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In light of the pressing need for practical materials and molecular solutions to renewable energy and health problems, to name just two examples, one wonders how to accelerate research and development in the chemical sciences, so as to address the time it takes to bring materials from initial discovery to commercialization. Artificial intelligence (AI)-based techniques, in particular, are having a transformative and accelerating impact on many if not most, technological domains. To shed light on these questions, the authors and participants gathered in person for the ASLLA Symposium on the theme of ‘Accelerated Chemical Science with AI’ at Gangneung, Republic of Korea. We present the findings, ideas, comments, and often contentious opinions expressed during four panel discussions related to the respective general topics: ‘Data’, ‘New applications’, ‘Machine learning algorithms’, and ‘Education’. All discussions were recorded, transcribed into text using Open AI's Whisper, and summarized using LG AI Research's EXAONE LLM, followed by revision by all authors. For the broader benefit of current researchers, educators in higher education, and academic bodies such as associations, publishers, librarians, and companies, we provide chemistry-specific recommendations and summarize the resulting conclusions.

Regression methods are fundamental for scientific and technological applications. However, fitted models can be highly unreliable outside of their training domain, and hence the quantification of their uncertainty is crucial in many of their applications. Based on the solution of a constrained optimization problem, we propose "prediction rigidities" as a method to obtain uncertainties of arbitrary pre-trained regressors. We establish a strong connection between our framework and Bayesian inference, and we develop a last-layer approximation that allows the new method to be applied to neural networks. This extension affords cheap uncertainties without any modification to the neural network itself or its training procedure. We show the effectiveness of our method on a wide range of regression tasks, ranging from simple toy models to applications in chemistry and meteorology.

Machine-learning models based on a point-cloud representation of a physical object are ubiquitous in scientific applications and particularly well-suited to the atomic-scale description of molecules and materials. Among the many different approaches that have been pursued, the description of local atomic environments in terms of their neighbor densities has been used widely and very succesfully. We propose a novel density-based method which involves computing ``Wigner kernels''. These are fully equivariant and body-ordered kernels that can be computed iteratively with a cost that is independent of the radial-chemical basis and grows only linearly with the maximum body-order considered. This is in marked contrast to feature-space models, which comprise an exponentially-growing number of terms with increasing order of correlations. We present several examples of the accuracy of models based on Wigner kernels in chemical applications, for both scalar and tensorial targets, reaching state-of-the-art accuracy on the popular QM9 benchmark dataset, and we discuss the broader relevance of these ideas to equivariant geometric machine-learning.

In this paper, we address the challenge of obtaining a comprehensive and symmetric representation of point particle groups, such as atoms in a molecule, which is crucial in physics and theoretical chemistry. The problem has become even more important with the widespread adoption of machine-learning techniques in science, as it underpins the capacity of models to accurately reproduce physical relationships while being consistent with fundamental symmetries and conservation laws. However, some of the descriptors that are commonly used to represent point clouds -- most notably those based on discretized correlations of the neighbor density, that underpin most of the existing ML models of matter at the atomic scale -- are unable to distinguish between special arrangements of particles in three dimensions. This makes it impossible to machine learn their properties. Atom-density correlations are provably complete in the limit in which they simultaneously describe the mutual relationship between all atoms, which is impractical. We present a novel approach to construct descriptors of \emph{finite} correlations based on the relative arrangement of particle triplets, which can be employed to create symmetry-adapted models with universal approximation capabilities, which have the resolution of the neighbor discretization as the sole convergence parameter. Our strategy is demonstrated on a class of atomic arrangements that are specifically built to defy a broad class of conventional symmetric descriptors, showcasing its potential for addressing their limitations.

