Four Generations of High-Dimensional Neural Network Potentials

MACE-OFF: Short-Range Transferable Machine Learning Force Fields for Organic Molecules

Classical empirical force fields have dominated biomolecular simulations for over 50 years. Although widely used in drug discovery, crystal structure prediction, and biomolecular dynamics, they generally lack the accuracy and transferability required for first-principles predictive modeling. In this paper, we introduce MACE-OFF, a series of short-range transferable force fields for organic molecules created using state-of-the-art machine learning technology and first-principles reference data computed with a high level of quantum mechanical theory. MACE-OFF demonstrates the remarkable capabilities of short-range models by accurately predicting a wide variety of gas- and condensed-phase properties of molecular systems. It produces accurate, easy-to-converge dihedral torsion scans of unseen molecules as well as reliable descriptions of molecular crystals and liquids, including quantum nuclear effects. We further demonstrate the capabilities of MACE-OFF by determining free energy surfaces in explicit solvent as well as the folding dynamics of peptides and nanosecond simulations of a fully solvated protein. These developments enable first-principles simulations of molecular systems for the broader chemistry community at high accuracy and relatively low computational cost.

Fundamental invariant-neural network as a correction to the intramolecular force field illustrated for the full-dimensional potential energy surface of propane

As a highly effective approach for constructing potential energy surfaces (PESs) with both precision and efficiency, Δ-machine learning has been widely used in PES development. Inspired by the Δ-machine learning framework, we develop a combined model of fundamental invariant-neural network (FI-NN) and force field. Fitting the difference between the force field and ab initio energy by the FI-NN method is able to improve the accuracy of the force field. We demonstrate this enhanced methodology through the development of an intramolecular force field for propane, where CCSD(T)-F12a/AVTZ energies are initially approximated by the force field and subsequently refined using the FI-NN approach. Compared to the PES fitted by FI-NN, this combined method reduces the root mean square error (RMSE) by 50%.

ReaxFF-nn: a reactive machine-learning potential in GULP/LAMMPS and its applications in the thermal conductivity calculations of carbon nanostructures

The term "ReaxFF-nn" refers to the reactive force field (ReaxFF) with neural networks. In the current work, we have incorporated it into the general utility lattice program (GULP) and the large-scale atomic/molecular massively parallel simulator (LAMMPS), which are programmed with modern FORTRAN and C++, respectively. The parameters of ReaxFF-nn can be trained using our I-ReaxFF package. By combining GULP, LAMMPS and ReaxFF-nn, various tasks, such as determination of thermal properties and crystal properties, and energy minimization, can be performed with precision at the quasi-density functional theory (DFT) level. Compared to other machine-learning potentials (MLPs), our approach does not involve the development of an entirely new machine-learning potential; instead, a small neural network was implemented to compute the bond order and bond energy. To validate the model in GULP and LAMMPS, the forces of graphene and carbon nanotube (CNT) structures were compared among the auto-differentiation, GULP, and LAMMPS packages with our codes. The differences between these calculations are within 10-5. After the potential was trained against DFT calculations with losses of forces up to 10-2 eV Å-1 per atom, an example study of the thermal conductivity (κ) of graphene and carbon nanotubes (CNTs) using the Boltzmann transport equation (BTE) and non-equilibrium molecular dynamics (NEMD) methods was conducted. The value of κ for graphene obtained using ReaxFF-nn closely matches the results obtained from DFT calculations. The size dependence and the relations with the CNT diameter are discussed through NEMD calculations.

The evolution of machine learning potentials for molecules, reactions and materials

Recent years have witnessed the fast development of machine learning potentials (MLPs) and their widespread applications in chemistry, physics, and material science. By fitting discrete ab initio data faithfully to continuous and symmetry-preserving mathematical forms, MLPs have enabled accurate and efficient atomistic simulations in a large scale from first principles. In this review, we provide an overview of the evolution of MLPs in the past two decades and focus on the state-of-the-art MLPs proposed in the last a few years for molecules, reactions, and materials. We discuss some representative applications of MLPs and the trend of developing universal potentials across a variety of systems. Finally, we outline a list of open challenges and opportunities in the development and applications of MLPs.

Computing Bulk Phase IR Spectra from Finite Cluster Data via Equivariant Neural Networks

Calculating accurate IR spectra from molecular dynamics simulations is crucial for understanding structural dynamics and benchmarking simulations. While machine learning has accelerated such calculations, leveraging finite-cluster data to compute condensed-phase IR spectra remains unexplored. In this work, we address a fundamental question: Can a machine learning model trained exclusively on electronic structure calculations of finite-size clusters reproduce the bulk IR spectrum? Using the atomic polar tensor as a target training property, we demonstrate that the corresponding equivariant neural network accurately recovers the bulk IR spectrum of liquid water, establishing the key link between finite-cluster data and bulk properties.

TrIP2: Expanding the Transformer Interatomic Potential Demonstrates Architectural Scalability for Organic Compounds

TrIP2 is an advanced version of the transformer interatomic potential (TrIP) trained on the expanded ANI-2x data set, including more diverse molecular configurations with sulfur, fluorine, and chlorine. It leverages the equivariant SE(3)-transformer architecture, incorporating physical biases and continuous atomic representations. TrIP was introduced as a highly promising transferable interatomic potential, which we show here to generalize to new atom types with no alterations to the underlying model design. Benchmarking on COMP6 energy and force calculations, structure minimization tasks, torsion drives, and applications to molecules with unexpected conformational energy minima demonstrates TrIP2's high accuracy and transferability. Direct architectural comparisons demonstrate superior performance against ANI-2x, while holistic model evaluations─including training data and level-of-theory considerations─show comparative performance with state-of-the-art models like AIMNet2 and MACE-OFF23. Notably, TrIP2 achieves state-of-the-art force prediction performance on the COMP6 benchmarks and closely approaches DFT-optimized structures in torsion drives and geometry optimization tasks. Without requiring any architectural modifications, TrIP2 successfully capitalizes on additional training data to deliver enhanced generalizability and precision, establishing itself as a robust and scalable framework capable of accommodating future expansions or applications to new domains with minimal reengineering.

Revisiting Machine Learning Potentials for Silicate Glasses: The Missing Role of Dispersion Interactions

Machine learning interatomic potentials (MLIPs) offer a promising alternative to traditional force fields and ab initio methods for simulating complex materials such as oxide glasses. In this work, we present the first evaluation of the pretrained MACE (Multi-ACE) model [D.P. Kovács et al., J. Chem. Phys. 159(2023), 044118] for silicate glasses, using sodium silicates as a test case. We compare its performance with a DeePMD-based MLIP specifically trained on sodium silicate compositions [M. Bertani et al., J. Chem. Theory Comput. 20(2024), 1358-1370] and assess their accuracy in reproducing structural and dynamical properties. Additionally, we investigate the role of dispersion interactions by incorporating the D3(BJ) correction in both models. Our results show that while MACE accurately reproduces neutron structure factors, pair distribution functions, and Si[Qn] speciation, it performs slightly worst for elastic properties calculations. However, it is suitable for the simulations of sodium silicate glasses. The inclusion of dispersion interactions significantly improves the reproduction of density and elastic properties for both MLIPs, highlighting their critical role in glass modeling. These findings provide insight into the transferability of general MLIPs to disordered systems and emphasize the need for dispersion-aware training data sets in developing accurate force fields for oxide glasses.

