activity descriptors, as well as the identification of the nature of active sites, and the rate-determining steps of the HOR and ORR. Among these, the structure and reactivity of interfacial water serve as key potential and pH-dependent kinetic factors that are helping elucidate the origins of the HOR and ORR activity differences in acids and bases. Additionally, deliberately modulating and controlling catalyst-support interactions have provided valuable insights for enhancing catalyst accessibility and durability during operation. The design and synthesis of highly conductive and durable alkaline membranes/ionomers have enabled AEMFCs to reach initial performance metrics equal to or higher than those of PEMFCs. We emphasize the importance of using membrane electrode assemblies (MEAs) to integrate the often separately pursued/optimized electrocatalyst/support and membranes/ionomer components. Operando/in situ methods, at multiscales, and ab initio simulations provide a mechanistic understanding of electron, ion, and mass transport at catalyst/ionomer/membrane interfaces and the necessary guidance to achieve fuel cell operation in air over thousands of hours. We hope that this Review will serve as a roadmap for advancing the scientific understanding of the fundamental factors governing electrochemical energy conversion in alkaline media with the ultimate goal of achieving ultralow Pt or precious-metal-free high-performance and durable alkaline fuel cells and related technologies.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory-Based Ab Initio Molecular Dynamics II: Extensions to the Isobaric-Isoenthalpic and Isobaric-Isothermal Ensembles

In the previous paper of this series [Ko, H.-Y. et al. J. Chem. Theory Comput. 2020, 16, 3757-3785], we presented a theoretical and algorithmic framework based on a localized representation of the occupied space that exploits the inherent sparsity in the real-space evaluation of the exact exchange (EXX) interaction in finite-gap systems. This was accompanied by a detailed description of exx, a massively parallel hybrid message-passing interface MPI/OpenMP implementation of this approach in Quantum ESPRESSO (QE) that enables linear scaling hybrid density functional theory (DFT)-based ab initio molecular dynamics (AIMD) in the microcanonical/canonical (NVE/NVT) ensembles of condensed-phase systems containing 500-1000 atoms (in fixed orthorhombic cells) with a wall time cost comparable to semi-local DFT. In this work, we extend the current capabilities of exx to enable hybrid DFT-based AIMD simulations of large-scale condensed-phase systems with general and fluctuating cells in the isobaric-isoenthalpic/isobaric-isothermal (NpH/NpT) ensembles. The theoretical extensions to this approach include an analytical derivation of the EXX contribution to the stress tensor for systems in general simulation cells with a computational complexity that scales linearly with system size. The corresponding algorithmic extensions to exx include optimized routines that (i) handle both static and fluctuating simulation cells with non-orthogonal lattice symmetries, (ii) solve Poisson's equation in general/non-orthogonal cells via an automated selection of the auxiliary grid directions in the Natan-Kronik representation of the discrete Laplacian operator, and (iii) evaluate the EXX contribution to the stress tensor. Using this approach, we perform a case study on a variety of condensed-phase systems (including liquid water, a benzene molecular crystal polymorph, and semi-conducting crystalline silicon) and demonstrate that the EXX contributions to the energy and stress tensor simultaneously converge with an appropriate choice of exx parameters. This is followed by a critical assessment of the computational performance of the extended exx module across several different high-performance computing architectures via case studies on (i) the computational complexity due to lattice symmetry during NpT simulations of three different ice polymorphs (i.e., ice Ih, II, and III) and (ii) the strong/weak parallel scaling during large-scale NpT simulations of liquid water. We demonstrate that the robust and highly scalable implementation of this approach in the extended exx module is capable of evaluating the EXX contribution to the stress tensor with negligible cost (<1%) as well as all other EXX-related quantities needed during NpT simulations of liquid water (with a very tight 150 Ry planewave cutoff) in ≈5.2 s ((H₂O)₁₂₈) and ≈6.8 s ((H₂O)₂₅₆) per AIMD step. As such, the extended exx module presented in this work brings us another step closer to routinely performing hybrid DFT-based AIMD simulations of sufficient duration for large-scale condensed-phase systems across a wide range of thermodynamic conditions.