Spherical harmonics provide a smooth, orthogonal, and symmetry-adapted basis to expand functions on a sphere, and they are used routinely in physical and theoretical chemistry as well as in different fields of science and technology, from geology and atmospheric sciences to signal processing and computer graphics. More recently, they have become a key component of rotationally equivariant models in geometric machine learning, including applications to atomic-scale modeling of molecules and materials. We present an elegant and efficient algorithm for the evaluation of the real-valued spherical harmonics. Our construction features many of the desirable properties of existing schemes and allows to compute Cartesian derivatives in a numerically stable and computationally efficient manner. To facilitate usage, we implement this algorithm in sphericart, a fast C++ library which also provides C bindings, a Python API, and a PyTorch implementation that includes a GPU kernel.

Point clouds are versatile representations of 3D objects and have found widespread application in science and engineering. Many successful deep-learning models have been proposed that use them as input. The domain of chemical and materials modeling is especially challenging because exact compliance with physical constraints is highly desirable for a model to be usable in practice. These constraints include smoothness and invariance with respect to translations, rotations, and permutations of identical atoms. If these requirements are not rigorously fulfilled, atomistic simulations might lead to absurd outcomes even if the model has excellent accuracy. Consequently, dedicated architectures, which achieve invariance by restricting their design space, have been developed. General-purpose point-cloud models are more varied but often disregard rotational symmetry. We propose a general symmetrization method that adds rotational equivariance to any given model while preserving all the other requirements. Our approach simplifies the development of better atomic-scale machine-learning schemes by relaxing the constraints on the design space and making it possible to incorporate ideas that proved effective in other domains. We demonstrate this idea by introducing the Point Edge Transformer (PET) architecture, which is not intrinsically equivariant but achieves state-of-the-art performance on several benchmark datasets of molecules and solids. A-posteriori application of our general protocol makes PET exactly equivariant, with minimal changes to its accuracy., Comment: Enhancing figures; minor polishing

Data-driven techniques are increasingly used to replace electronic-structure calculations of matter. In this context, a relevant question is whether machine learning (ML) should be applied directly to predict the desired properties or be combined explicitly with physically-grounded operations. We present an example of an integrated modeling approach, in which a symmetry-adapted ML model of an effective Hamiltonian is trained to reproduce electronic excitations from a quantum-mechanical calculation. The resulting model can make predictions for molecules that are much larger and more complex than those that it is trained on, and allows for dramatic computational savings by indirectly targeting the outputs of well-converged calculations while using a parameterization corresponding to a minimal atom-centered basis. These results emphasize the merits of intertwining data-driven techniques with physical approximations, improving the transferability and interpretability of ML models without affecting their accuracy and computational efficiency, and providing a blueprint for developing ML-augmented electronic-structure methods.

One essential ingredient in many machine learning (ML) based methods for atomistic modeling of materials and molecules is the use of locality. While allowing better system-size scaling, this systematically neglects long-range (LR) effects, such as electrostatics or dispersion interaction. We present an extension of the long distance equivariant (LODE) framework that can handle diverse LR interactions in a consistent way, and seamlessly integrates with preexisting methods by building new sets of atom centered features. We provide a direct physical interpretation of these using the multipole expansion, which allows for simpler and more efficient implementations. The framework is applied to simple toy systems as proof of concept, and a heterogeneous set of molecular dimers to push the method to its limits. By generalizing LODE to arbitrary asymptotic behaviors, we provide a coherent approach to treat arbitrary two- and many-body non-bonded interactions in the data-driven modeling of matter.

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighbourhood of each atom in the system. Symmetry considerations support the use of spherical harmonics to expand the angular dependence of this density, but there is as yet no clear rationale to choose one radial basis over another. Here we investigate the basis that results from the solution of the Laplacian eigenvalue problem within a sphere around the atom of interest. We show that this generates the smoothest possible basis of a given size within the sphere, and that a tensor product of Laplacian eigenstates also provides the smoothest possible basis for expanding any higher-order correlation of the atomic density within the appropriate hypersphere. We consider several unsupervised metrics of the quality of a basis for a given dataset, and show that the Laplacian eigenstate basis has a performance that is much better than some widely used basis sets and is competitive with data-driven bases that numerically optimize each metric. In supervised machine learning tests, we find that the optimal function smoothness of the Laplacian eigenstates leads to comparable or better performance than can be obtained from a data-driven basis of a similar size that has been optimized to describe the atom-density correlation for the specific dataset. We conclude that the smoothness of the basis functions is a key and hitherto largely overlooked aspect of successful atomic density representations.

