Automatic selection of atomic fingerprints and reference configurations for machine-learning potentials

Thermal transport in C6N7monolayer: a machine learning based molecular dynamics study

The successful synthesis of a novel C6N7carbon nitride monolayer offers expansive prospects for applications in the fields of semiconductors, sensors, and gas separation technologies, in which the thermal transport properties of C6N7are crucial for optimizing the functionality and reliability of these applications. In this work, based on our developed machine learning potential (MLP), molecular dynamics (MD) simulations including homogeneous non-equilibrium, non-equilibrium, and their respective spectral decomposition methods are performed to investigate the effects of phonon transport, temperature, and length on the thermal conductivity of C6N7monolayer. Our results reveal that low-frequency and in-plane phonon modes dominate the thermal conductivity. Notably, thermal conductivity decreases with an increase in temperature due to temperature-induced increase in phonon-phonon scattering of in-plane phonon modes, while it increases with an extension in sample length. Our findings based on MD simulations with MLP contribute new insights into the lattice thermal conductivity of holey carbon nitride compounds, which is helpful for the development of next-generation electronic and photonic devices.

Accuracy, transferability, and computational efficiency of interatomic potentials for simulations of carbon under extreme conditions

Large-scale atomistic molecular dynamics (MD) simulations provide an exceptional opportunity to advance the fundamental understanding of carbon under extreme conditions of high pressures and temperatures. However, the fidelity of these simulations depends heavily on the accuracy of classical interatomic potentials governing the dynamics of many-atom systems. This study critically assesses several popular empirical potentials for carbon, as well as machine learning interatomic potentials (MLIPs), in their ability to simulate a range of physical properties at high pressures and temperatures, including the diamond equation of state, its melting line, shock Hugoniot, uniaxial compressions, and the structure of liquid carbon. Empirical potentials fail to accurately predict the behavior of carbon under high pressure-temperature conditions. In contrast, MLIPs demonstrate quantum accuracy, with Spectral Neighbor Analysis Potential (SNAP) and atomic cluster expansion (ACE) being the most accurate in reproducing the density functional theory results. ACE displays remarkable transferability despite not being specifically trained for extreme conditions. Furthermore, ACE and SNAP exhibit superior computational performance on graphics processing unit-based systems in billion atom MD simulations, with SNAP emerging as the fastest. In addition to offering practical guidance in selecting an interatomic potential with a fine balance of accuracy, transferability, and computational efficiency, this work also highlights transformative opportunities for groundbreaking scientific discoveries facilitated by quantum-accurate MD simulations with MLIPs on emerging exascale supercomputers.

HydraScreen: A Generalizable Structure-Based Deep Learning Approach to Drug Discovery

We propose HydraScreen, a deep-learning framework for safe and robust accelerated drug discovery. HydraScreen utilizes a state-of-the-art 3D convolutional neural network designed for the effective representation of molecular structures and interactions in protein-ligand binding. We designed an end-to-end pipeline for high-throughput screening and lead optimization, targeting applications in structure-based drug design. We assessed our approach using established public benchmarks based on the CASF-2016 core set, achieving top-tier results in affinity and pose prediction (Pearson's r = 0.86, RMSE = 1.15, Top-1 = 0.95). We introduced a novel approach for interaction profiling, aimed at detecting potential biases within both the model and data sets. This approach not only enhanced interpretability but also reinforced the impartiality of our methodology. Finally, we demonstrated HydraScreen's ability to generalize effectively across novel proteins and ligands through a temporal split. We also provide insights into potential avenues for future development aimed at enhancing the robustness of machine learning scoring functions. HydraScreen (accessible at http://hydrascreen.ro5.ai/paper) provides a user-friendly GUI and a public API, facilitating the easy-access assessment of protein-ligand complexes.

Multi-Level Protocol for Mechanistic Reaction Studies Using Semi-Local Fitted Potential Energy Surfaces

In this work, we propose a multi-level protocol for routine theoretical studies of chemical reaction mechanisms. The initial reaction paths of our investigated systems are sampled using the Nudged Elastic Band (NEB) method driven by a cheap electronic structure method. Forces recalculated at the more accurate electronic structure theory for a set of points on the path are fitted with a machine learning technique (in our case symmetric gradient domain machine learning or sGDML) to produce a semi-local reactive potential energy surface (PES), embracing reactants, products and transition state (TS) regions. This approach has been successfully applied to a unimolecular (Bergman cyclization of enediyne) and a bimolecular (SN2 substitution) reaction. In particular, we demonstrate that with only 50 to 150 energy-force evaluations with the accurate reference methods (here complete-active-space self-consistent field, CASSCF, and coupled-cluster singles and doubles, CCSD) it is possible to construct a semi-local PES giving qualitative agreement for stationary-point geometries, intrinsic reaction coordinates and barriers. Furthermore, we find a qualitative agreement in vibrational frequencies and reaction rate coefficients. The key aspect of the method's performance is its multi-level nature, which not only saves computational effort but also allows extracting meaningful information along the reaction path, characterized by zero gradients in all but one direction. Agnostic to the nature of the TS and computationally economic, the protocol can be readily automated and routinely used for mechanistic reaction studies.

Minimizing Redundancy and Data Requirements of Machine Learning Potential: A Case Study in Interface Combustion

The machine learning potential has emerged as a promising approach for addressing the accuracy-versus-efficiency dilemma in molecular modeling. Efficiently exploring chemical spaces with high accuracy presents a significant challenge, particularly for the interface reaction system. This study introduces a workflow aimed at achieving this goal by incorporating the classical SOAP descriptor and practical PCA strategy to minimize redundancy and data requirements, while successfully capturing the features of complex potential energy surfaces. Specifically, the study focuses on interface combustion behaviors within promising alloy-based solid propellants. A neural network potential model tailored for modeling AlLi-AP interface reactions under varying conditions is constructed, showcasing excellent predictive capabilities in energy prediction, force estimation, and bond energies. A series of large-scale MD simulations reveal that Li doping significantly influences the initial combustion stage, enhancing reactivity and reducing thermal conductivity. Mass transfer analysis also highlights the considerably higher diffusion coefficient of Li compared to Al, with the former being three times greater. Consequently, the overall combustion process is accelerated by approximately 10%. These breakthroughs pave the way for virtual screening and the rational design of advanced propellant formulations and microstructures incorporating alloy-formula propellants.