Modeling Liquid Water by Climbing up Jacob's Ladder in Density Functional Theory Facilitated by Using Deep Neural Network Potentials

Within the framework of Kohn-Sham density functional theory (DFT), the ability to provide good predictions of water properties by employing a strongly constrained and appropriately normed (SCAN) functional has been extensively demonstrated in recent years. Here, we further advance the modeling of water by building a more accurate model on the fourth rung of Jacob's ladder with the hybrid functional, SCAN0. In particular, we carry out both classical and Feynman path-integral molecular dynamics calculations of water with the SCAN0 functional and the isobaric-isothermal ensemble. To generate the equilibrated structure of water, a deep neural network potential is trained from the atomic potential energy surface based on ab initio data obtained from SCAN0 DFT calculations. For the electronic properties of water, a separate deep neural network potential is trained by using the Deep Wannier method based on the maximally localized Wannier functions of the equilibrated trajectory at the SCAN0 level. The structural, dynamic, and electric properties of water were analyzed. The hydrogen-bond structures, density, infrared spectra, diffusion coefficients, and dielectric constants of water, in the electronic ground state, are computed by using a large simulation box and long simulation time. For the properties involving electronic excitations, we apply the GW approximation within many-body perturbation theory to calculate the quasiparticle density of states and bandgap of water. Compared to the SCAN functional, mixing exact exchange mitigates the self-interaction error in the meta-generalized-gradient approximation and further softens liquid water toward the experimental direction. For most of the water properties, the SCAN0 functional shows a systematic improvement over the SCAN functional. However, some important discrepancies remain. The H-bond network predicted by the SCAN0 functional is still slightly overstructured compared to the experimental results.

Nuclear Quantum Effect and Its Temperature Dependence in Liquid Water from Random Phase Approximation via Artificial Neural Network

We report structural and dynamical properties of liquid water described by the random phase approximation (RPA) correlation together with the exact exchange energy (EXX) within density functional theory. By utilizing thermostated ring polymer molecular dynamics, we examine the nuclear quantum effects and their temperature dependence. We circumvent the computational limitation of performing direct first-principles molecular dynamics simulation at this high level of electronic structure theory by adapting an artificial neural network model. We show that the EXX+RPA level of theory accurately describes liquid water in terms of both dynamical and structural properties.

Dielectric Constant of Liquid Water Determined with Neural Network Quantum Molecular Dynamics

The static dielectric constant ϵ_{0} and its temperature dependence for liquid water is investigated using neural network quantum molecular dynamics (NNQMD). We compute the exact dielectric constant in canonical ensemble from NNQMD trajectories using fluctuations in macroscopic polarization computed from maximally localized Wannier functions (MLWF). Two deep neural networks are constructed. The first, NNQMD, is trained on QMD configurations for liquid water under a variety of temperature and density conditions to learn potential energy surface and forces and then perform molecular dynamics simulations. The second network, NNMLWF, is trained to predict locations of MLWF of individual molecules using the atomic configurations from NNQMD. Training data for both the neural networks is produced using a highly accurate quantum-mechanical method, DFT-SCAN that yields an excellent description of liquid water. We produce 280×10^{6} configurations of water at 7 temperatures using NNQMD and predict MLWF centers using NNMLWF to compute the polarization fluctuations. The length of trajectories needed for a converged value of the dielectric constant at 0°C is found to be 20 ns (40×10^{6} configurations with 0.5 fs time step). The computed dielectric constants for 0, 15, 30, 45, 60, 75, and 90°C are in good agreement with experiments. Our scalable scheme to compute dielectric constants with quantum accuracy is also applicable to other polar molecular liquids.