Machine-learning potentials are usually trained on the ground-state, Born-Oppenheimer energy surface, which depends exclusively on the atomic positions and not on the simulation temperature. This disregards the effect of thermally-excited electrons, that is important in metals, and essential to the description of warm dense matter. An accurate physical description of these effects requires that the nuclei move on a temperature-dependent electronic free energy. We propose a method to obtain machine-learning predictions of this free energy at an arbitrary electron temperature using exclusively training data from ground-state calculations, avoiding the need to train temperature-dependent potentials, and benchmark it on metallic liquid hydrogen at the conditions of the core of gas giants and brown dwarfs. This work demonstrates the advantages of hybrid schemes that use physical consideration to combine machine-learning predictions, providing a blueprint for the development of similar approaches that extend the reach of atomistic modelling by removing the barrier between physics and data-driven methodologies.

Data-driven schemes that associate molecular and crystal structures with their microscopic properties share the need for a concise, effective description of the arrangement of their atomic constituents. Many types of models rely on descriptions of atom-centered environments, that are associated with an atomic property or with an atomic contribution to an extensive macroscopic quantity. Frameworks in this class can be understood in terms of atom-centered density correlations (ACDC), that are used as a basis for a body-ordered, symmetry-adapted expansion of the targets. Several other schemes, that gather information on the relationship between neighboring atoms using "message-passing" ideas, cannot be directly mapped to correlations centered around a single atom. We generalize the ACDC framework to include multi-centered information, generating representations that provide a complete linear basis to regress symmetric functions of atomic coordinates, and provides a coherent foundation to systematize our understanding of both atom-centered and message-passing, invariant and equivariant machine-learning schemes.

Graph neural networks (GNN) are very popular methods in machine learning and have been applied very successfully to the prediction of the properties of molecules and materials. First-order GNNs are well known to be incomplete, i.e., there exist graphs that are distinct but appear identical when seen through the lens of the GNN. More complicated schemes have thus been designed to increase their resolving power. Applications to molecules (and more generally, point clouds), however, add a geometric dimension to the problem. The most straightforward and prevalent approach to construct graph representation for molecules regards atoms as vertices in a graph and draws a bond between each pair of atoms within a chosen cutoff. Bonds can be decorated with the distance between atoms, and the resulting "distance graph NNs" (dGNN) have empirically demonstrated excellent resolving power and are widely used in chemical ML, with all known indistinguishable configurations being resolved in the fully-connected limit, which is equivalent to infinite or sufficiently large cutoff. Here we present a counterexample that proves that dGNNs are not complete even for the restricted case of fully-connected graphs induced by 3D atom clouds. We construct pairs of distinct point clouds whose associated graphs are, for any cutoff radius, equivalent based on a first-order Weisfeiler-Lehman test. This class of degenerate structures includes chemically-plausible configurations, both for isolated structures and for infinite structures that are periodic in 1, 2, and 3 dimensions. The existence of indistinguishable configurations sets an ultimate limit to the expressive power of some of the well-established GNN architectures for atomistic machine learning. Models that explicitly use angular or directional information in the description of atomic environments can resolve this class of degeneracies.

We provide an introduction to Gaussian process regression (GPR) machinelearning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

The first step in the construction of a regression model or a data-driven analysis, aiming to predict or elucidate the relationship between the atomic-scale structure of matter and its properties, involves transforming the Cartesian coordinates of the atoms into a suitable representation. The development of atomic-scale representations has played, and continues to play, a central role in the success of machine-learning methods for chemistry and materials science. This review summarizes the current understanding of the nature and characteristics of the most commonly used structural and chemical descriptions of atomistic structures, highlighting the deep underlying connections between different frameworks and the ideas that lead to computationally efficient and universally applicable models. It emphasizes the link between properties, structures, their physical chemistry, and their mathematical description, provides examples of recent applications to a diverse set of chemical and materials science problems, and outlines the open questions and the most promising research directions in the field.