Superdiffusive Rotation of Interfacial Water on Noble Metal Surface

Interfacial water on a metal surface acts as an active layer through the reorientation of water, thereby facilitating the energy transfer and chemical reaction across the metal surface in various physicochemical and industrial processes. However, how this active interfacial water collectively behaves on flat noble metal substrates remains largely unknown due to the experimental limitation in capturing librational vibrational motion of interfacial water and prohibitive computational costs at the first-principles level. Herein, by implementing a machine-learning approach to train neural network potentials, we enable performing advanced molecular dynamics simulations with ab initio accuracy at a nanosecond scale to map the distinct rotational motion of water molecules on a metal surface at room temperature. The vibrational density of states of the interfacial water with two-layer profiles reveals that the rotation and vibration of water within the strong adsorption layer on the metal surface behave as if the water molecules in the bulk ice, wherein the O-H stretching frequency is well consistent with the experimental results. Unexpectedly, the water molecules within the adjacent weak adsorption layer exhibit superdiffusive rotation, contrary to the conventional diffusive rotation of bulk water, while the vibrational motion maintains the characteristic of bulk water. The mechanism underlying this abnormal superdiffusive rotation is attributed to the translation-rotation decoupling of water, in which the translation is restrained by the strong hydrogen bonding within the bilayer interfacial water, whereas the rotation is accelerated freely by the asymmetric water environment. This superdiffusive rotation dynamics may elucidate the experimentally observed large fluctuation of the potential of zero charge on Pt and thereby the conventional Helmholtz layer model revised by including the contribution of interfacial water orientation. The surprising superdiffusive rotation of vicinal water next to noble metals will shed new light on the physicochemical processes and the activity of water molecules near metal electrodes or catalysts.

Amorphous MoS2 from a machine learning inter-atomic potential

Amorphous molybdenum disulfide has shown potential as a hydrogen evolution catalyst, but the origin of its high activity is unclear, as is its atomic structure. Here, we have developed a classical inter-atomic potential using the charge equilibration neural network method, and we have employed it to generate atomic models of amorphous MoS2 by melting and quenching processes. The amorphous phase contains an abundance of molybdenum and sulfur atoms in low coordination. Besides the 6-coordinated molybdenum typical of the crystalline phases, a substantial fraction displays coordinations 4 and 5. The amorphous phase is also characterized by the appearance of direct S-S bonds. Density functional theory shows that the amorphous phase is metallic, with a considerable contribution of the 4-coordinated molybdenum to the density of states at the Fermi level. S-S bonds are related to the reduction of sulfur, with the excess electrons spread over several molybdenum atoms. Moreover, S-S bond formation is associated with a distinctive broadening of the 3s states, which could be exploited for experimental characterization of the amorphous phases. The large variety of local environments and the high density of electronic states at the Fermi level may play a positive role in increasing the electrocatalytic activity of this compound.

A reactive neural network framework for water-loaded acidic zeolites

Under operating conditions, the dynamics of water and ions confined within protonic aluminosilicate zeolite micropores are responsible for many of their properties, including hydrothermal stability, acidity and catalytic activity. However, due to high computational cost, operando studies of acidic zeolites are currently rare and limited to specific cases and simplified models. In this work, we have developed a reactive neural network potential (NNP) attempting to cover the entire class of acidic zeolites, including the full range of experimentally relevant water concentrations and Si/Al ratios. This NNP has the potential to dramatically improve sampling, retaining the (meta)GGA DFT level accuracy, with the capacity for discovery of new chemistry, such as collective defect formation mechanisms at the zeolite surface. Furthermore, we exemplify how the NNP can be used as a basis for further extensions/improvements which include data-efficient adoption of higher-level (hybrid) references via Δ-learning and the acceleration of rare event sampling via automatic construction of collective variables. These developments represent a significant step towards accurate simulations of realistic catalysts under operando conditions.

Machine learning interatomic potential: Bridge the gap between small-scale models and realistic device-scale simulations

Machine learning interatomic potential (MLIP) overcomes the challenges of high computational costs in density-functional theory and the relatively low accuracy in classical large-scale molecular dynamics, facilitating more efficient and precise simulations in materials research and design. In this review, the current state of the four essential stages of MLIP is discussed, including data generation methods, material structure descriptors, six unique machine learning algorithms, and available software. Furthermore, the applications of MLIP in various fields are investigated, notably in phase-change memory materials, structure searching, material properties predicting, and the pre-trained universal models. Eventually, the future perspectives, consisting of standard datasets, transferability, generalization, and trade-off between accuracy and complexity in MLIPs, are reported.

Exploring Challenging Properties of Liquid Metallic Systems through Machine Learning: Liquid La and Li4Pb Systems

In this machine learning (ML) study, we delved into the unique properties of liquid lanthanum and the Li4Pb alloy, revealing some unexpected features and also firmly establishing some of the debated characteristics. Leveraging interatomic potentials derived from ab initio calculations, our investigation achieved a level of precision comparable to first-principles methods while at the same time entering the hydrodynamic regime. We compared the structure factors and pair distribution functions to experimental data and unearthed distinctive collective excitations with intriguing features. Liquid lanthanum unveiled two transverse collective excitation branches, each closely tied to specific peaks in the velocity autocorrelation function spectrum. Furthermore, the analysis of the generalized specific heat ratio in the hydrodynamic regime investigated with the ML molecular dynamics simulations uncovered a peculiar behavior, impossible to discern with only ab initio simulations. Liquid Li4Pb, on the other hand, challenged existing claims by showcasing a rich array of branches in its longitudinal dispersion relation, including a high-frequency LiLi mode with a nonhydrodynamic optical character that maintains a finite value as q → 0. Additionally, we conducted an in-depth analysis of various transport coefficients, expanding our understanding of these liquid metallic systems. In summary, our ML approach yielded precise results, offering new and captivating insights into the structural and dynamic aspects of these materials.