Achieving an Order of Magnitude Speedup in Hybrid-Functional- and Plane-Wave-Based Ab Initio Molecular Dynamics: Applications to Proton-Transfer Reactions in Enzymes and in Solution

Ab initio molecular dynamics (MD) with hybrid density functionals and a plane wave basis is computationally expensive due to the high computational cost of exact exchange energy evaluation. Recently, we proposed a strategy to combine adaptively compressed exchange (ACE) operator formulation and a multiple time step integration scheme to reduce the computational cost significantly [J. Chem. Phys. 2019, 151, 151102 ]. However, it was found that the construction of the ACE operator, which has to be done at least once in every MD time step, is computationally expensive. In the present work, systematic improvements are introduced to further speed up by employing localized orbitals for the construction of the ACE operator. By this, we could achieve a computational speedup of an order of magnitude for a periodic system containing 32 water molecules. Benchmark calculations were carried out to show the accuracy and efficiency of the method in predicting the structural and dynamical properties of bulk water. To demonstrate the applicability, computationally intensive free-energy computations at the level of hybrid density functional theory were performed to investigate (a) methyl formate hydrolysis reaction in neutral aqueous media and (b) proton-transfer reaction within the active-site residues of the class C β-lactamase enzyme.

On the role of water in the hydrogen bond network in DESs: an ab initio molecular dynamics and quantum mechanical study on the urea–betaine system

We herein report an ab initio molecular dynamics study on a natural DES composed of urea and betaine in a 3 : 2 ratio, as a test case for evaluating the water effect.

Simulation of Liquids with the Tight-Binding Density-Functional Approach and Improved Atomic Charges

Theoretical description of liquids, especially liquid water, is an ongoing subject with important implications in various domains such as homogeneous catalysis; solvation of molecular, ionic, and biomolecular species; and reactivity. Various formalisms exist to describe liquids, each one displaying its own balance between accuracy and computational cost that defines its range of applications. The present article revisits the ability of the density-functional-based tight-binding (SCC-DFTB) approach to model liquids by focusing on liquid water and liquid benzene under ambient conditions. To do so, we benchmark a recent correction for the SCC-DFTB atomic charges that allows for a drastic improvement of the pair radial distribution functions of liquid water as compared to both experimental data and density-functional theory results performed in the generalized-gradient approximation. We also report the coupling of the deMonNano and i-PI codes to perform path-integral molecular dynamics. This allows us to rationalize the impact of nuclear quantum effects on the SCC-DFTB description of liquid water. This study evidences the rather good ability of SCC-DFTB to describe liquid water and liquid benzene. As the first example of application, we also present results for a benzene molecule solvated in water with the perspectives of further studies devoted to solvent/water interfaces.

Efficient computation of free energy surfaces of chemical reactions using ab initio molecular dynamics with hybrid functionals and plane waves

Ab initio molecular dynamics (AIMD) simulations employing density functional theory (DFT) and plane waves are routinely carried out using density functionals at the level of generalized gradient approximation (GGA). AIMD simulations employing hybrid density functionals are of great interest as it offers a more accurate description of structural and dynamic properties than the GGA functionals. However, the computational cost for carrying out calculations using hybrid functionals and plane wave basis set is at least two orders of magnitude higher than that using GGA functionals. Recently, we proposed a strategy that combined the adaptively compressed exchange operator formulation and the multiple time step integration scheme to reduce the computational cost by an order of magnitude [J. Chem. Phys. 151, 151102 (2019)]. In this work, we demonstrate the application of this method to study chemical reactions, in particular, formamide hydrolysis in an alkaline aqueous medium. By actuating our implementation with the well-sliced metadynamics scheme, we can compute the two-dimensional free energy surface of this reaction at the level of hybrid-DFT. This work also investigates the accuracy of the PBE0 (hybrid) and the PBE (GGA) functionals in predicting the free energetics of this chemical reaction.

Enabling Large-Scale Condensed-Phase Hybrid Density Functional Theory Based Ab Initio Molecular Dynamics. 1. Theory, Algorithm, and Performance