Free energy profiles for chemical reactions in solution from high-dimensional neural network potentials: The case of the Strecker synthesis

Machine learning potentials (MLPs) have become a popular tool in chemistry and materials science as they combine the accuracy of electronic structure calculations with the high computational efficiency of analytic potentials. MLPs are particularly useful for computationally demanding simulations such as the determination of free energy profiles governing chemical reactions in solution, but to date, such applications are still rare. In this work, we show how umbrella sampling simulations can be combined with active learning of high-dimensional neural network potentials (HDNNPs) to construct free energy profiles in a systematic way. For the example of the first step of Strecker synthesis of glycine in aqueous solution, we provide a detailed analysis of the improving quality of HDNNPs for datasets of increasing size. We find that, in addition to the typical quantification of energy and force errors with respect to the underlying density functional theory data, the long-term stability of the simulations and the convergence of physical properties should be rigorously monitored to obtain reliable and converged free energy profiles of chemical reactions in solution.

Machine learning applications for thermochemical and kinetic property prediction

Detailed kinetic models play a crucial role in comprehending and enhancing chemical processes. A cornerstone of these models is accurate thermodynamic and kinetic properties, ensuring fundamental insights into the processes they describe. The prediction of these thermochemical and kinetic properties presents an opportunity for machine learning, given the challenges associated with their experimental or quantum chemical determination. This study reviews recent advancements in predicting thermochemical and kinetic properties for gas-phase, liquid-phase, and catalytic processes within kinetic modeling. We assess the state-of-the-art of machine learning in property prediction, focusing on three core aspects: data, representation, and model. Moreover, emphasis is placed on machine learning techniques to efficiently utilize available data, thereby enhancing model performance. Finally, we pinpoint the lack of high-quality data as a key obstacle in applying machine learning to detailed kinetic models. Accordingly, the generation of large new datasets and further development of data-efficient machine learning techniques are identified as pivotal steps in advancing machine learning's role in kinetic modeling.

Extending atomic decomposition and many-body representation with a chemistry-motivated approach to machine learning potentials

Most widely used machine learning potentials for condensed-phase applications rely on many-body permutationally invariant polynomial or atom-centered neural networks. However, these approaches face challenges in achieving chemical interpretability in atomistic energy decomposition and fully matching the computational efficiency of traditional force fields. Here we present a method that combines aspects of both approaches and balances accuracy and force-field-level speed. This method utilizes a monomer-centered representation, where the potential energy is decomposed into the sum of chemically meaningful monomeric energies. The structural descriptors of monomers are described by one-body and two-body effective interactions, enforced by appropriate sets of permutationally invariant polynomials as inputs to the feed-forward neural networks. Systematic assessments of models for gas-phase water trimer, liquid water, methane-water cluster and liquid carbon dioxide are performed. The improved accuracy, efficiency and flexibility of this method have promise for constructing accurate machine learning potentials and enabling large-scale quantum and classical simulations for complex molecular systems.

Accounting for the vibrational contribution to the configurational entropy in disordered solids with machine learned forcefields: a case study of garnet electrolyte Li7La3Zr2O12

Accounting for lattice vibrations to accurately determine the phase stabilities of site-disordered solids is a long-standing challenge in computational material designs, due to the high computational cost associated with sampling the vast configurational space to obtain the converged thermodynamic quantities. One example is the garnet electrolyte Li7La3Zr2O12, the high-temperature and high-ion-mobility cubic phase of which is disordered in its Li+ site occupations, such that both the vibrational and configurational entropic contributions to its phase stability cannot be ignored. Understanding the subtle interplay between vibrational and configurational entropies in this material will therefore play a critical role in the rational manipulation of dopants and defects to stabilise cubic Li7La3Zr2O12 at room temperature for practical applications. Here, by developing machine learned forcefields based on an equivariant message-passing neural network SO3KRATES, we follow a strict statistical thermodynamic protocol to quantify the phase stability of cubic Li7La3Zr2O12 through structural optimisations, as well as molecular dynamics simulations at 300 and 1500 K, for a total of 70 120 configurations of cubic Li7La3Zr2O12. Although this only covers a tiny fraction of the configurational space (∼7 × 1034 configurations in total), we are able to deterministically show that the vibrational contributions to the total configurational free energy at 1500 K are significant (on the order of 1 eV per atom) in correctly ordering the stability of the cubic Li7La3Zr2O12 over its tetragonal counterpart, thanks to the high data efficiency, accuracy, stability and good transferability of the transformer-based equivariant network architecture behind SO3KRATES. Therefore, our work opens up new avenues to accelerate the accurate computational designs of disordered solids, such as solid electrolytes, for technologically important applications.

AIMNet2: a neural network potential to meet your neutral, charged, organic, and elemental-organic needs

Machine learned interatomic potentials (MLIPs) are reshaping computational chemistry practices because of their ability to drastically exceed the accuracy-length/time scale tradeoff. Despite this attraction, the benefits of such efficiency are only impactful when an MLIP uniquely enables insight into a target system or is broadly transferable outside of the training dataset. In this work, we present the 2nd generation of our atoms-in-molecules neural network potential (AIMNet2), which is applicable to species composed of up to 14 chemical elements in both neutral and charged states, making it a valuable method for modeling the majority of non-metallic compounds. Using an exhaustive dataset of 2 × 107 hybrid DFT level of theory quantum chemical calculations, AIMNet2 combines ML-parameterized short-range and physics-based long-range terms to attain generalizability that reaches from simple organics to diverse molecules with "exotic" element-organic bonding. We show that AIMNet2 outperforms semi-empirical GFN2-xTB and is on par with reference density functional theory for interaction energy contributions, conformer search tasks, torsion rotation profiles, and molecular-to-macromolecular geometry optimization. Overall, the demonstrated chemical coverage and computational efficiency of AIMNet2 is a significant step toward providing access to MLIPs that avoid the crucial limitation of curating additional quantum chemical data and retraining with each new application.