Data-Driven Path Collective Variables

Identifying optimal collective variables to model transformations using atomic-scale simulations is a long-standing challenge. We propose a new method for the generation, optimization, and comparison of collective variables that can be thought of as a data-driven generalization of the path collective variable concept. It consists of a kernel ridge regression of the committor probability, which encodes a transformation's progress. The resulting collective variable is one-dimensional, interpretable, and differentiable, making it appropriate for enhanced sampling simulations requiring biasing. We demonstrate the validity of the method on two different applications: a precipitation model and the association of Li+ and F- in water. For the former, we show that global descriptors such as the permutation invariant vector allow reaching an accuracy far from the one achieved via simpler, more intuitive variables. For the latter, we show that information correlated with the transformation mechanism is contained in the first solvation shell only and that inertial effects prevent the derivation of optimal collective variables from the atomic positions only.

From Organic Fragments to Photoswitchable Catalysts: The OFF-ON Structural Repository for Transferable Kernel-Based Potentials

Structurally and conformationally diverse databases are needed to train accurate neural networks or kernel-based potentials capable of exploring the complex free energy landscape of flexible functional organic molecules. Curating such databases for species beyond "simple" drug-like compounds or molecules composed of well-defined building blocks (e.g., peptides) is challenging as it requires thorough chemical space mapping and evaluation of both chemical and conformational diversities. Here, we introduce the OFF-ON (organic fragments from organocatalysts that are non-modular) database, a repository of 7869 equilibrium and 67,457 nonequilibrium geometries of organic compounds and dimers aimed at describing conformationally flexible functional organic molecules, with an emphasis on photoswitchable organocatalysts. The relevance of this database is then demonstrated by training a local kernel regression model on a low-cost semiempirical baseline and comparing it with a PBE0-D3 reference for several known catalysts, notably the free energy surfaces of exemplary photoswitchable organocatalysts. Our results demonstrate that the OFF-ON data set offers reliable predictions for simulating the conformational behavior of virtually any (photoswitchable) organocatalyst or organic compound composed of H, C, N, O, F, and S atoms, thereby opening a computationally feasible route to explore complex free energy surfaces in order to rationalize and predict catalytic behavior.

Local-environment-guided selection of atomic structures for the development of machine-learning potentials

Machine learning potentials (MLPs) have attracted significant attention in computational chemistry and materials science due to their high accuracy and computational efficiency. The proper selection of atomic structures is crucial for developing reliable MLPs. Insufficient or redundant atomic structures can impede the training process and potentially result in a poor quality MLP. Here, we propose a local-environment-guided screening algorithm for efficient dataset selection in MLP development. The algorithm utilizes a local environment bank to store unique local environments of atoms. The dissimilarity between a particular local environment and those stored in the bank is evaluated using the Euclidean distance. A new structure is selected only if its local environment is significantly different from those already present in the bank. Consequently, the bank is then updated with all the new local environments found in the selected structure. To demonstrate the effectiveness of our algorithm, we applied it to select structures for a Ge system and a Pd13H2 particle system. The algorithm reduced the training data size by around 80% for both without compromising the performance of the MLP models. We verified that the results were independent of the selection and ordering of the initial structures. We also compared the performance of our method with the farthest point sampling algorithm, and the results show that our algorithm is superior in both robustness and computational efficiency. Furthermore, the generated local environment bank can be continuously updated and can potentially serve as a growing database of feature local environments, aiding in efficient dataset maintenance for constructing accurate MLPs.

Mechanism of Charge Transport in Lithium Thiophosphate

Lithium ortho-thiophosphate (Li3PS4) has emerged as a promising candidate for solid-state electrolyte batteries, thanks to its highly conductive phases, cheap components, and large electrochemical stability range. Nonetheless, the microscopic mechanisms of Li-ion transport in Li3PS4 are far from being fully understood, the role of PS4 dynamics in charge transport still being controversial. In this work, we build machine learning potentials targeting state-of-the-art DFT references (PBEsol, r2SCAN, and PBE0) to tackle this problem in all known phases of Li3PS4 (α, β, and γ), for large system sizes and time scales. We discuss the physical origin of the observed superionic behavior of Li3PS4: the activation of PS4 flipping drives a structural transition to a highly conductive phase, characterized by an increase in Li-site availability and by a drastic reduction in the activation energy of Li-ion diffusion. We also rule out any paddle-wheel effects of PS4 tetrahedra in the superionic phases-previously claimed to enhance Li-ion diffusion-due to the orders-of-magnitude difference between the rate of PS4 flips and Li-ion hops at all temperatures below melting. We finally elucidate the role of interionic dynamical correlations in charge transport, by highlighting the failure of the Nernst-Einstein approximation to estimate the electrical conductivity. Our results show a strong dependence on the target DFT reference, with PBE0 yielding the best quantitative agreement with experimental measurements not only for the electronic band gap but also for the electrical conductivity of β- and α-Li3PS4.

Machine-Learned Potentials by Active Learning from Organic Crystal Structure Prediction Landscapes

A primary challenge in organic molecular crystal structure prediction (CSP) is accurately ranking the energies of potential structures. While high-level solid-state density functional theory (DFT) methods allow for mostly reliable discrimination of the low-energy structures, their high computational cost is problematic because of the need to evaluate tens to hundreds of thousands of trial crystal structures to fully explore typical crystal energy landscapes. Consequently, lower-cost but less accurate empirical force fields are often used, sometimes as the first stage of a hierarchical scheme involving multiple stages of increasingly accurate energy calculations. Machine-learned interatomic potentials (MLIPs), trained to reproduce the results of ab initio methods with computational costs close to those of force fields, can improve the efficiency of the CSP by reducing or eliminating the need for costly DFT calculations. Here, we investigate active learning methods for training MLIPs with CSP datasets. The combination of active learning with the well-developed sampling methods from CSP yields potentials in a highly automated workflow that are relevant over a wide range of the crystal packing space. To demonstrate these potentials, we illustrate efficiently reranking large, diverse crystal structure landscapes to near-DFT accuracy from force field-based CSP, improving the reliability of the final energy ranking. Furthermore, we demonstrate how these potentials can be extended to more accurately model structures far from lattice energy minima through additional on-the-fly training within Monte Carlo simulations.