By including a fraction of exact exchange (EXX), hybrid functionals reduce the self-interaction error in semilocal density functional theory (DFT) and thereby furnish a more accurate and reliable description of the underlying electronic structure in systems throughout biology, chemistry, physics, and materials science. However, the high computational cost associated with the evaluation of all required EXX quantities has limited the applicability of hybrid DFT in the treatment of large molecules and complex condensed-phase materials. To overcome this limitation, we describe a linear-scaling approach that utilizes a local representation of the occupied orbitals (e.g., maximally localized Wannier functions (MLWFs)) to exploit the sparsity in the real-space evaluation of the quantum mechanical exchange interaction in finite-gap systems. In this work, we present a detailed description of the theoretical and algorithmic advances required to perform MLWF-based ab initio molecular dynamics (AIMD) simulations of large-scale condensed-phase systems of interest at the hybrid DFT level. We focus our theoretical discussion on the integration of this approach into the framework of Car-Parrinello AIMD, and highlight the central role played by the MLWF-product potential (i.e., the solution of Poisson's equation for each corresponding MLWF-product density) in the evaluation of the EXX energy and wave function forces. We then provide a comprehensive description of the exx algorithm implemented in the open-source Quantum ESPRESSO program, which employs a hybrid MPI/OpenMP parallelization scheme to efficiently utilize the high-performance computing (HPC) resources available on current- and next-generation supercomputer architectures. This is followed by a critical assessment of the accuracy and parallel performance (e.g., strong and weak scaling) of this approach when AIMD simulations of liquid water are performed in the canonical (NVT) ensemble. With access to HPC resources, we demonstrate that exx enables hybrid DFT-based AIMD simulations of condensed-phase systems containing 500-1000 atoms (e.g., (H₂O)₂₅₆) with a wall time cost that is comparable to that of semilocal DFT. In doing so, exx takes us one step closer to routinely performing AIMD simulations of complex and large-scale condensed-phase systems for sufficiently long time scales at the hybrid DFT level of theory.

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.

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.

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.

Picture of the wet electron: a localized transient state in liquid water

A transient state of the excess electron in liquid water preceding the development of the solvation shell, the so-called wet electron, has been invoked to explain spectroscopic observations, but its binding energy and atomic structure have remained highly elusive. Here, we carry out hybrid functional molecular dynamics to unveil the ultrafast solvation mechanism leading to the hydrated electron. In the pre-hydrated regime, the electron is found to repeatedly switch between a quasi-free electron state in the conduction band and a localized state with a binding energy of 0.26 eV, which we assign to the wet electron. This transient state self-traps in a region of the liquid which extends up to ∼4.5 Å and involves a severe disruption of the hydrogen-bond network. Our picture provides an unprecedented view on the nature of the wet electron, which is instrumental to understanding the properties of this fundamental species in liquid water.

Isotope Effects in Water: Differences of Structure, Dynamics, Spectrum, and Proton Transport between Heavy and Light Water from ReaxFF Reactive Force Field Simulations

Investigating properties of both heavy and light water at the atomistic level is essential to understanding chemical and biological processes in aqueous solution. However, appropriately describing their difference on the nanoscale is still challenging. Employing ReaxFF reactive molecular dynamics simulations, we systematically study the structure, dynamics, and spectra of heavy and light water. With the water force field potential we developed, the different features between heavy and light water can be simulated appropriately by the classical treatment on large size and time scale. Here, we also report the structural difference between D₃O⁺ and H₃O⁺ in bulk heavy/light water. In addition, the diffusion constants of heavy and light water are successfully reproduced, and the Grotthuss hopping mechanism of proton transport in liquid water is properly described as well. It allows us to study a complex system in heavy/light aqueous environments, such as proton transport, chemical reaction, and tracing the reaction mechanism with an isotope substitute.

Predicting vapor liquid equilibria using density functional theory: A case study of argon

Predicting vapor liquid equilibria (VLE) of molecules governed by weak van der Waals (vdW) interactions using the first principles approach is a significant challenge. Due to the poor scaling of the post Hartree-Fock wave function theory with system size/basis functions, the Kohn-Sham density functional theory (DFT) is preferred for systems with a large number of molecules. However, traditional DFT cannot adequately account for medium to long range correlations which are necessary for modeling vdW interactions. Recent developments in DFT such as dispersion corrected models and nonlocal van der Waals functionals have attempted to address this weakness with a varying degree of success. In this work, we predict the VLE of argon and assess the performance of several density functionals and the second order Møller-Plesset perturbation theory (MP2) by determining critical and structural properties via first principles Monte Carlo simulations. PBE-D3, BLYP-D3, and rVV10 functionals were used to compute vapor liquid coexistence curves, while PBE0-D3, M06-2X-D3, and MP2 were used for computing liquid density at a single state point. The performance of the PBE-D3 functional for VLE is superior to other functionals (BLYP-D3 and rVV10). At T = 85 K and P = 1 bar, MP2 performs well for the density and structural features of the first solvation shell 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.