Machine Learning-Driven Insights for Phase-Stable FA x Cs1-x Pb(I y Br1-y )3 Perovskites in Tandem Solar Cells

The inherent chemical tunability of perovskite materials has spurred extensive research into composition engineering within the perovskite community. However, identifying the optimal composition across a broad range of variations still remains a significant challenge. Conventional trial-and-error methods are prohibitively expensive and environmentally taxing for comprehensive screening. Here, we employed machine learning-accelerated atomic simulation to guide the design of stable perovskite solar cells absorbers. Our approach entailed training of a neural network (NN) potential using data generated from first-principles calculations, yielding a perovskite NN potential exhibiting high accuracy. Utilizing this NN potential, we constructed a phase diagram for FA x Cs1-x Pb(I y Br1-y )3 (where 0 ≤ x ≤ 1 and 0 ≤ y ≤ 1, FA denotes formamidinium cation). Integrating this with a band gap diagram, we successfully identified global optimal perovskite compositions for tandem applications with 1.7 and 1.8 eV band gaps. We have identified that all FA x Cs1-x Pb(I y Br1-y )3 with >1.8 eV band gaps are thermodynamically vulnerable to phase segregation and developed a strategy to stabilize thermodynamically unstable phases by suppressing phase segregation kinetics. Finally, theoretical predictions were confirmed by the corresponding experiments. Our results suggest that creating perovskites/Si tandem solar cells with 1.7 eV FA x Cs1-x Pb(I y Br1-y )3 encounters less severe challenges in addressing phase segregation issues than perovskites/perovskites tandem solar cells with 1.8 eV FA x Cs1-x Pb(I y Br1-y )3.

A Perspective on Foundation Models in Chemistry

Foundation models are an emerging paradigm in artificial intelligence (AI), with successful examples like ChatGPT transforming daily workflows. Generally, foundation models are large-scale, pretrained models capable of adapting to various downstream tasks by leveraging extensive data and model scaling. Their success has inspired researchers to develop foundation models for a wide range of chemical challenges, from materials discovery to understanding structure-property relationships, areas where conventional machine learning (ML) models often face limitations. In addition, foundation models hold promise for addressing persistent ML challenges in chemistry, such as data scarcity and poor generalization. In this perspective, we review recent progress in the development of foundation models in chemistry across applications of varying scope. We also discuss emerging trends and provide an outlook on promising approaches for advancing foundation models in chemistry.

Controlling Stereoselectivity with Noncovalent Interactions in Chiral Phosphoric Acid Organocatalysis

Chiral phosphoric acids (CPAs) have emerged as highly effective Brønsted acid catalysts in an expanding range of asymmetric transformations, often through novel multifunctional substrate activation modes. Versatile and broadly appealing, these catalysts benefit from modular and tunable structures, and compatibility with additives. Given the unique types of noncovalent interactions (NCIs) that can be established between CPAs and various reactants─such as hydrogen bonding, aromatic interactions, and van der Waals forces─it is unsurprising that these catalyst systems have become a promising approach for accessing diverse chiral product outcomes. This review aims to provide an in-depth exploration of the mechanisms by which CPAs impart stereoselectivity, positioning NCIs as the central feature that connects a broad spectrum of catalytic reactions. Spanning literature from 2004 to 2024, it covers nucleophilic additions, radical transformations, and atroposelective bond formations, highlighting the applicability of CPA organocatalysis. Special emphasis is placed on the structural and mechanistic features that govern CPA-substrate interactions, as well as the tools and techniques developed to enhance our understanding of their catalytic behavior. In addition to emphasizing mechanistic details and stereocontrolling elements in individual reactions, we have carefully structured this review to provide a natural progression from these specifics to a broader, class-level perspective. Overall, these findings underscore the critical role of NCIs in CPA catalysis and their significant contributions to advancing asymmetric synthesis.

Accurate Determination of Isotope Effects on the Dynamics of H-Bond Breaking and Making in Liquid Water

Isotopic substitution of light hydrogen atoms with heavier deuterium atoms in liquid water renders the resulting liquid, heavy water (D2O), poisonous to most organisms when it replaces a critical fraction of water in living organisms. The mechanisms through which heavy water disrupts biological function are challenging to disentangle experimentally. Isotopic substitution has long been known to affect the H-bond dynamics of liquid water, but experiments have yet to quantify the extent of the differences in the time scales of H-bond breaking and making processes between H2O and D2O. In this work, we analyze H-bond dynamics through extensive coupled cluster-quality path integral simulations of H2O and D2O under ambient conditions that grant access to unambiguous molecular analyses. We find substantial isotope substitution effects on the rates of H-bond formation and breaking, and H-bond lifetimes, with dynamics in D2O ∼25% slower than in H2O. The toxicity of D2O can thus be ascribed, at least in part, to the effect of slowed H-bond dynamics on biochemical reactions.

Fast and flexible long-range models for atomistic machine learning

Most atomistic machine learning (ML) models rely on a locality ansatz and decompose the energy into a sum of short-ranged, atom-centered contributions. This leads to clear limitations when trying to describe problems that are dominated by long-range physical effects-most notably electrostatics. Many approaches have been proposed to overcome these limitations, but efforts to make them efficient and widely available are hampered by the need to incorporate an ad hoc implementation of methods to treat long-range interactions. We develop a framework aiming to bring some of the established algorithms to evaluate non-bonded interactions-including Ewald summation, classical particle-mesh Ewald, and particle-particle/particle-mesh Ewald-into atomistic ML. We provide a reference implementation for PyTorch as well as an experimental one for JAX. Beyond Coulomb and more general long-range potentials, we introduce purified descriptors that disregard the immediate neighborhood of each atom and are more suitable for general long-range ML applications. Our implementations are fast, feature-rich, and modular: They provide an accurate evaluation of physical long-range forces that can be used in the construction of (semi)empirical baseline potentials; they exploit the availability of automatic differentiation to seamlessly combine long-range models with conventional, local ML schemes; and they are sufficiently flexible to implement more complex architectures that use physical interactions as building blocks. We benchmark and demonstrate our torch-pme and jax-pme libraries to perform molecular dynamics simulations, train ML potentials, and evaluate long-range equivariant descriptors of atomic structures.

Structures and Ion Transport Properties of Hydrate-Melt Electrolytes: A Machine-Learning Potential Molecular Dynamics Study

High-concentration aqueous electrolytes (hydrate-melts) have attracted significant attention for lithium-ion batteries due to their nonflammability and low toxicity. In these electrolytes, the static and dynamic structures of the solvent play a crucial role in determining various properties, such as the ionic conductivity, of the system. To clarify the solvent structure and ion diffusion mechanism, we conducted molecular dynamics simulations using a machine learning potential for Li and Na hydrate-melts. By analyzing the dynamical interaction between ions and their coordinating molecules, we found the ligand exchange of H2O molecules coordinated to cations occurs frequently. As a result, it is considered that the kinetic energy of H2O is transferred to cations and drives the diffusion of cations in the hydrate-melts. This ion transport mechanism is different from the conventionally understood vehicle-type or hopping-type ion transport mechanism. The comparison of Na hydrate-melts and Li hydrate-melts shows the higher diffusion of Na relative to Li. It was suggested that there exists an optimal value for the strength of interaction between cations and H2O molecules, which influences ion diffusion, and that the interaction for Na is close to this optimal value compared to that of the Li.