Exploring torsional conformer space with physical prior mean function-driven meta-Gaussian processes

We present a novel approach for systematically exploring the conformational space of small molecules with multiple internal torsions. Identifying unique conformers through a systematic conformational search is important for obtaining accurate thermodynamic functions (e.g., free energy), encompassing contributions from the ensemble of all local minima. Traditional geometry optimizers focus on one structure at a time, lacking transferability from the local potential-energy surface (PES) around a specific minimum to optimize other conformers. In this work, we introduce a physics-driven meta-Gaussian processes (meta-GPs) method that not only enables efficient exploration of target PES for locating local minima but, critically, incorporates physical surrogates that can be applied universally across the optimization of all conformers of the same molecule. Meta-GPs construct surrogate PESs based on the optimization history of prior conformers, dynamically selecting the most suitable prior mean function (representing prior knowledge in Bayesian learning) as a function of the optimization progress. We systematically benchmarked the performance of multiple GP variants for brute-force conformational search of amino acids. Our findings highlight the superior performance of meta-GPs in terms of efficiency, comprehensiveness of conformer discovery, and the distribution of conformers compared to conventional non-surrogate optimizers and other non-meta-GPs. Furthermore, we demonstrate that by concurrently optimizing, training GPs on the fly, and learning PESs, meta-GPs exhibit the capacity to generate high-quality PESs in the torsional space without extensive training data. This represents a promising avenue for physics-based transfer learning via meta-GPs with adaptive priors in exploring torsional conformer space.

How to train a neural network potential

The introduction of modern Machine Learning Potentials (MLPs) has led to a paradigm change in the development of potential energy surfaces for atomistic simulations. By providing efficient access to energies and forces, they allow us to perform large-scale simulations of extended systems, which are not directly accessible by demanding first-principles methods. In these simulations, MLPs can reach the accuracy of electronic structure calculations, provided that they have been properly trained and validated using a suitable set of reference data. Due to their highly flexible functional form, the construction of MLPs has to be done with great care. In this Tutorial, we describe the necessary key steps for training reliable MLPs, from data generation via training to final validation. The procedure, which is illustrated for the example of a high-dimensional neural network potential, is general and applicable to many types of MLPs.

scikit-matter : A Suite of Generalisable Machine Learning Methods Born out of Chemistry and Materials Science

Easy-to-use libraries such as scikit-learn have accelerated the adoption and application of machine learning (ML) workflows and data-driven methods. While many of the algorithms implemented in these libraries originated in specific scientific fields, they have gained in popularity in part because of their generalisability across multiple domains. Over the past two decades, researchers in the chemical and materials science community have put forward general-purpose machine learning methods. The deployment of these methods into workflows of other domains, however, is often burdensome due to the entanglement with domainspecific functionalities. We present the python library scikit-matter that targets domain-agnostic implementations of methods developed in the computational chemical and materials science community, following the scikit-learn API and coding guidelines to promote usability and interoperability with existing workflows.

scikit-matter : A Suite of Generalisable Machine Learning Methods Born out of Chemistry and Materials Science

Easy-to-use libraries such as scikit-learn have accelerated the adoption and application of machine learning (ML) workflows and data-driven methods. While many of the algorithms implemented in these libraries originated in specific scientific fields, they have gained in popularity in part because of their generalisability across multiple domains. Over the past two decades, researchers in the chemical and materials science community have put forward general-purpose machine learning methods. The deployment of these methods into workflows of other domains, however, is often burdensome due to the entanglement with domainspecific functionalities. We present the python library scikit-matter that targets domain-agnostic implementations of methods developed in the computational chemical and materials science community, following the scikit-learn API and coding guidelines to promote usability and interoperability with existing workflows.

Determination of hyper-parameters in the atomic descriptors for efficient and robust molecular dynamics simulations with machine learning forces

The atomic descriptors used in machine learning to predict forces are often high dimensional. In general, by retrieving a significant amount of structural information from these descriptors, accurate force predictions can be achieved. On the other hand, to acquire higher robustness for transferability without overfitting, sufficient reduction of descriptors should be necessary. In this study, we propose a method to automatically determine hyperparameters in the atomic descriptors, aiming to obtain accurate machine learning forces while using a small number of descriptors. Our method focuses on identifying an appropriate threshold cut-off for the variance value of the descriptor components. To demonstrate the effectiveness of our method, we apply it to crystalline, liquid, and amorphous structures in SiO₂, SiGe, and Si systems. By using both conventional two-body descriptors and our introduced split-type three-body descriptors, we demonstrate that our method can provide machine learning forces that enable efficient and robust molecular dynamics simulations.

Efficient interatomic descriptors for accurate machine learning force fields of extended molecules

Machine learning force fields (MLFFs) are gradually evolving towards enabling molecular dynamics simulations of molecules and materials with ab initio accuracy but at a small fraction of the computational cost. However, several challenges remain to be addressed to enable predictive MLFF simulations of realistic molecules, including: (1) developing efficient descriptors for non-local interatomic interactions, which are essential to capture long-range molecular fluctuations, and (2) reducing the dimensionality of the descriptors to enhance the applicability and interpretability of MLFFs. Here we propose an automatized approach to substantially reduce the number of interatomic descriptor features while preserving the accuracy and increasing the efficiency of MLFFs. To simultaneously address the two stated challenges, we illustrate our approach on the example of the global GDML MLFF. We found that non-local features (atoms separated by as far as 15 Å in studied systems) are crucial to retain the overall accuracy of the MLFF for peptides, DNA base pairs, fatty acids, and supramolecular complexes. Interestingly, the number of required non-local features in the reduced descriptors becomes comparable to the number of local interatomic features (those below 5 Å). These results pave the way to constructing global molecular MLFFs whose cost increases linearly, instead of quadratically, with system size.