Infrared optical constants of liquid palm oil and palm oil biodiesel determined by the combined ellipsometry-transmission method

The optical constants of vegetable oils and biodiesels are the basic input parameters in the study of the thermal radiation transfer and monitoring the productivity of vegetable oils converting to biodiesels. In this work, a combined ellipsometry-transmission method is presented to obtain the optical constants of palm oil and palm oil biodiesel between 20°C and 150°C in the spectral range 600-4100  cm^-1 and to study the temperature effect on the optical constants. In the combined method, a modified ellipsometry method is used to measure the optical constants of palm oil and palm oil biodiesel for the whole researched wave bands. For the weak absorption regions in which the ellipsometry method cannot give precise absorption indices, the transmission method is conducted to get the absorption indices using the refractive indices obtained by the proposed ellipsometry method. Deionized water and methanol are taken as examples to verify the combined ellipsometry-transmission method. It is shown that the combined method can overcome the deficiencies of the traditional ellipsometry and transmission method, which can be used for the measurements of both strong and weak absorption wave bands. The experimental analyses indicate that temperature exerts a noticeable influence on the infrared optical constants of palm oil and palm oil biodiesel. With the increase of temperature, the refractive indices at certain wavenumbers decrease nearly linearly, and the amplitudes of dominant absorption peaks show a decreasing trend. The absorption peaks located around 3550  cm^-1 show blueshift trends as temperature increases. Comparing these two kinds of oils, palm oil presents larger values in refractive indices and dominant absorption peaks.

Performance of the AMOEBA Water Model in the Vicinity of QM Solutes: A Diagnosis Using Energy Decomposition Analysis

The importance of incorporating solvent polarization effects into the modeling of solvation processes has been well-recognized, and therefore a new generation of hybrid quantum mechanics/molecular mechanics (QM/MM) approaches that accounts for this effect is desirable. We present a fully self-consistent, mutually polarizable QM/MM scheme using the AMOEBA force field, in which the total energy of the system is variationally minimized with respect to both the QM electronic density and the MM induced dipoles. This QM/AMOEBA model is implemented through the Q-Chem/LibEFP code interface and then applied to the evaluation of solute-solvent interaction energies for various systems ranging from the water dimer to neutral and ionic solutes (NH₃, NH₄⁺, CN^-) surrounded by increasing numbers of water molecules (up to 100). In order to analyze the resulting interaction energies, we also utilize an energy decomposition analysis (EDA) scheme which identifies contributions from permanent electrostatics, polarization, and van der Waals (vdW) interaction for the interaction between the QM solute and the solvent molecules described by AMOEBA. This facilitates a component-wise comparison against full QM calculations where the corresponding energy components are obtained via a modified version of the absolutely localized molecular orbitals (ALMO)-EDA. The results show that the present QM/AMOEBA model can yield reasonable solute-solvent interaction energies for neutral and cationic species, while further scrutiny reveals that this accuracy highly relies on the delicate balance between insufficiently favorable permanent electrostatics and softened vdW interaction. For anionic solutes where the charge penetration effect becomes more pronounced, the QM/MM interface turns out to be unbalanced. These results are consistent with and further elucidate our findings in a previous study using a slightly different QM/AMOEBA model ( Dziedzic et al. J. Chem. Phys. 2016 , 145 , 124106 ). The implications of these results for further refinement of this model are also discussed.