Methods for Theoretical Treatment of Local Fields in Proteins and Enzymes

Electric fields generated by protein scaffolds are crucial in enzymatic catalysis. This review surveys theoretical approaches for detecting, analyzing, and comparing electric fields, electrostatic potentials, and their effects on the charge density within enzyme active sites. Pioneering methods like the empirical valence bond approach rely on evaluating ionic and covalent resonance forms influenced by the field. Strategies employing polarizable force fields also facilitate field detection. The vibrational Stark effect connects computational simulations to experimental Stark spectroscopy, enabling direct comparisons. We highlight how protein dynamics induce fluctuations in local fields, influencing enzyme activity. Recent techniques assess electric fields throughout the active site volume rather than only at specific bonds, and machine learning helps relate these global fields to reactivity. Quantum theory of atoms in molecules captures the entire electron density landscape, providing a chemically intuitive perspective on field-driven catalysis. Overall, these methodologies show protein-generated fields are highly dynamic and heterogeneous, and understanding both aspects is critical for elucidating enzyme mechanisms. This holistic view empowers rational enzyme engineering by tuning electric fields, promising new avenues in drug design, biocatalysis, and industrial applications. Future directions include incorporating electric fields as explicit design targets to enhance catalytic performance and biochemical functionalities.

Diabatic States of Charge Transfer with Constrained Charge Equilibration

Charge transfer (CT) processes that are electronically nonadiabatic are ubiquitous in chemistry, biology, and materials science, but their theoretical description requires diabatic states or adiabatic excited states. For complex systems, these latter states are more difficult to calculate than the adiabatic ground state. Here, we propose a simple method to obtain diabatic states, including energies and charges, by constraining the atomic charges within the charge equilibration framework. For two-state systems, the exact diabatic coupling can be determined, from which the adiabatic excited-state energy can also be calculated. The method can be viewed as an affordable alternative to constrained density functional theory (CDFT), and so we call it constrained charge equilibration (CQEq). We test the CQEq method on the anthracene-tetracyanoethylene CT complex and the reductive decomposition of ethylene carbonate on a lithium metal surface. We find that CQEq predicts diabatic energies, charges, and adiabatic excitation energies in good agreement with CDFT, and we propose that CQEq is promising for combination with machine learning force fields to study nonadiabatic CT in the condensed phase.

A beginner's approach to deep learning applied to VS and MD techniques

It has become impossible to imagine the fields of biochemistry and medicinal chemistry without computational chemistry and molecular modelling techniques. In many steps of the drug development process in silico methods have become indispensable. Virtual screening (VS) can tremendously expedite the early discovery phase, whilst the use of molecular dynamics (MD) simulations forms a powerful additional tool to in vitro methods throughout the entire drug discovery process. In the field of biochemistry, MD has also become a compelling method for studying biophysical systems (e.g., protein folding) complementary to experimental techniques. However, both VS and MD come with their own limitations and methodological difficulties, from hardware limitations to restrictions in algorithmic capabilities. One solution to overcoming these difficulties lies in the field of machine learning (ML), and more specifically deep learning (DL). There are many ways in which DL can be applied to these molecular modelling techniques to achieve more accurate results in a more efficient manner or expedite the data analysis of the acquired results. Despite steadily increasing interest in DL amidst computational chemists, knowledge is still limited and scattered over different resources. This review is aimed at computational chemists with knowledge of molecular modelling, who wish to possibly integrate DL approaches in their research and already have a basic understanding of the fundamentals of DL. This review focusses on a survey of recent applications of DL in molecular modelling techniques. The different sections are logically subdivided, based on where DL is integrated in the research: (1) for the improvement of VS workflows, (2) for the improvement of certain workflows in MD simulations, (3) for aiding in the calculations of interatomic forces, or (4) for data analysis of MD trajectories. It will become clear that DL has the capacity to completely transform the way molecular modelling is carried out.

Transferability Across Different Molecular Systems and Levels of Theory with the Data-Driven Coupled-Cluster Scheme

Machine learning has recently been introduced into the arsenal of tools that are available to computational chemists. In the past few years, we have seen an increase in the applicability of these tools on a plethora of applications, including the automated exploration of a large fraction of the chemical space, the reduction of repetitive computational tasks, the detection of outliers on large databases, and the acceleration of molecular simulations. An attractive application of machine learning in molecular electronic structure theory is the "recycling" of molecular wave functions for faster and more accurate completion of complex quantum chemical calculations. Along these lines, we have developed hybrid quantum chemical/machine learning workflows that utilize information from low-level wave functions for the accurate prediction of higher-level wave functions. The data-driven coupled-cluster (DDCC) family of methods is discussed in this article together with the importance of the inclusion of physical properties in such hybrid workflows. After a short introduction to the philosophy and the capabilities of DDCC, we present our recent progress in extending its applicability to larger and more complex molecular structures and data sets. A significant advantage offered by DDCC is its transferability, with respect to different molecular systems and different excitation levels. As we show here, predicted wave functions at the coupled-cluster singles and doubles level of theory can be used for the accurate prediction of the perturbative triples of the CCSD(T) scheme. We conclude with some personal considerations with respect to future directions related to the development of the next generation of such hybrid quantum chemical/machine learning models.

X2-PEC: A Neural Network Model Based on Atomic Pair Energy Corrections

With the development of artificial neural networks (ANNs), its applications in chemistry have become increasingly widespread, especially in the prediction of various molecular properties. This work introduces the X2-PEC method, that is, the second generalization of the X1 series of ANN methods developed in our group, utilizing pair energy correction (PEC). The essence of the X2 model lies in its feature vector construction, using overlap integrals and core Hamiltonian integrals to incorporate physical and chemical information into the feature vectors to describe atomic interactions. It aims to enhance the accuracy of low-rung density functional theory (DFT) calculations, such as those from the widely used BLYP/6-31G(d) or B3LYP/6-31G(2df,p) methods, to the level of top-rung DFT calculations, such as those from the highly accurate doubly hybrid XYGJ-OS/GTLarge method. Trained on the QM9 dataset, X2-PEC excels in predicting the atomization energies of isomers such as C6H8 and C4H4N2O with varying bonding structures. The performance of the X2-PEC model on standard enthalpies of formation for datasets such as G2-HCNOF, PSH36, ALKANE28, BIGMOL20, and HEDM45, as well as a HCNOF subset of BH9 for reaction barriers, is equally commendable, demonstrating its good generalization ability and predictive accuracy, as well as its potential for further development to achieve greater accuracy. These outcomes highlight the practical significance of the X2-PEC model in elevating the results from lower-rung DFT calculations to the level of higher-rung DFT calculations through deep learning.

Iterative charge equilibration for fourth-generation high-dimensional neural network potentials

Machine learning potentials allow performing large-scale molecular dynamics simulations with about the same accuracy as electronic structure calculations, provided that the selected model is able to capture the relevant physics of the system. For systems exhibiting long-range charge transfer, fourth-generation machine learning potentials need to be used, which take global information about the system and electrostatic interactions into account. This can be achieved in a charge equilibration step, but the direct solution of the set of linear equations results in an unfavorable cubic scaling with system size, making this step computationally demanding for large systems. In this work, we propose an alternative approach that is based on the iterative solution of the charge equilibration problem (iQEq) to determine the atomic partial charges. We have implemented the iQEq method, which scales quadratically with system size, in the parallel molecular dynamics software LAMMPS for the example of a fourth-generation high-dimensional neural network potential (4G-HDNNP) intended to be used in combination with the n2p2 library. The method itself is general and applicable to many different types of fourth-generation MLPs. An assessment of the accuracy and the efficiency is presented for a benchmark system of FeCl3 in water.