A machine learning potential for simulating infrared spectra of nanosilicate clusters

The use of machine learning (ML) in chemical physics has enabled the construction of interatomic potentials having the accuracy of ab initio methods and a computational cost comparable to that of classical force fields. Training an ML model requires an efficient method for the generation of training data. Here, we apply an accurate and efficient protocol to collect training data for constructing a neural network-based ML interatomic potential for nanosilicate clusters. Initial training data are taken from normal modes and farthest point sampling. Later on, the set of training data is extended via an active learning strategy in which new data are identified by the disagreement between an ensemble of ML models. The whole process is further accelerated by parallel sampling over structures. We use the ML model to run molecular dynamics simulations of nanosilicate clusters with various sizes, from which infrared spectra with anharmonicity included can be extracted. Such spectroscopic data are needed for understanding the properties of silicate dust grains in the interstellar medium and in circumstellar environments.

A fully quantum-mechanical treatment for kaolinite

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

Proton Transport in Perfluorinated Ionomer Simulated by Machine-Learned Interatomic Potential

Polymers are a class of materials that are highly challenging to deal with using first-principles methods. Here, we present an application of machine-learned interatomic potentials to predict structural and dynamical properties of dry and hydrated perfluorinated ionomers. An improved active-learning algorithm using a small number of descriptors allows to efficiently construct an accurate and transferable model for this multielemental amorphous polymer. Molecular dynamics simulations accelerated by the machine-learned potentials accurately reproduce the heterogeneous hydrophilic and hydrophobic domains formed in this material as well as proton and water diffusion coefficients under a variety of humidity conditions. Our results reveal pronounced contributions of Grotthuss chains consisting of two to three water molecules to the high proton mobility under strongly humidified conditions.

Algorithmic Graph Theory, Reinforcement Learning and Game Theory in MD Simulations: From 3D Structures to Topological 2D-Molecular Graphs (2D-MolGraphs) and Vice Versa

This paper reviews graph-theory-based methods that were recently developed in our group for post-processing molecular dynamics trajectories. We show that the use of algorithmic graph theory not only provides a direct and fast methodology to identify conformers sampled over time but also allows to follow the interconversions between the conformers through graphs of transitions in time. Examples of gas phase molecules and inhomogeneous aqueous solid interfaces are presented to demonstrate the power of topological 2D graphs and their versatility for post-processing molecular dynamics trajectories. An even more complex challenge is to predict 3D structures from topological 2D graphs. Our first attempts to tackle such a challenge are presented with the development of game theory and reinforcement learning methods for predicting the 3D structure of a gas-phase peptide.

A neural network potential with self-trained atomic fingerprints: A test with the mW water potential

We present a neural network (NN) potential based on a new set of atomic fingerprints built upon two- and three-body contributions that probe distances and local orientational order, respectively. Compared with the existing NN potentials, the atomic fingerprints depend on a small set of tunable parameters that are trained together with the NN weights. In addition to simplifying the selection of the atomic fingerprints, this strategy can also considerably increase the overall accuracy of the network representation. To tackle the simultaneous training of the atomic fingerprint parameters and NN weights, we adopt an annealing protocol that progressively cycles the learning rate, significantly improving the accuracy of the NN potential. We test the performance of the network potential against the mW model of water, which is a classical three-body potential that well captures the anomalies of the liquid phase. Trained on just three state points, the NN potential is able to reproduce the mW model in a very wide range of densities and temperatures, from negative pressures to several GPa, capturing the transition from an open random tetrahedral network to a dense interpenetrated network. The NN potential also reproduces very well properties for which it was not explicitly trained, such as dynamical properties and the structure of the stable crystalline phases of mW.

Electronic Descriptors for Supervised Spectroscopic Predictions

Spectroscopic properties of molecules hold great importance for the description of the molecular response under the effect of UV/vis electromagnetic radiation. Computationally expensive ab initio (e.g., MultiConfigurational SCF, Coupled Cluster) or TDDFT methods are commonly used by the quantum chemistry community to compute these properties. In this work, we propose a (supervised) Machine Learning approach to model the absorption spectra of organic molecules. Several supervised ML methods have been tested such as Kernel Ridge Regression (KRR), Multiperceptron Neural Networs (MLP), and Convolutional Neural Networks. [Ramakrishnan et al. J. Chem. Phys. 2015, 143, 084111. Ghosh et al. Adv. Sci. 2019, 6, 1801367.] The use of only geometrical-atomic number descriptors (e.g., Coulomb Matrix) proved to be insufficient for an accurate training. [Ramakrishnan et al. J. Chem. Phys. 2015, 143, 084111.] Inspired by the TDDFT theory, we propose to use a set of electronic descriptors obtained from low-cost DFT methods: orbital energy differences (Δϵ_ia = ϵ_a - ϵ_i), transition dipole moment between occupied and unoccupied Kohn-Sham orbitals (⟨ϕ_i|r|ϕ_a⟩), and when relevant, charge-transfer character of monoexcitations (R_ia). We demonstrate that with these electronic descriptors and the use of Neural Networks we can predict not only a density of excited states but also get a very good estimation of the absorption spectrum and charge-transfer character of the electronic excited states, reaching results close to chemical accuracy (∼2 kcal/mol or ∼0.1 eV).

Size and Quality of Quantum Mechanical Data Set for Training Neural Network Force Fields for Liquid Water

Molecular dynamics simulations have been used in different scientific fields to investigate a broad range of physical systems. However, the accuracy of calculation is based on the model considered to describe the atomic interactions. In particular, ab initio molecular dynamics (AIMD) has the accuracy of density functional theory (DFT) and thus is limited to small systems and a relatively short simulation time. In this scenario, Neural Network Force Fields (NNFFs) have an important role, since they provide a way to circumvent these caveats. In this work, we investigate NNFFs designed at the level of DFT to describe liquid water, focusing on the size and quality of the training data set considered. We show that structural properties are less dependent on the size of the training data set compared to dynamical ones (such as the diffusion coefficient), and a good sampling (selecting data reference for the training process) can lead to a small sample with good precision.

Machine Learning Exciton Hamiltonians in Light-Harvesting Complexes

We propose a machine learning (ML)-based strategy for an inexpensive calculation of excitonic properties of light-harvesting complexes (LHCs). The strategy uses classical molecular dynamics simulations of LHCs in their natural environment in combination with ML prediction of the excitonic Hamiltonian of the embedded aggregate of pigments. The proposed ML model can reproduce the effects of geometrical fluctuations together with those due to electrostatic and polarization interactions between the pigments and the protein. The training is performed on the chlorophylls of the major LHC of plants, but we demonstrate that the model is able to extrapolate well beyond the initial training set. Moreover, the accuracy in predicting the effects of the environment is tested on the simulation of the small changes observed in the absorption spectra of the wild-type and a mutant of a minor LHC.