We provide an introduction to Gaussian process regression (GPR) machinelearning methods in computational materials science and chemistry. The focus of the present review is on the regression of atomistic properties: in particular, on the construction of interatomic potentials, or force fields, in the Gaussian Approximation Potential (GAP) framework; beyond this, we also discuss the fitting of arbitrary scalar, vectorial, and tensorial quantities. Methodological aspects of reference data generation, representation, and regression, as well as the question of how a data-driven model may be validated, are reviewed and critically discussed. A survey of applications to a variety of research questions in chemistry and materials science illustrates the rapid growth in the field. A vision is outlined for the development of the methodology in the years to come.

The input of almost every machine learning algorithm targeting the properties of matter at the atomic scale involves a transformation of the list of Cartesian atomic coordinates into a more symmetric representation. Many of the most popular representations can be seen as an expansion of the symmetrized correlations of the atom density, and differ mainly by the choice of basis. Considerable effort has been dedicated to the optimization of the basis set, typically driven by heuristic considerations on the behavior of the regression target. Here we take a different, unsupervised viewpoint, aiming to determine the basis that encodes in the most compact way possible the structural information that is relevant for the dataset at hand. For each training dataset and number of basis functions, one can determine a unique basis that is optimal in this sense, and can be computed at no additional cost with respect to the primitive basis by approximating it with splines. We demonstrate that this construction yields representations that are accurate and computationally efficient, particularly when constructing representations that correspond to high-body order correlations. We present examples that involve both molecular and condensed-phase machine-learning models.

The nature of the bulk hydrated electron has been a challenge for both experiment and theory due to its short lifetime and high reactivity, and the need for a high-level of electronic structure theory to achieve predictive accuracy. The lack of a classical atomistic structural formula makes it exceedingly difficult to model the solvated electron using conventional empirical force fields, which describe the system in terms of interactions between point particles associated with atomic nuclei. Here we overcome this problem using a machine-learning model, that is sufficiently flexible to describe the effect of the excess electron on the structure of the surrounding water, without including the electron in the model explicitly. The resulting potential is not only able to reproduce the stable cavity structure but also recovers the correct localization dynamics that follow the injection of an electron in neat water. The machine learning model achieves the accuracy of the state-of-the-art correlated wave function method it is trained on. It is sufficiently inexpensive to afford a full quantum statistical and dynamical description and allows us to achieve accurate determination of the structure, diffusion mechanisms, and vibrational spectroscopy of the solvated electron.

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.

Machine learning encompasses tools and algorithms that are now becoming popular in almost all scientific and technological fields. This is true for molecular dynamics as well, where machine learning offers promises of extracting valuable information from the enormous amounts of data generated by simulation of complex systems. We provide here a review of our current understanding of goals, benefits, and limitations of machine learning techniques for computational studies on atomistic systems, focusing on the construction of empirical force fields from ab initio databases and the determination of reaction coordinates for free energy computation and enhanced sampling.

Data analyses based on linear methods constitute the simplest, most robust, and transparent approaches to the automatic processing of large amounts of data for building supervised or unsupervised machine learning models. Principal covariates regression (PCovR) is an underappreciated method that interpolates between principal component analysis and linear regression, and can be used to conveniently reveal structure-property relations in terms of simple-to-interpret, low-dimensional maps. Here we provide a pedagogic overview of these data analysis schemes, including the use of the kernel trick to introduce an element of non-linearity, while maintaining most of the convenience and the simplicity of linear approaches. We then introduce a kernelized version of PCovR and a sparsified extension, and demonstrate the performance of this approach in revealing and predicting structure-property relations in chemistry and materials science, showing a variety of examples including elemental carbon, porous silicate frameworks, organic molecules, amino acid conformers, and molecular materials.