From Ab Initio to Instrumentation: A Field Guide to Characterizing Multivalent Liquid Electrolytes

In this field guide, we outline empirical and theory-based approaches to characterize the fundamental properties of liquid multivalent-ion battery electrolytes, including (i) structure and chemistry, (ii) transport, and (iii) electrochemical properties. When detailed molecular-scale understanding of the multivalent electrolyte behavior is insufficient we use examples from well-studied lithium-ion electrolytes. In recognition that coupling empirical and theory-based techniques is highly effective, but often nontrivial, we also highlight recent electrolyte characterization efforts that uncover a more comprehensive and nuanced understanding of the underlying structures, processes, and reactions that drive performance and system-level behavior. We hope the insights from these discussions will guide the design of future electrolyte studies, accelerate development of next-generation multivalent-ion batteries through coupling of modeling with experiments, and help to avoid pitfalls and ensure reproducibility of modeling results.

Comparative Study of UMCM-9 Polymorphs: Structural, Dynamic, and Hydrogen Storage Properties via Atomistic Simulations

The structural and dynamic properties of two polymorphs of the metal-organic framework UMCM-9 (UMCM-9-α and -β) have been studied via molecular dynamics (MD) simulations in conjunction with density functional tight binding (DFTB) as well as the newly developed MACE-MP neural network potential (NNP). Based on these calculations, a novel UMCM-9-β polymorph is proposed that exhibits reduced linker strain and increased flexibility compared to UMCM-9-α, which is shown to be energetically less stable. UMCM-9-β exhibits enhanced diffusion of molecular hydrogen due to weaker host-guest interactions, whereas UMCM-9-α exhibits stronger interactions, leading to improved hydrogen adsorption. The results suggest that synthesis conditions may control the formation of both polymorphs: UMCM-9-β is likely to be the thermodynamic product, forming under stable conditions, while UMCM-9-α may be the kinetic product, forming under accelerated synthesis conditions. This study highlights the potential for optimizing MOFs for specific gas storage applications to achieve the desired structural and associated gas storage properties.

Active phase discovery in heterogeneous catalysis via topology-guided sampling and machine learning

Understanding active phases across interfaces, interphases, and even within the bulk under varying external conditions and environmental species is critical for advancing heterogeneous catalysis. Describing these phases through computational models faces the challenges in the generation and calculation of a vast array of atomic configurations. Here, we present a framework for the automatic and efficient exploration of active phases. This approach utilizes a topology-based algorithm leveraging persistent homology to systematically sample configurations across diverse coordination environments and material morphologies. Simultaneously, efficient machine learning force fields enable rapid computations. We demonstrate the effectiveness of this framework in two systems: hydrogen absorption in Pd, where hydrogen penetrates subsurface layers and the bulk, inducing a "hex" reconstruction critical for CO2 electroreduction, explored through 50,000 sampled configurations; and the oxidation dynamics of Pt clusters, where oxygen incorporation renders the clusters less active during oxygen reduction reactions, investigated through 100,000 sampled configurations. In both cases, the predicted active phases and their impacts on catalytic mechanisms closely align with previous experimental observations, indicating that the proposed strategy can model complex catalytic systems and discovery active phases under specific environmental conditions.

Machine Learning Force Field for Optimization of Isolated and Supported Transition Metal Particles

Computational modeling is an integral part of catalysis research. With it, new methodologies are being developed and implemented to improve the accuracy of simulations while reducing the computational cost. In particular, specific machine-learning techniques have been applied to build interatomic potential from ab initio results. Here, we report an energy-free machine-learning calculator that combines three individually trained neural networks to predict the energy and atomic forces of metallic particles. The investigated structures were a monometallic Pd nanoparticle, a bimetallic AuPd nanoalloy, and supported Pd metal crystallites on silica. Atomic energies were predicted via a graph neural network, leading to a mean absolute error (MAE) within 0.004 eV from density functional theory (DFT) calculations. The task of predicting atomic forces was split over two feed-forward networks, one predicting the force norm and another its direction. The force prediction resulted in a MAE within 0.080 eV/Å against DFT results. The interpretability of the graph neural network predictions was demonstrated by underlying the physics of the monometallic particle in the form of cohesion energy.

Automatic Process Exploration through Machine Learning Assisted Transition State Searches

We present an efficient automatic process explorer (APE) framework to overcome the reliance on human intuition to empirically establish relevant elementary processes of a given system, e.g., in prevalent kinetic Monte Carlo (kMC) simulations based on fixed process lists. Use of a fuzzy machine learning classification algorithm minimizes redundancy in the transition-state searches by driving them toward hitherto unexplored local atomic environments. APE application to island diffusion at a Pd(100) surface immediately reveals a large number of, up to now, disregarded low-barrier collective processes that lead to a significant increase in the kMC-determined island diffusivity as compared to classic surface hopping and exchange diffusion mechanisms.

Machine learning in molecular biophysics: Protein allostery, multi-level free energy simulations, and lipid phase transitions

Machine learning (ML) techniques have been making major impacts on all areas of science and engineering, including biophysics. In this review, we discuss several applications of ML to biophysical problems based on our recent research. The topics include the use of ML techniques to identify hotspot residues in allosteric proteins using deep mutational scanning data and to analyze how mutations of these hotspots perturb co-operativity in the framework of a statistical thermodynamic model, to improve the accuracy of free energy simulations by integrating data from different levels of potential energy functions, and to determine the phase transition temperature of lipid membranes. Through these examples, we illustrate the unique value of ML in extracting patterns or parameters from complex data sets, as well as the remaining limitations. By implementing the ML approaches in the context of physically motivated models or computational frameworks, we are able to gain a deeper mechanistic understanding or better convergence in numerical simulations. We conclude by briefly discussing how the introduced models can be further expanded to tackle more complex problems.

Δ-EGNN Method Accelerates the Construction of Machine Learning Potential

Recent advancements in molecular simulations highlight the substantial computational demands of generating high-precision quantum mechanical labels for training neural network potentials. These challenges emphasize the need for improvements in delta-machine learning techniques. The Equivariant Graph Neural Network (EGNN) framework, grounded in a message-passing mechanism that preserves structural equivariance, enables refined atomic representations through interaction-driven updates. We introduce the Δ-EGNN model, which achieves high prediction accuracy for both molecular and condensed-phase systems. For example, in periodic water box systems, a mean absolute error of 1.722 meV/atom for energy (global property) and 0.0027 e for partial charge (local property) were achieved with training on just 800 labels. Δ-EGNN is computationally efficient, achieving speedups of 1-2 orders of magnitude compared to conventional methods at the MP2 level. In contrast to models directly trained on total energies, such as NequIP, MACE, and Allegro, the Δ-EGNN model employs delta-machine learning to predict the difference between energies derived from low- and high-level electronic structure methods, providing a significant advantage in reducing computational costs while preserving high accuracy. In summary, Δ-EGNN opens a new avenue for exploring energy landscapes and constructing machine learning potentials with afforable computational overhead, facilitating routine quantum mechanical calculations for complex molecular systems.