Artificial Neural Network-Derived Unified Six-Dimensional Potential Energy Surface for Tetra Atomic Isomers of the Biogenic [H, C, N, O] System

Recognition of different structural patterns in different potential energy surface regions, such as in isomerizing quasilinear tetra atomic molecules, is important for understanding the details of underlying physics and chemistry. In this respect, using three variants of artificial neural networks (ANNs), we investigated the six-dimensional (6-D) singlet potential energy surfaces (PES) of tetra atomic isomers of the biogenic [H, C, N, O] system. At first, we constructed a separate ANN potential for each of the studied isomers. In the next step, a comparative assessment of the separate ANN models led to the setting up of a unified 6-D singlet PES equally and accurately describing all studied isomers. The constructed unified model yields relative energies comparable to those obtained either from the gold standard CCSD(T) method or from separate ANNs for each of the studied isomers. The accuracy of the unified singlet PES is on the order of 10^-4 Hartrees (0.1 kcal/mol). The developed PES in this work captures the main features of nonlinear and quasilinear tetra atomic isomers of this biogenic system.

A data-driven interpretation of the stability of organic molecular crystals

Due to the subtle balance of intermolecular interactions that govern structure-property relations, predicting the stability of crystal structures formed from molecular building blocks is a highly non-trivial scientific problem. A particularly active and fruitful approach involves classifying the different combinations of interacting chemical moieties, as understanding the relative energetics of different interactions enables the design of molecular crystals and fine-tuning of their stabilities. While this is usually performed based on the empirical observation of the most commonly encountered motifs in known crystal structures, we propose to apply a combination of supervised and unsupervised machine-learning techniques to automate the construction of an extensive library of molecular building blocks. We introduce a structural descriptor tailored to the prediction of the binding (lattice) energy and apply it to a curated dataset of organic crystals, exploiting its atom-centered nature to obtain a data-driven assessment of the contribution of different chemical groups to the lattice energy of the crystal. We then interpret this library using a low-dimensional representation of the structure-energy landscape and discuss selected examples of the insights into crystal engineering that can be extracted from this analysis, providing a complete database to guide the design of molecular materials.

Oxidation and de-alloying of PtMn particle models: a computational investigation

We present a computational study of the energetics and mechanisms of oxidation of Pt-Mn systems. We use slab models and simulate the oxidation process over the most stable (111) facet at a given Pt₂Mn composition to make the problem computationally affordable, and combine Density-Functional Theory (DFT) with neural network potentials and metadynamics simulations to accelerate the mechanistic search. We find, first, that Mn has a strong tendency to alloy with Pt. This tendency is optimally realized when Pt and Mn are mixed in the bulk, but, at a composition in which the Mn content is high enough such as for Pt₂Mn, Mn atoms will also be found in the surface outmost layer. These surface Mn atoms can dissociate O₂ and generate MnO_x species, transforming the surface-alloyed Mn atoms into MnO_x surface oxide structures supported on a metallic framework in which one or more vacancy sites are simultaneously created. The thus-formed vacancies promote the successive steps of the oxidation process: the vacancy sites can be filled by surface oxygen atoms, which can then interact with Mn atoms in deeper layers, or subsurface Mn atoms can intercalate into interstitial sites. Both these steps facilitate the extraction of further bulk Mn atoms into MnO_x oxide surface structures, and thus the progress of the oxidation process, with typical rate-determining energy barriers in the range 0.9-1.0 eV.

A smooth basis for atomistic machine learning

Machine learning frameworks based on correlations of interatomic positions begin with a discretized description of the density of other atoms in the neighborhood 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 of 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 a basis of controllable smoothness within the sphere (in the same sense as plane waves provide a basis with controllable smoothness for a problem with periodic boundaries) and that a tensor product of Laplacian eigenstates also provides a smooth 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 competitive with data-driven bases that numerically optimize each metric. Finally, we investigate the role of the basis in building models of the potential energy. In these tests, we find that a combination of the Laplacian eigenstate basis and target-oriented heuristics leads to equal or improved regression performance when compared to both heuristic and data-driven bases in the literature. We conclude that the smoothness of the basis functions is a key aspect of successful atomic density representations.

Electronic-Structure Properties from Atom-Centered Predictions of the Electron Density

The electron density of a molecule or material has recently received major attention as a target quantity of machine-learning models. A natural choice to construct a model that yields transferable and linear-scaling predictions is to represent the scalar field using a multicentered atomic basis analogous to that routinely used in density fitting approximations. However, the nonorthogonality of the basis poses challenges for the learning exercise, as it requires accounting for all the atomic density components at once. We devise a gradient-based approach to directly minimize the loss function of the regression problem in an optimized and highly sparse feature space. In so doing, we overcome the limitations associated with adopting an atom-centered model to learn the electron density over arbitrarily complex data sets, obtaining very accurate predictions using a comparatively small training set. The enhanced framework is tested on 32-molecule periodic cells of liquid water, presenting enough complexity to require an optimal balance between accuracy and computational efficiency. We show that starting from the predicted density a single Kohn-Sham diagonalization step can be performed to access total energy components that carry an error of just 0.1 meV/atom with respect to the reference density functional calculations. Finally, we test our method on the highly heterogeneous QM9 benchmark data set, showing that a small fraction of the training data is enough to derive ground-state total energies within chemical accuracy.

Coupled Cluster Molecular Dynamics of Condensed Phase Systems Enabled by Machine Learning Potentials: Liquid Water Benchmark

Coupled cluster theory is a general and systematic electronic structure method, but in particular the highly accurate "gold standard" coupled cluster singles, doubles and perturbative triples, CCSD(T), can only be applied to small systems. To overcome this limitation, we introduce a framework to transfer CCSD(T) accuracy of finite molecular clusters to extended condensed phase systems using a high-dimensional neural network potential. This approach, which is automated, allows one to perform high-quality coupled cluster molecular dynamics, CCMD, as we demonstrate for liquid water including nuclear quantum effects. The machine learning strategy is very efficient, generic, can be systematically improved, and is applicable to a variety of complex systems.