Selecting the most relevant features and samples out of a large set of candidates is a task that occurs very often in the context of automated data analysis, where it can be used to improve the computational performance, and also often the transferability, of a model. Here we focus on two popular sub-selection schemes which have been applied to this end: CUR decomposition, that is based on a low-rank approximation of the feature matrix and Farthest Point Sampling, that relies on the iterative identification of the most diverse samples and discriminating features. We modify these unsupervised approaches, incorporating a supervised component following the same spirit as the Principal Covariates Regression (PCovR) method. We show that incorporating target information provides selections that perform better in supervised tasks, which we demonstrate with ridge regression, kernel ridge regression, and sparse kernel regression. We also show that incorporating aspects of simple supervised learning models can improve the accuracy of more complex models, such as feed-forward neural networks. We present adjustments to minimize the impact that any subselection may incur when performing unsupervised tasks. We demonstrate the significant improvements associated with the use of PCov-CUR and PCov-FPS selections for applications to chemistry and materials science, typically reducing by a factor of two the number of features and samples which are required to achieve a given level of regression accuracy.

Machine learning models have emerged as a very effective strategy to sidestep time-consuming electronic-structure calculations, enabling accurate simulations of greater size, time scale and complexity. Given the interpolative nature of these models, the reliability of predictions depends on the position in phase space, and it is crucial to obtain an estimate of the error that derives from the finite number of reference structures included during the training of the model. When using a machine-learning potential to sample a finite-temperature ensemble, the uncertainty on individual configurations translates into an error on thermodynamic averages, and provides an indication for the loss of accuracy when the simulation enters a previously unexplored region. Here we discuss how uncertainty quantification can be used, together with a baseline energy model, or a more robust although less accurate interatomic potential, to obtain more resilient simulations and to support active-learning strategies. Furthermore, we introduce an on-the-fly reweighing scheme that makes it possible to estimate the uncertainty in the thermodynamic averages extracted from long trajectories. We present examples covering different types of structural and thermodynamic properties, and systems as diverse as water and liquid gallium., Comment: 17 pages, 9 figures

The nature of the liquid–solid interface determines the characteristics of a variety of physical phenomena, including catalysis, electrochemistry, lubrication, and crystal growth. Most of the established models for crystal growth are based on macroscopic thermodynamics, neglecting the atomistic nature of the liquid–solid interface. Here, experimental observations and molecular dynamics simulations are employed to identify the 3D nature of an atomic‐scale ordering of liquid Ga in contact with solid GaAs in a nanowire growth configuration. An interplay between the liquid ordering and the formation of a new bilayer is revealed, which, contrary to the established theories, suggests that the preference for a certain polarity and polytypism is influenced by the atomic structure of the interface. The conclusions of this work open new avenues for the understanding of crystal growth, as well as other processes and systems involving a liquid–solid interface.

Infrared pump-probe spectroscopy provides detailed information about the dynamics of hydrogen-bonded liquids. Due to dissipation of the absorbed pump pulse energy, thermal equilibration dynamics also contributes to the observed signal. Disentangling this contribution from the molecular response remains a challenge. By performing non-equilibrium molecular dynamics simulations of liquid-deuterated methanol, we show that faster molecular vibrational relaxation and slower heat diffusion are decoupled and occur on different length scales. Transient structures of the hydrogen bonding network influence thermal relaxation by affecting thermal diffusivity over a length scale of several nanometers.

