Fundamental Invariant Neural Network (FI-NN) Potential Energy Surface for the OH + CH3OH Reaction with Analytical Forces

The hydrogen abstraction reaction of OH + CH3OH plays a great role in combustion and atmospheric and interstellar chemistry and has been extensively studied theoretically and experimentally. Theoretically, the numerical gradients with respect to the Cartesian coordinates of atoms in molecular simulations on our recent potential energy surface (PES) for the title reaction trained using the permutationally invariant polynomial neural network (PIP-NN) approach hinder the extensive calculation because of the unaffordable computation cost. To address this issue, we in this work report a new full-dimensional accurate analytical PES for the title reaction using the fundamental invariant neural network (FI-NN) approach based on 140,192 points of the quality UCCSD(T)-F12a/AVTZ. Besides, the spin-orbit (SO) corrections of OH in the entrance channel were determined at the level of complete active space self-consistent field with the AVTZ basis set. As a compromise between computational cost and efficiency, the Δ-machine learning approach was employed to construct the SO-corrected PES. Based on this new FI-NN PES with analytical forces, thermal rate coefficients and various dynamic properties, including the integral cross sections, the differential cross sections, and the product energy partitioning, were determined by running a total of 5.5 million trajectories. The use of analytical gradients of the FI-NN PES accelerated simulations and about 99% of computation cost was saved, compared to that for the PIP-NN PES with numerical gradients. Such a significant acceleration is achieved mainly by replacing PIPs with FIs.

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.

Proton Conducting Neuromorphic Materials and Devices

Neuromorphic computing and artificial intelligence hardware generally aims to emulate features found in biological neural circuit components and to enable the development of energy-efficient machines. In the biological brain, ionic currents and temporal concentration gradients control information flow and storage. It is therefore of interest to examine materials and devices for neuromorphic computing wherein ionic and electronic currents can propagate. Protons being mobile under an external electric field offers a compelling avenue for facilitating biological functionalities in artificial synapses and neurons. In this review, we first highlight the interesting biological analog of protons as neurotransmitters in various animals. We then discuss the experimental approaches and mechanisms of proton doping in various classes of inorganic and organic proton-conducting materials for the advancement of neuromorphic architectures. Since hydrogen is among the lightest of elements, characterization in a solid matrix requires advanced techniques. We review powerful synchrotron-based spectroscopic techniques for characterizing hydrogen doping in various materials as well as complementary scattering techniques to detect hydrogen. First-principles calculations are then discussed as they help provide an understanding of proton migration and electronic structure modification. Outstanding scientific challenges to further our understanding of proton doping and its use in emerging neuromorphic electronics are pointed out.

A Machine-Learning-Assisted Crystalline Structure Prediction Framework To Accelerate Materials Discovery

Modern crystal structure prediction methods based on structure generation algorithms and first-principles calculations play important roles in the design of new materials. However, the cost of these methods is very expensive because their success mostly relies on the efficient sampling of structures and the accurate evaluation of energies for those sampled structures. Herein, we develop a Machine-learning-Assisted CRYStalline Materials sAmpling sysTem (MAXMAT) aiming to accelerate the prediction of new crystal structures. For a given chemical composition, MAXMAT can generate efficient crystal structures with the help of a Python package for crystal structure generation (PyXtal) and can quickly evaluate the energies of these generated structures using a well-developed machine learning interaction potential model (M3GNET). We have used MAXMAT to perform crystal structure searches for three different chemical systems (TiO2, MgAl2O4, and BaBOF3) to test its accuracy and efficiency. Furthermore, we apply MAXMAT to predict new nonlinear optical materials, suggesting several thermodynamically synthesizable structures with high performance in LiZnGaS3 and CaBOF3 systems.

Development of a machine learning interatomic potential for exploring pressure-dependent kinetics of phase transitions in germanium

We introduce a data-driven potential aimed at the investigation of pressure-dependent phase transitions in bulk germanium, including the estimate of kinetic barriers. This is achieved by suitably building a database including several configurations along minimum energy paths, as computed using the solid-state nudged elastic band method. After training the model based on density functional theory (DFT)-computed energies, forces, and stresses, we provide validation and rigorously test the potential on unexplored paths. The resulting agreement with the DFT calculations is remarkable in a wide range of pressures. The potential is exploited in large-scale isothermal-isobaric simulations, displaying local nucleation in the R8 to β-Sn pressure-induced phase transformation, taken here as an illustrative example.

Constructing and Evaluating Machine-Learned Interatomic Potentials for Li-Based Disordered Rocksalts