Temperature Dependent Properties of the Aqueous Electron

The temperature‐dependent properties of the aqueous electron have been extensively studied using mixed quantum‐classical simulations in a wide range of thermodynamic conditions based on one‐electron pseudopotentials. While the cavity model appears to explain most of the physical properties of the aqueous electron, only a non‐cavity model has so far been successful in accounting for the temperature dependence of the absorption spectrum. Here, we present an accurate and efficient description of the aqueous electron under various thermodynamic conditions by combining hybrid functional‐based molecular dynamics, machine learning techniques, and multiple time‐step methods. Our advanced simulations accurately describe the temperature dependence of the absorption maximum in the presence of cavity formation. Specifically, our work reveals that the red shift of the absorption maximum results from an increasing gyration radius with temperature, rather than from global density variations as previously suggested.

Accelerating the theoretical study of Li-polysulfide adsorption on single-atom catalysts via machine learning approaches

Li-S batteries are a promising alternative to Li-ion batteries, offering large energy storage capacity and wide operating temperature range. However, their performance is heavily affected by the Li-polysulfide (LiPS) shuttling. Computational screening of LiPS adsorption on single-atom catalyst (SAC) substrates is of great aid to the design of Li-S batteries which are robust against the LiPS shuttling from the cathode to the anode and the electrolyte. To facilitate this process, we develop a machine learning (ML) protocol to accelerate the systematic mapping of dominant local energy minima found with calculations based on the density functional theory (DFT), and, in turn, fast screening of LiPS adsorption properties on SACs. We first validate the approach by probing the potential energy surface for LiPS adsorbed on graphene decorated with a Fe-N4-C SAC. We identify minima whose binding energies are better or on par with the one previously reported in the literature. We then move to analyze the adsorption trends on Zn-N4-C SAC and observe similar adsorption strength and behavior with the Fe-N4-C SAC, highlighting the good predictive power of our protocol. Our approach offers a comprehensive and computationally efficient alternative to conventional approaches studying LiPS adsorption.

Quantum neural networks force fields generation

Accurate molecular force fields are of paramount importance for the efficient implementation of molecular dynamics techniques at large scales. In the last decade, machine learning (ML) methods have demonstrated impressive performances in predicting accurate values for energy and forces when trained on finite size ensembles generated with ab initio techniques. At the same time, quantum computers have recently started to offer new viable computational paradigms to tackle such problems. On the one hand, quantum algorithms may notably be used to extend the reach of electronic structure calculations. On the other hand, quantum ML is also emerging as an alternative and promising path to quantum advantage. Here we follow this second route and establish a direct connection between classical and quantum solutions for learning neural network (NN) potentials. To this end, we design a quantum NN architecture and apply it successfully to different molecules of growing complexity. The quantum models exhibit larger effective dimension with respect to classical counterparts and can reach competitive performances, thus pointing towards potential quantum advantages in natural science applications via quantum ML.

UV-Visible Absorption Spectra of Solvated Molecules by Quantum Chemical Machine Learning

Predicting UV-visible absorption spectra is essential to understand photochemical processes and design energy materials. Quantum chemical methods can deliver accurate calculations of UV-visible absorption spectra, but they are computationally expensive, especially for large systems or when one computes line shapes from thermal averages. Here, we present an approach to predict UV-visible absorption spectra of solvated aromatic molecules by quantum chemistry (QC) and machine learning (ML). We show that a ML model, trained on the high-level QC calculation of the excitation energy of a set of aromatic molecules, can accurately predict the line shape of the lowest-energy UV-visible absorption band of several related molecules with less than 0.1 eV deviation with respect to reference experimental spectra. Applying linear decomposition analysis on the excitation energies, we unveil that our ML models probe vertical excitations of these aromatic molecules primarily by learning the atomic environment of their phenyl rings, which align with the physical origin of the π →π* electronic transition. Our study provides an effective workflow that combines ML with quantum chemical methods to accelerate the calculations of UV-visible absorption spectra for various molecular systems.

Fast atomic structure optimization with on-the-fly sparse Gaussian process potentials. JOURNAL OF PHYSICS. CONDENSED MATTER : AN INSTITUTE OF PHYSICS JOURNAL 2022;34:344007. [PMID: 35675808 DOI: 10.1088/1361-648x/ac76ff]

We apply on-the-fly machine learning potentials (MLPs) using the sparse Gaussian process regression (SGPR) algorithm for fast optimization of atomic structures. Great acceleration is achieved even in the context of a single local optimization. Although for finding the exact local minimum, due to limited accuracy of MLPs, switching to another algorithm may be needed. For random gold clusters, the forces are reduced to ∼0.1 eV Å^-1within less than ten first-principles (FP) calculations. Because of highly transferable MLPs, this algorithm is specially suitable for global optimization methods such as random or evolutionary structure searching or basin hopping. This is demonstrated by sequential optimization of random gold clusters for which, after only a few optimizations, FP calculations were rarely needed.

Flexible machine-learning interatomic potential for simulating structural disordering behavior of Li7La3Zr2O12 solid electrolytes

Batteries based on solid-state electrolytes, including Li₇La₃Zr₂O₁₂ (LLZO), promise improved safety and increased energy density; however, atomic disorder at grain boundaries and phase boundaries can severely deteriorate their performance. Machine-learning (ML) interatomic potentials offer a uniquely compelling solution for simulating chemical processes, rare events, and phase transitions associated with these complex interfaces by mixing high scalability with quantum-level accuracy, provided that they can be trained to properly address atomic disorder. To this end, we report the construction and validation of an ML potential that is specifically designed to simulate crystalline, disordered, and amorphous LLZO systems across a wide range of conditions. The ML model is based on a neural network algorithm and is trained using ab initio data. Performance tests prove that the developed ML potential can predict accurate structural and vibrational characteristics, elastic properties, and Li diffusivity of LLZO comparable to ab initio simulations. As a demonstration of its applicability to larger systems, we show that the potential can correctly capture grain boundary effects on diffusivity, as well as the thermal transition behavior of LLZO. These examples show that the ML potential enables simulations of transitions between well-defined and disordered structures with quantum-level accuracy at speeds thousands of times faster than ab initio methods.