Ab initio molecular dynamics simulations of liquid water using high quality meta-GGA functionals

We have used ab initio molecular dynamics (AIMD) to characterize water properties using two meta-generalized gradient approximation (meta-GGA) functionals, M06-L-D3 and B97M-rV, and compared their performance against a standard GGA corrected for dispersion, revPBE-D3, at ambient conditions (298 K, and 1 g cm-3 or 1 atm). Simulations of the equilibrium density, radial distribution functions, self-diffusivity, the infrared spectrum, liquid dipole moments, and characterizations of the hydrogen bond network show that all three functionals have overcome the problem of the early AIMD simulations that erroneously found ambient water to be highly structured, but they differ substantially among themselves in agreement with experiment on this range of water properties. We show directly using water cluster data up through the pentamer that revPBE-D3 benefits from a cancellation of its intrinsic functional error by running classical trajectories, whereas the meta-GGA functionals are demonstrably more accurate and would require the simulation of nuclear quantum effects to realize better agreement with all cluster and condensed phase properties.

Local and Global Effects of Dissolved Sodium Chloride on the Structure of Water

Determining how the structure of water is modified by the presence of salts is instrumental to understanding the solvation of biomolecules and, in general, the role played by salts in biochemical processes. However, the extent of hydrogen bonding disruption induced by salts remains controversial. We performed extensive first-principles simulations of solutions of a simple salt (NaCl) and found that, while the cation does not significantly change the structure of water beyond the first solvation shell, the anion has a further reaching effect, modifying the hydrogen-bond network even outside its second solvation shell. We found that a distinctive fingerprint of hydrogen bonding modification is the change in polarizability of water molecules. Molecular dipole moments are instead insensitive probes of long-range modifications induced by Na⁺ and Cl^- ions. Though noticeable, the long-range effect of Cl^- is expected to be too weak to affect solubility of large biomolecules.

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

Understanding the reactivity and spectroscopy of aqueous solutions at the atomistic level is crucial for the elucidation and design of chemical processes. However, the simulation of these systems requires addressing the formidable challenges of treating the quantum nature of both the electrons and nuclei. Exploiting our recently developed methods that provide acceleration by up to 2 orders of magnitude, we combine path integral simulations with on-the-fly evaluation of the electronic structure at the hybrid density functional theory level to capture the interplay between nuclear quantum effects and the electronic surface. Here we show that this combination provides accurate structure and dynamics, including the full infrared and Raman spectra of liquid water. This allows us to demonstrate and explain the failings of lower-level density functionals for dynamics and vibrational spectroscopy when the nuclei are treated quantum mechanically. These insights thus provide a foundation for the reliable investigation of spectroscopy and reactivity in aqueous environments.

Modelling heterogeneous interfaces for solar water splitting

The generation of hydrogen from water and sunlight offers a promising approach for producing scalable and sustainable carbon-free energy. The key of a successful solar-to-fuel technology is the design of efficient, long-lasting and low-cost photoelectrochemical cells, which are responsible for absorbing sunlight and driving water splitting reactions. To this end, a detailed understanding and control of heterogeneous interfaces between photoabsorbers, electrolytes and catalysts present in photoelectrochemical cells is essential. Here we review recent progress and open challenges in predicting physicochemical properties of heterogeneous interfaces for solar water splitting applications using first-principles-based approaches, and highlights the key role of these calculations in interpreting increasingly complex experiments.

The fate of carbon dioxide in water-rich fluids under extreme conditions

Investigating the fate of dissolved carbon dioxide under extreme conditions is critical to understanding the deep carbon cycle in Earth, a process that ultimately influences global climate change. We used first-principles molecular dynamics simulations to study carbonates and carbon dioxide dissolved in water at pressures (P) and temperatures (T) approximating the conditions of Earth's upper mantle. Contrary to popular geochemical models assuming that molecular CO₂(aq) is the major carbon species present in water under deep Earth conditions, we found that at 11 GPa and 1000 K, carbon exists almost entirely in the forms of solvated carbonate ([Formula: see text]) and bicarbonate ([Formula: see text]) ions and that even carbonic acid [H₂CO₃(aq)] is more abundant than CO₂(aq). Furthermore, our simulations revealed that ion pairing between Na⁺ and [Formula: see text]/[Formula: see text] is greatly affected by P-T conditions, decreasing with increasing pressure at 800 to 1000 K. Our results suggest that in Earth's upper mantle, water-rich geofluids transport a majority of carbon in the form of rapidly interconverting [Formula: see text] and [Formula: see text] ions, not solvated CO₂(aq) molecules.