Structure and Dynamics of the Magnetite(001)/Water Interface from Molecular Dynamics Simulations Based on a Neural Network Potential

The magnetite/water interface is commonly found in nature and plays a crucial role in various technological applications. However, our understanding of its structural and dynamical properties at the molecular scale remains still limited. In this study, we developed an efficient Behler-Parrinello neural network potential (NNP) for the magnetite/water system, paying particular attention to the accurate generation of reference data with density functional theory. Using this NNP, we performed extensive molecular dynamics simulations of the magnetite (001) surface across a wide range of water coverages, from single molecules to bulk water. Our simulations revealed several new ground states of low coverage water on the Subsurface Cation Vacancy (SCV) model and yielded a density profile of water at the surface that exhibits marked layering. By calculating mean square displacements, we obtained quantitative information on the diffusion of water molecules on the SCV for different coverages, revealing significant anisotropy. Additionally, our simulations provided qualitative insights into the dissociation mechanisms of water molecules at the surface.

Revealing the molecular interplay of coverage, wettability, and capacitive response at the Pt(111)-water solution interface under bias

While electrified interfaces are crucial for electrocatalysis and corrosion, their molecular morphology remains largely unknown. Through highly realistic ab initio molecular dynamics simulations of the Pt(111)-water solution interface in reducing conditions, we reveal a deep interconnection among electrode coverage, wettability, capacitive response, and catalytic activity. We identify computationally the experimentally hypothesised states for adsorbed hydrogen on Pt, HUPD and HOPD, revealing their role in governing interfacial water reorientation and hydrogen evolution. The transition between these two H states with increasing potential, induces a shift from a hydrophobic to a hydrophilic interface and correlates with a change in the primary electrode screening mechanism. This results in a slope change in differential capacitance, marking the onset of the experimentally observed peak around the potential of zero charge. Our work produces crucial insights for advancing electrocatalytic energy conversion, developing deep understanding of electrified interfaces.

Ab Initio Valence Bond Molecular Dynamics: A Study of SN2 Reaction Mechanisms

In this paper, a molecular dynamics (MD) approach based on ab initio classical valence bond (VB) theory, referred to as AIVBMD, is presented. To validate AIVBMD, a novel algorithm that enables efficient computation of energy gradients based on nonorthogonal orbitals is introduced. Taking the gas-phase SN2 reaction as an example, a compact VB wave function gives reasonable accuracy with only 27 VB structures, compared to the full active space of 5292 VB structures. Furthermore, AIVBMD provides intuitive chemical insights into the reaction process, detailing the breaking and formation of chemical bonds, thereby elucidating the reaction mechanism. In summary, as the first attempt at the ab initio classical VB method-based MD approach, this paper demonstrates that VB theory offers a novel perspective and significant potential for investigating chemical reaction dynamics and mechanisms.

Outlier-detection for reactive machine learned potential energy surfaces

Uncertainty quantification (UQ) to detect samples with large expected errors (outliers) is applied to reactive molecular potential energy surfaces (PESs). Three methods-Ensembles, deep evidential regression (DER), and Gaussian Mixture Models (GMM)-were applied to the H-transfer reaction between syn-Criegee and vinyl hydroxyperoxide. The results indicate that ensemble models provide the best results for detecting outliers, followed by GMM. For example, from a pool of 1000 structures with the largest uncertainty, the detection quality for outliers is ~90% and ~50%, respectively, if 25 or 1000 structures with large errors are sought. On the contrary, the limitations of the statistical assumptions of DER greatly impact its prediction capabilities. Finally, a structure-based indicator was found to be correlated with large average error, which may help to rapidly classify new structures into those that provide an advantage for refining the neural network.

When theory meets experiment: What does it take to accurately predict 1H NMR dipolar relaxation rates in neat liquid water from theory?

In this contribution, we compute the 1H nuclear magnetic resonance (NMR) relaxation rate of liquid water at ambient conditions. We are using structural and dynamical information from Coupled Cluster Molecular Dynamics (CCMD) trajectories generated at CCSD(T) electronic structure accuracy while also considering nuclear quantum effects in addition to consulting information from x-ray and neutron scattering experiments. Our analysis is based on a recently presented computational framework for determining the frequency-dependent NMR dipole-dipole relaxation rate of spin 1/2 nuclei from Molecular Dynamics (MD) simulations, which allows for an effective disentanglement of its structural and dynamical contributions and includes a correction for finite-size effects inherent to MD simulations with periodic boundary conditions. A close to perfect agreement with experimental relaxation data is achieved if structural and dynamical information from CCMD trajectories is considered, leading to a re-balancing of the rotational and translational dynamics, which can also be expressed by the product of the self-diffusion coefficient and the reorientational correlation time of the H-H vector D0 × τHH. The simulations show that this balance is significantly altered when nuclear quantum effects are taken into account. Our analysis suggests that the intermolecular and intramolecular contributions to the 1H NMR relaxation rate of liquid water are almost similar in magnitude, unlike what was predicted earlier from fully classical MD simulations.

Machine Learning in Solid-State Hydrogen Storage Materials: Challenges and Perspectives

Machine learning (ML) has emerged as a pioneering tool in advancing the research application of high-performance solid-state hydrogen storage materials (HSMs). This review summarizes the state-of-the-art research of ML in resolving crucial issues such as low hydrogen storage capacity and unfavorable de-/hydrogenation cycling conditions. First, the datasets, feature descriptors, and prevalent ML models tailored for HSMs are described. Specific examples include the successful application of ML in titanium-based, rare-earth-based, solid solution, magnesium-based, and complex HSMs, showcasing its role in exploiting composition-structure-property relationships and designing novel HSMs for specific applications. One of the representative ML works is the single-phase Ti-based HSM with superior cost-effective and comprehensive properties, tailored to fuel cell hydrogen feeding system at ambient temperature and pressure through high-throughput composition-performance scanning. More importantly, this review also identifies and critically analyzes the key challenges faced by ML in this domain, including poor data quality and availability, and the balance between model interpretability and accuracy, together with feasible countermeasures suggested to ameliorate these problems. In summary, this work outlines a roadmap for enhancing ML's utilization in solid-state hydrogen storage research, promoting more efficient and sustainable energy storage solutions.

Alchemical Free-Energy Calculations at Quantum-Chemical Precision

In the past decade, machine-learned potentials (MLP) have demonstrated the capability to predict various QM properties learned from a set of reference QM calculations. Accordingly, hybrid QM/MM simulations can be accelerated by replacement of expensive QM calculations with efficient MLP energy predictions. At the same time, alchemical free-energy perturbations (FEP) remain unachievable at the QM level of theory. In this work, we extend the capabilities of the Buffer Region Neural Network (BuRNN) QM/MM scheme toward FEP. BuRNN introduces a buffer region that experiences full electronic polarization by the QM region to minimize artifacts at the QM/MM interface. An MLP is used to predict the energies for the QM region and its interactions with the buffer region. Furthermore, BuRNN allows us to implement FEP directly into the MLP Hamiltonian. Here, we describe the alchemical change from methanol to methane in water at the MLP/MM level as a proof of concept.