Hydrogen exhibits unusual behaviors at megabar pressures, with consequences for planetary science, condensed matter physics and materials science. Experiments at such extreme conditions are challenging, often resulting in hard-to-interpret and controversial observations. We present a theoretical study of the phase diagram of dense hydrogen, using machine learning to overcome time and length scale limitations while describing accurately interatomic forces. We reproduce the re-entrant melting behavior and the polymorphism of the solid phase. In simulations based on the machine learning potential we find evidence for continuous metallization in the liquid, as a first-order liquid-liquid transition is pre-empted by freezing. This suggests a smooth transition between insulating and metallic layers in giant gas planets, and reconciles existing discrepancies between experiments as a manifestation of supercritical behavior.

Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the final quantity of interest. Methods such as clustering and dimensionality reduction have been used to provide a simplified, coarse-grained representation of the structure and dynamics of complex systems from proteins to nanoparticles. In recent years, the rise of machine learning has led to an even more widespread use of these algorithms in atomistic modeling and to consider different classification and inference techniques as part of a coherent toolbox of data-driven approaches. This perspective briefly reviews some of the unsupervised machine-learning methods—that are geared toward classification and coarse-graining of molecular simulations—seen in relation to the fundamental mathematical concepts that underlie all machine-learning techniques. It discusses the importance of using concise yet complete representations of atomic structures as the starting point of the analyses and highlights the risk of introducing preconceived biases when using machine learning to rationalize and understand structure-property relations. Supervised machine-learning techniques that explicitly attempt to predict the properties of a material given its structure are less susceptible to such biases. Current developments in the field suggest that using these two classes of approaches side-by-side and in a fully integrated mode, while keeping in mind the relations between the data analysis framework and the fundamental physical principles, will be key to realizing the full potential of machine learning to help understand the behavior of complex molecules and materials.

Infrared pump-probe spectroscopy provides detailed information about the dynamics of hydrogen-bonded liquids. Due to dissipation of the absorbed pump pulse energy, thermal equilibration dynamics also contributes to the observed signal. Disentangling this contribution from the molecular response remains a challenge. By performing non-equilibrium molecular dynamics simulations of liquid-deuterated methanol, we show that faster molecular vibrational relaxation and slower heat diffusion are decoupled and occur on different length scales. Transient structures of the hydrogen bonding network influence thermal relaxation by affecting thermal diffusivity over a length scale of several nanometers.

Automated analyses of the outcome of a simulation have been an important part of atomistic modeling since the early days, addressing the need of linking the behavior of individual atoms and the collective properties that are usually the final quantity of interest. Methods such as clustering and dimensionality reduction have been used to provide a simplified, coarse-grained representation of the structure and dynamics of complex systems from proteins to nanoparticles. In recent years, the rise of machine learning has led to an even more widespread use of these algorithms in atomistic modeling and to consider different classification and inference techniques as part of a coherent toolbox of data-driven approaches. This perspective briefly reviews some of the unsupervised machine-learning methods—that are geared toward classification and coarse-graining of molecular simulations—seen in relation to the fundamental mathematical concepts that underlie all machine-learning techniques. It discusses the importance of using concise yet complete representations of atomic structures as the starting point of the analyses and highlights the risk of introducing preconceived biases when using machine learning to rationalize and understand structure-property relations. Supervised machine-learning techniques that explicitly attempt to predict the properties of a material given its structure are less susceptible to such biases. Current developments in the field suggest that using these two classes of approaches side-by-side and in a fully integrated mode, while keeping in mind the relations between the data analysis framework and the fundamental physical principles, will be key to realizing the full potential of machine learning to help understand the behavior of complex molecules and materials.

Hydrogen exhibits unusual behaviors at megabar pressures, with consequences for planetary science, condensed matter physics and materials science. Experiments at such extreme conditions are challenging, often resulting in hard-to-interpret and controversial observations. We present a theoretical study of the phase diagram of dense hydrogen, using machine learning to overcome time and length scale limitations while describing accurately interatomic forces. We reproduce the re-entrant melting behavior and the polymorphism of the solid phase. In simulations based on the machine learning potential we find evidence for continuous metallization in the liquid, as a first-order liquid-liquid transition is pre-empted by freezing. This suggests a smooth transition between insulating and metallic layers in giant gas planets, and reconciles existing discrepancies between experiments as a manifestation of supercritical behavior.