Machine learning molecular dynamics simulations toward exploration of high-temperature properties of nuclear fuel materials: case study of thorium dioxide

Predicting materials properties of nuclear fuel compounds is a challenging task in materials science. Their thermodynamical behaviors around and above the operational temperature are essential for the design of nuclear reactors. However, they are not easy to measure, because the target temperature range is too high to perform various standard experiments safely and accurately. Moreover, theoretical methods such as first-principles calculations also suffer from the computational limitations in calculating thermodynamical properties due to their high calculation-costs and complicated electronic structures stemming from f-orbital occupations of valence electrons in actinide elements. Here, we demonstrate, for the first time, machine-learning molecular-dynamics to theoretically explore high-temperature thermodynamical properties of a nuclear fuel material, thorium dioxide. The target compound satisfies first-principles calculation accuracy because f-electron occupation coincidentally diminishes and the scheme meets sampling sufficiency because it works at the computational cost of classical molecular-dynamics levels. We prepare a set of training data using first-principles molecular dynamics with small number of atoms, which cannot directly evaluate thermodynamical properties but captures essential atomistic dynamics at the high temperature range. Then, we construct a machine-learning molecular-dynamics potential and carry out large-scale molecular-dynamics calculations. Consequently, we successfully access two kinds of thermodynamic phase transitions, namely the melting and the anomalous \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\lambda$$\end{document}λ transition induced by large diffusions of oxygen atoms. Furthermore, we quantitatively reproduce various experimental data in the best agreement manner by selecting a density functional scheme known as SCAN. Our results suggest that the present scale-up simulation-scheme using machine-learning techniques opens up a new pathway on theoretical studies of not only nuclear fuel compounds, but also a variety of similar materials that contain both heavy and light elements, like thorium dioxide.

Unified theory of atom-centered representations and message-passing machine-learning schemes

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, which 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), which 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 provide a coherent foundation to systematize our understanding of both atom-centered and message-passing and invariant and equivariant machine-learning schemes.

Accurate, affordable, and generalizable machine learning simulations of transition metal x-ray absorption spectra using the XANESNET deep neural network

The affordable, accurate, and generalizable prediction of spectroscopic observables plays a key role in the analysis of increasingly complex experiments. In this article, we develop and deploy a deep neural network-XANESNET-for predicting the lineshape of first-row transition metal K-edge x-ray absorption near-edge structure (XANES) spectra. XANESNET predicts the spectral intensities using only information about the local coordination geometry of the transition metal complexes encoded in a feature vector of weighted atom-centered symmetry functions. We address in detail the calibration of the feature vector for the particularities of the problem at hand, and we explore the individual feature importance to reveal the physical insight that XANESNET obtains at the Fe K-edge. XANESNET relies on only a few judiciously selected features-radial information on the first and second coordination shells suffices along with angular information sufficient to separate satisfactorily key coordination geometries. The feature importance is found to reflect the XANES spectral window under consideration and is consistent with the expected underlying physics. We subsequently apply XANESNET at nine first-row transition metal (Ti-Zn) K-edges. It can be optimized in as little as a minute, predicts instantaneously, and provides K-edge XANES spectra with an average accuracy of ∼±2%-4% in which the positions of prominent peaks are matched with a >90% hit rate to sub-eV (∼0.8 eV) error.

Graph neural networks accelerated molecular dynamics

Molecular Dynamics (MD) simulation is a powerful tool for understanding the dynamics and structure of matter. Since the resolution of MD is atomic-scale, achieving long timescale simulations with femtosecond integration is very expensive. In each MD step, numerous iterative computations are performed to calculate energy based on different types of interaction and their corresponding spatial gradients. These repetitive computations can be learned and surrogated by a deep learning model, such as a Graph Neural Network (GNN). In this work, we developed a GNN Accelerated MD (GAMD) model that directly predicts forces, given the state of the system (atom positions, atom types), bypassing the evaluation of potential energy. By training the GNN on a variety of data sources (simulation data derived from classical MD and density functional theory), we show that GAMD can predict the dynamics of two typical molecular systems, Lennard-Jones system and water system, in the NVT ensemble with velocities regulated by a thermostat. We further show that GAMD’s learning and inference are agnostic to the scale, where it can scale to much larger systems at test time. We also perform a comprehensive benchmark test comparing our implementation of GAMD to production-level MD software, showing GAMD’s competitive performance on the large-scale simulation.

Assessing the persistence of chalcogen bonds in solution with neural network potentials

Non-covalent bonding patterns are commonly harvested as a design principle in the field of catalysis, supramolecular chemistry and functional materials to name a few. Yet, their computational description generally neglects finite temperature and environment effects, which promote competing interactions and alter their static gas-phase properties. Recently, neural network potentials (NNPs) trained on Density Functional Theory (DFT) data have become increasingly popular to simulate molecular phenomena in condensed phase with an accuracy comparable to ab initio methods. To date, most applications have centered on solid-state materials or fairly simple molecules made of a limited number of elements. Herein, we focus on the persistence and strength of chalcogen bonds involving a benzotelluradiazole in condensed phase. While the tellurium-containing heteroaromatic molecules are known to exhibit pronounced interactions with anions and lone pairs of different atoms, the relevance of competing intermolecular interactions, notably with the solvent, is complicated to monitor experimentally but also challenging to model at an accurate electronic structure level. Here, we train direct and baselined NNPs to reproduce hybrid DFT energies and forces in order to identify what are the most prevalent non-covalent interactions occurring in a solute-Cl$^-$-THF mixture. The simulations in explicit solvent highlight competition with chalcogen bonds formed with the solvent and the short-range directionality of the interaction with direct consequences for the molecular properties in the solution. The comparison with other potentials (e.g., AMOEBA, direct NNP and continuum solvent model) also demonstrates that baselined NNPs offer a reliable picture of the non-covalent interaction interplay occurring in solution.