Mechanism of Fe(II) Chemisorption on Hematite(001) Revealed by Reactive Neural Network Potential Molecular Dynamics

Atomic-scale understanding of important geochemical processes including sorption, dissolution, nucleation, and crystal growth is difficult to obtain from experimental measurements alone and would benefit from strong continuous progress in molecular simulation. To this end, we present a reactive neural network potential-based molecular dynamics approach to simulate the interaction of aqueous ions on mineral surfaces in contact with liquid water, taking Fe(II) on hematite(001) as a model system. We show that a single neural network potential predicts rate constants for water exchange for aqueous Fe(II) and for the exergonic chemisorption of aqueous Fe(II) on hematite(001) in good agreement with experimental observations. The neural network potential developed herein allows one to converge free energy profiles and transmission coefficients at density functional theory-level accuracy outperforming state-of-the-art classical force field potentials. This suggests that machine learning potential molecular dynamics should become the method of choice for atomistic studies of geochemical processes.

Application of modern artificial intelligence techniques in the development of organic molecular force fields

The molecular force field (FF) determines the accuracy of molecular dynamics (MD) and is one of the major bottlenecks that limits the application of MD in molecular design. Recently, artificial intelligence (AI) techniques, such as machine-learning potentials (MLPs), have been rapidly reshaping the landscape of MD. Meanwhile, organic molecular systems feature unique characteristics, and require more careful treatment in both model construction, optimization, and validation. While an accurate and generic organic molecular force field is still missing, significant progress has been made with the facilitation of AI, warranting a promising future. In this review, we provide an overview of the various types of AI techniques used in molecular FF development and discuss both the advantages and weaknesses of these methodologies. We show how AI methods provide unprecedented capabilities in many tasks such as potential fitting, atom typification, and automatic optimization. Meanwhile, it is also worth noting that more efforts are needed to improve the transferability of the model, develop a more comprehensive database, and establish more standardized validation procedures. With these discussions, we hope to inspire more efforts to solve the existing problems, eventually leading to the birth of next-generation generic organic FFs.

Efficient Sampling for Machine Learning Electron Density and Its Response in Real Space

Electron density is a fundamental quantity that can in principle determine all ground state electronic properties of a given system. Although machine learning (ML) models for electron density based on either an atom-centered basis or a real-space grid have been proposed, the demand for a number of high-order basis functions or grid points is enormous. In this work, we propose an efficient grid-point sampling strategy that combines targeted sampling favoring a large density and a screening of grid points associated with linearly independent atomic features. This new sampling strategy is integrated with a field-induced recursively embedded atom neural network model to develop a real-space grid-based ML model for the electron density and its response to an electric field. This approach is applied to a QM9 molecular data set, a H2O/Pt(111) interfacial system, an Au(100) electrode, and an Au nanoparticle under an electric field. The number of training points is found to be much smaller than previous models, while yielding comparably accurate predictions for the electron density of the entire grid. The resultant machine-learned electron density model enables us to properly partition partial charge onto each atom and analyze the charge variation upon proton transfer in the H2O/Pt(111) system. The machine-learning electronic response model allows us to predict charge transfer and the electrostatic potential change induced by an electric field applied to an Au(100) electrode or an Au nanoparticle.

Directed Electrostatics Strategy Integrated as a Graph Neural Network Approach for Accelerated Cluster Structure Prediction

We present a directed electrostatics strategy integrated as a graph neural network (DESIGNN) approach for predicting stable nanocluster structures on their potential energy surfaces (PESs). The DESIGNN approach is a graph neural network (GNN)-based model for building structures of large atomic clusters with specific sizes and point-group symmetry. This model assists in the structure building of atomic metal clusters by predicting molecular electrostatic potential (MESP) topography minima on their structural evolution paths. The DESIGNN approach is benchmarked on the prototype Mgn clusters with n < 150. The predicted MESP topography minima of Mgn clusters, n < 70, fairly agrees with the whole-molecule MESP topography calculations. Moreover, the ground-state structures of Mgn (n = 4-32) clusters generated through the DESIGNN approach corroborate well with the global minimum structures reported in the literature. Furthermore, this approach could generate novel symmetric isomers of medium to large Mgn clusters in the size regime, n < 150, by constraining the point-group symmetry of the parent clusters. The parent growth potential (GP) of a cluster gives a measure of its parent cluster to accommodate more atoms and characterize the structures on the DESIGNN-guided path. The GP of a cluster can also be interpreted as a measure of the cooperative interaction relative to its parent cluster. Along the highest GP paths, the DESIGNN approach is further employed to generate stable Mgn nanoclusters with n = 228, 236, 257, 260. Therefore, the DESIGNN approach holds great promise in accelerating the structure search and prediction of large metal clusters guided through MESP topography.

Random Sampling Versus Active Learning Algorithms for Machine Learning Potentials of Quantum Liquid Water

Training accurate machine learning potentials requires electronic structure data comprehensively covering the configurational space of the system of interest. As the construction of this data is computationally demanding, many schemes for identifying the most important structures have been proposed. Here, we compare the performance of high-dimensional neural network potentials (HDNNPs) for quantum liquid water at ambient conditions trained to data sets constructed using random sampling as well as various flavors of active learning based on query by committee. Contrary to the common understanding of active learning, we find that for a given data set size, random sampling leads to smaller test errors for structures not included in the training process. In our analysis, we show that this can be related to small energy offsets caused by a bias in structures added in active learning, which can be overcome by using instead energy correlations as an error measure that is invariant to such shifts. Still, all HDNNPs yield very similar and accurate structural properties of quantum liquid water, which demonstrates the robustness of the training procedure with respect to the training set construction algorithm even when trained to as few as 200 structures. However, we find that for active learning based on preliminary potentials, a reasonable initial data set is important to avoid an unnecessary extension of the covered configuration space to less relevant regions.

EOSnet: Embedded Overlap Structures for Graph Neural Networks in Predicting Material Properties

Graph Neural Networks (GNNs) have emerged as powerful tools for predicting material properties, yet they often struggle to capture many-body interactions and require extensive manual feature engineering. Here, we present EOSnet (Embedded Overlap Structures for Graph Neural Networks), a novel approach that addresses these limitations by incorporating Gaussian Overlap Matrix (GOM) fingerprints as node features within the GNN architecture. Unlike models that rely on explicit angular terms or human-engineered features, EOSnet efficiently encodes many-body interactions through orbital overlap matrices, providing a rotationally invariant and transferable representation of atomic environments. The model demonstrates superior performance across various prediction tasks of materials' properties, achieving particularly notable results in properties sensitive to many-body interactions. For band gap prediction, EOSnet achieves a mean absolute error of 0.163 eV, surpassing previous state-of-the-art models. The model also excels in predicting mechanical properties and classifying materials, with 97.7% accuracy in metal/nonmetal classification. These results demonstrate that embedding GOM fingerprints into node features enhances the ability of GNNs to capture complex atomic interactions, making EOSnet a powerful tool for materials' discovery and property prediction.