Water molecules adsorbed on inorganic substrates play an important role in several technological applications. In the presence of light atoms in adsorbates, nuclear quantum effects (NQEs) influence the structural stability and the dynamical properties of these systems. In this work, we explore the impact of NQEs on the dissociation of water wires on stepped Pt(221) surfaces. By performing ab initio molecular dynamics simulations with van der Waals corrected density functional theory, we note that several competing minima for both intact and dissociated structures are accessible at finite temperatures, making it important to assess whether harmonic estimates of the quantum free energy are sufficient to determine the relative stability of the different states. We thus perform ab initio path integral molecular dynamics (PIMD) in order to calculate these contributions taking into account the conformational entropy and anharmonicities at finite temperatures. We propose that when adsorption is weak and NQEs on the substrate are negligible, PIMD simulations can be performed through a simple partition of the system, resulting in considerable computational savings. We then calculate the full contribution of NQEs to the free energies, including also anharmonic terms. We find that they result in an increase of up to 20% of the quantum contribution to the dissociation free energy compared with the harmonic estimates. We also find that the dissociation process has a negligible contribution from tunneling but is dominated by zero point energies, which can enhance the rate of dissociation by three orders of magnitude. Finally we highlight how both temperature and NQEs indirectly impact dipoles and the redistribution of electron density, causing work function changes of up to 0.4 eV with respect to static estimates. This quantitative determination of the change in the work function provides a possible approach to determine experimentally the most stable configurations of water olig

Atomistic simulations of chemical, biological and materials systems have become increasingly precise and predictive owing to the development of accurate and efficient techniques that describe the quantum mechanical behaviour of electrons. Nevertheless, the overwhelming majority of such simulations still assumes that the nuclei behave as classical particles. Historically, this approximation could sometimes be justified owing to the complexity and computational overhead. However, neglecting nuclear quantum effects has become one of the largest sources of error, especially when systems containing light atoms are treated using current state‐of‐the-art descriptions of chemical interactions. Over the past decade, this realization has spurred a series of methodological advances that have dramatically reduced the cost of including these important physical effects in the structure and dynamics of chemical systems. Here, we discuss how these developments are now allowing nuclear quantum effects to become a mainstream feature of molecular simulations. These advances have led to new insights into phenomena that are relevant to different areas of science — from biochemistry to condensed matter — and open the door to many exciting future opportunities

Water molecules adsorbed on inorganic substrates play an important role in several technological applications. In the presence of light atoms in adsorbates, nuclear quantum effects (NQEs) influence the structural stability and the dynamical properties of these systems. In this work, we explore the impact of NQEs on the dissociation of water wires on stepped Pt(221) surfaces. By performing ab initio molecular dynamics simulations with van der Waals corrected density functional theory, we note that several competing minima for both intact and dissociated structures are accessible at finite temperatures, making it important to assess whether harmonic estimates of the quantum free energy are sufficient to determine the relative stability of the different states. We thus perform ab initio path integral molecular dynamics (PIMD) in order to calculate these contributions taking into account the conformational entropy and anharmonicities at finite temperatures. We propose that when adsorption is weak and NQEs on the substrate are negligible, PIMD simulations can be performed through a simple partition of the system, resulting in considerable computational savings. We then calculate the full contribution of NQEs to the free energies, including also anharmonic terms. We find that they result in an increase of up to 20% of the quantum contribution to the dissociation free energy compared with the harmonic estimates. We also find that the dissociation process has a negligible contribution from tunneling but is dominated by zero point energies, which can enhance the rate of dissociation by three orders of magnitude. Finally we highlight how both temperature and NQEs indirectly impact dipoles and the redistribution of electron density, causing work function changes of up to 0.4 eV with respect to static estimates. This quantitative determination of the change in the work function provides a possible approach to determine experimentally the most stable configurations of water olig