The design space of E(3)-equivariant atom-centred interatomic potentials

Molecular dynamics simulation is an important tool in computational materials science and chemistry, and in the past decade it has been revolutionized by machine learning. This rapid progress in machine learning interatomic potentials has produced a number of new architectures in just the past few years. Particularly notable among these are the atomic cluster expansion, which unified many of the earlier ideas around atom-density-based descriptors, and Neural Equivariant Interatomic Potentials (NequIP), a message-passing neural network with equivariant features that exhibited state-of-the-art accuracy at the time. Here we construct a mathematical framework that unifies these models: atomic cluster expansion is extended and recast as one layer of a multi-layer architecture, while the linearized version of NequIP is understood as a particular sparsification of a much larger polynomial model. Our framework also provides a practical tool for systematically probing different choices in this unified design space. An ablation study of NequIP, via a set of experiments looking at in- and out-of-domain accuracy and smooth extrapolation very far from the training data, sheds some light on which design choices are critical to achieving high accuracy. A much-simplified version of NequIP, which we call BOTnet (for body-ordered tensor network), has an interpretable architecture and maintains its accuracy on benchmark datasets.

ArcaNN: automated enhanced sampling generation of training sets for chemically reactive machine learning interatomic potentials

The emergence of artificial intelligence is profoundly impacting computational chemistry, particularly through machine-learning interatomic potentials (MLIPs). Unlike traditional potential energy surface representations, MLIPs overcome the conventional computational scaling limitations by offering an effective combination of accuracy and efficiency for calculating atomic energies and forces to be used in molecular simulations. These MLIPs have significantly enhanced molecular simulations across various applications, including large-scale simulations of materials, interfaces, chemical reactions, and beyond. Despite these advances, the construction of training datasets-a critical component for the accuracy of MLIPs-has not received proportional attention, especially in the context of chemical reactivity, which depends on rare barrier-crossing events that are not easily included in the datasets. Here we address this gap by introducing ArcaNN, a comprehensive framework designed for generating training datasets for reactive MLIPs. ArcaNN employs a concurrent learning approach combined with advanced sampling techniques to ensure an accurate representation of high-energy geometries. The framework integrates automated processes for iterative training, exploration, new configuration selection, and energy and force labeling, all while ensuring reproducibility and documentation. We demonstrate ArcaNN's capabilities through two paradigm reactions: a nucleophilic substitution and a Diels-Alder reaction. These examples showcase its effectiveness, the uniformly low error of the resulting MLIP everywhere along the chemical reaction coordinate, and its potential for broad applications in reactive molecular dynamics. Finally, we provide guidelines for assessing the quality of MLIPs in reactive systems.

Modelling ligand exchange in metal complexes with machine learning potentials

Metal ions are irreplaceable in many areas of chemistry, including (bio)catalysis, self-assembly and charge transfer processes. Yet, modelling their structural and dynamic properties in diverse chemical environments remains challenging for both force fields and ab initio methods. Here, we introduce a strategy to train machine learning potentials (MLPs) using MACE, an equivariant message-passing neural network, for metal-ligand complexes in explicit solvents. We explore the structure and ligand exchange dynamics of Mg2+ in water and Pd2+ in acetonitrile as two illustrative model systems. The trained potentials accurately reproduce equilibrium structures of the complexes in solution, including different coordination numbers and geometries. Furthermore, the MLPs can model structural changes between metal ions and ligands in the first coordination shell, and reproduce the free energy barriers for the corresponding ligand exchange. The strategy presented here provides a computationally efficient approach to model metal ions in solution, paving the way for modelling larger and more diverse metal complexes relevant to biomolecules and supramolecular assemblies.

Overcoming Inaccuracies in Machine Learning Interatomic Potential Implementation for Ionic Vacancy Simulations

Machine learning interatomic potentials, particularly ones based on deep neural networks, have taken significant strides in accelerating first-principles simulations, expanding the length and time scales of the simulations with accuracies akin to first-principles simulations. Notwithstanding their success in accurately describing the physical properties of pristine ionic systems with multiple oxidation states, herein we show that an implementation of deep neural network potentials (DNPs) yield vacancy formation energies in MgO with a significant ∼3 eV error. In contrast, we show that moment tensor potentials can accurately describe all properties of the oxide, including vacancy formation energies. We show that the vacancy formation energy errors in DNPs correlate with the strength of ionic interactions in the system as evidenced by contrasting MgO with the less ionic systems CuxOy and AgxOy. Our findings suggest that descriptors employed in the DNP may be inadequate and cannot accurately describe vacancies in ionic systems.

Data-Efficient Active Learning for Thermodynamic Integration: Acidity Constants of BiVO4 in Water

The protonation state of molecules and surfaces is pivotal in various disciplines, including (electro-)catalysis, geochemistry, biochemistry, and pharmaceutics. Accurately and efficiently determining acidity constants is critical yet challenging, particularly when explicitly considering the electronic structure, thermal fluctuations, anharmonic vibrations, and solvation effects. In this research, we employ thermodynamic integration accelerated by committee Neural Network potentials, training a single machine learning model that accurately describes the relevant protonated, deprotonated, and intermediate states. We investigate two deprotonation reactions at the BiVO4 (010)-water interface, a promising candidate for efficient photocatalytic water splitting. Our results illustrate the convergence of the required ensemble averages over simulation time and of the final acidity constant as a function of the Kirkwood coupling parameter. We demonstrate that simulation times on the order of nanoseconds are required for statistical convergence. This time scale is currently unachievable with explicit ab-initio molecular dynamics simulations at the hybrid DFT level of theory. In contrast, our machine learning workflow only requires a few hundred DFT single point calculations for training and testing. Exploiting the extended time scales accessible, we furthermore asses the effect of commonly applied bias potentials. Thus, our study significantly advances calculating free energy differences with ab-initio accuracy.

Computational Modeling of Reticular Materials: The Past, the Present, and the Future

Reticular materials rely on a unique building concept where inorganic and organic building units are stitched together giving access to an almost limitless number of structured ordered porous materials. Given the versatility of chemical elements, underlying nets, and topologies, reticular materials provide a unique platform to design materials for timely technological applications. Reticular materials have now found their way in important societal applications, like carbon capture to address climate change, water harvesting to extract atmospheric moisture in arid environments, and clean energy applications. Combining predictions from computational materials chemistry with advanced experimental characterization and synthesis procedures unlocks a design strategy to synthesize new materials with the desired properties and functions. Within this review, the current status of modeling reticular materials is addressed and supplemented with topical examples highlighting the necessity of advanced molecular modeling to design materials for technological applications. This review is structured as a templated molecular modeling study starting from the molecular structure of a realistic material towards the prediction of properties and functions of the materials. At the end, the authors provide their perspective on the past, present of future in modeling reticular materials and formulate open challenges to inspire future model and method developments.