Atomistic simulations of chemical, biological and materials systems have become increasingly precise and predictive owing to the development of accurate and efficient techniques that describe the quantum mechanical behaviour of electrons. Nevertheless, the overwhelming majority of such simulations still assumes that the nuclei behave as classical particles. Historically, this approximation could sometimes be justified owing to the complexity and computational overhead. However, neglecting nuclear quantum effects has become one of the largest sources of error, especially when systems containing light atoms are treated using current state‐of‐the-art descriptions of chemical interactions. Over the past decade, this realization has spurred a series of methodological advances that have dramatically reduced the cost of including these important physical effects in the structure and dynamics of chemical systems. Here, we discuss how these developments are now allowing nuclear quantum effects to become a mainstream feature of molecular simulations. These advances have led to new insights into phenomena that are relevant to different areas of science — from biochemistry to condensed matter — and open the door to many exciting future opportunities

We introduce a nonequilibrium molecular dynamics simulation approach, based on the generalized Langevin equation, to study vibrational energy relaxation in pump-probe spectroscopy. A colored noise thermostat is used to selectively excite a set of vibrational modes, leaving the other modes nearly unperturbed, to mimic the effect of a monochromatic laser pump. Energy relaxation is probed by analyzing the evolution of the system after excitation in the microcanonical ensemble, thus providing direct information about the energy redistribution paths at the molecular level and their time scale. The method is applied to hydrogen-bonded molecular liquids, specifically deuterated methanol and water, providing a robust picture of energy relaxation at the molecular scale.

We introduce a nonequilibrium molecular dynamics simulation approach, based on the generalized Langevin equation, to study vibrational energy relaxation in pump-probe spectroscopy. A colored noise thermostat is used to selectively excite a set of vibrational modes, leaving the other modes nearly unperturbed, to mimic the effect of a monochromatic laser pump. Energy relaxation is probed by analyzing the evolution of the system after excitation in the microcanonical ensemble, thus providing direct information about the energy redistribution paths at the molecular level and their time scale. The method is applied to hydrogen-bonded molecular liquids, specifically deuterated methanol and water, providing a robust picture of energy relaxation at the molecular scale.

Nuclear quantum effects influence the structure and dynamics of hydrogen-bonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, theory, and simulation of nuclear quantum effects in water. Novel experimental techniques, such as deep inelastic neutron scattering, now provide a detailed view of the role of nuclear quantum effects in water's properties. These have been combined with theoretical developments such as the introduction of the principle of competing quantum effects that allows the subtle interplay of water's quantum effects and their manifestation in experimental observables to be explained. We discuss how this principle has recently been used to explain the apparent dichotomy in water's isotope effects, which can range from very large to almost nonexistent depending on the property and conditions. We then review the latest major developments in simulation algorithms and theory that have enabled the efficient inclusion of nuclear quantum effects in molecular simulations, permitting their combination with on-the-fly evaluation of the potential energy surface using electronic structure theory. Finally, we identify current challenges and future opportunities in this area of research.

Nuclear quantum effects influence the structure and dynamics of hydrogen-bonded systems, such as water, which impacts their observed properties with widely varying magnitudes. This review highlights the recent significant developments in the experiment, theory, and simulation of nuclear quantum effects in water. Novel experimental techniques, such as deep inelastic neutron scattering, now provide a detailed view of the role of nuclear quantum effects in water's properties. These have been combined with theoretical developments such as the introduction of the principle of competing quantum effects that allows the subtle interplay of water's quantum effects and their manifestation in experimental observables to be explained. We discuss how this principle has recently been used to explain the apparent dichotomy in water's isotope effects, which can range from very large to almost nonexistent depending on the property and conditions. We then review the latest major developments in simulation algorithms and theory that have enabled the efficient inclusion of nuclear quantum effects in molecular simulations, permitting their combination with on-the-fly evaluation of the potential energy surface using electronic structure theory. Finally, we identify current challenges and future opportunities in this area of research.