Lithium-based disordered rocksalts (LDRs), which are an important class of positive electrode materials that can increase the energy density of current Li-ion batteries, represent a significantly complex chemical and configurational space for conventional density functional theory (DFT)-based high-throughput screening approaches. Notably, atom-centered machine-learned interatomic potentials (MLIPs) are a promising pathway to accurately model the potential energy surface of highly disordered chemical spaces, such as LDRs, where the performance of such MLIPs has not been rigorously explored yet. Here, we represent a comprehensive evaluation of the accuracy, transferability, and ease of training of five atom-centered MLIPs, including the artificial neural network potentials developed by the atomic energy network (AENET), the Gaussian approximation potential (GAP), the spectral neighbor analysis potential (SNAP) and its quadratic extension (qSNAP), and the moment tensor potential (MTP), in modeling a 11-component LDR chemical space. Specifically, we generate a DFT-calculated data set of 10,842 configurations of disordered LiTMO2 and TMO2 compositions, where TM = Sc, Ti, V, Cr, Mn, Fe, Co, Ni, and/or Cu. To provide a point-of-comparison on the performance of atom-centered MLIPs, we also trained the neural equivariant interatomic potential (NequIP) on a subset of our data. Importantly, we find AENET to be the best potential in terms of accuracy and transferability for energy predictions, while MTP is the best for atomic forces. While AENET is the fastest to train among the MLIPs considered at low number of epochs (300), the training time increases significantly as epochs increase (3300), with a corresponding reduction in training errors (∼60%). Note that AENET and GAP tend to overfit in small data sets, with the extent of overfitting reducing with larger data sets. Finally, we observe AENET to provide reasonable predictions of average Li-intercalation voltages in layered, single-TM LiTMO2 frameworks, compared to DFT (∼10% error on average). Our study should pave the way both for discovering novel disordered rocksalt electrodes and for modeling other configurationally complex systems, such as high-entropy ceramics and alloys.

Comparing ANI-2x, ANI-1ccx neural networks, force field, and DFT methods for predicting conformational potential energy of organic molecules

In this study, the conformational potential energy surfaces of Amylmetacresol, Benzocaine, Dopamine, Betazole, and Betahistine molecules were scanned and analyzed using the neural network architecture ANI-2 × and ANI-1ccx, the force field method OPLS, and density functional theory with the exchange-correlation functional B3LYP and the basis set 6-31G(d). The ANI-1ccx and ANI-2 × methods demonstrated the highest accuracy in predicting torsional energy profiles, effectively capturing the minimum and maximum values of these profiles. Conformational potential energy values calculated by B3LYP and the OPLS force field method differ from those calculated by ANI-1ccx and ANI-2x, which account for non-bonded intramolecular interactions, since the B3LYP functional and OPLS force field weakly consider van der Waals and other intramolecular forces in torsional energy profiles. For a more comprehensive analysis, electronic parameters such as dipole moment, HOMO, and LUMO energies for different torsional angles were calculated at two levels of theory, B3LYP/6-31G(d) and ωB97X/6-31G(d). These calculations confirmed that ANI predictions are more accurate than density functional theory calculations with B3LYP functional and OPLS force field for determining potential energy surfaces. This research successfully addressed the challenges in determining conformational potential energy levels and shows how machine learning and deep neural networks offer a more accurate, cost-effective, and rapid alternative for predicting torsional energy profiles.

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.

Encoding a Many-Body Potential Energy Surface into a Grid-Based Matrix Product Operator

An efficient algorithm for compressing a given many-body potential energy surface (PES) of molecular systems into a grid-based matrix product operator (MPO) is proposed. The PES is once represented by a full-dimensional or truncated many-body expansion form, which is obtained by ab initio calculations at each grid mesh point, and then all terms in the expansion are compressed and merged into a single MPO while maintaining the bond dimension of the MPO as small as possible. It was shown that the ab initio PES of the H2CO was compressed by more than 2 orders of magnitude in the size of the site operators without loss of accuracy. By the use of grid basis, the tensor rank of the site operators of the MPO is reduced from four to three due to the diagonal nature of the position-dependent operators on grid basis, which significantly reduces the computational cost of the tensor contractions required in the real and imaginary time evolution of the matrix product state (MPS) wave functions with the grid-based MPO (Grid-MPO) Hamiltonian. Similar to other grid-based methods, Grid-MPO is easily applicable to any kinds of potentials of molecular systems, such as analytical empirical model potentials expressed by position operators and ab initio potentials, if the values at the grid points are available. Using the Grid-MPO combined with the MPS, we calculated the time correlation function of the Eigen cation H 3 O + ( H 2 O ) 3 to predict the infrared spectrum and compared with the experimental and the previous theoretical studies. The actual scaling with the size of systems was examined for the multidimensional Henon-Heiles Hamiltonian. It was shown that the method is considerably accelerated by the graphic processing unit (GPU) because the sizes of site operators were kept small and all tensors were able to be stored on the VRAM of a GPU.

No Headache for PIPs: A PIP Potential for Aspirin Runs Much Faster and with Similar Precision Than Other Machine-Learned Potentials

Assessments of machine-learning (ML) potentials are an important aspect of the rapid development of this field. We recently reported an assessment of the linear-regression permutationally invariant polynomial (PIP) method for ethanol, using the widely used (revised) rMD17 data set. We demonstrated that the PIP approach outperformed numerous other methods, e.g., ANI, PhysNet, sGDML, and p-KRR, with respect to precision and notably with respect to speed [Houston et al., J. Chem. Phys. 2022, 156, 044120]. Here, we extend this assessment to the 21-atom aspirin molecule, using the rMD17 data set, with a focus on the speed of evaluation. Both energies and forces are used for training, and the precision of several PIPs is examined for both. Normal mode frequencies, the methyl torsional potential, and 1d vibrational energies for an OH stretch are presented. We show that the PIP approach achieves the level of precision obtained from other ML methods, e.g., atom-centered neural network methods, linear regression ACE, and kernel methods, as reported by Kovács et al. in J. Chem. Theory Comput. 2021, 17, 7696-7711. More significantly, we show that the PIP PESs run much faster than all other ML methods, whose timings were evaluated in that paper. We also show that the PIP PES extrapolates well enough to describe several internal motions of aspirin, including an OH stretch.

Training machine learning potentials for reactive systems: A Colab tutorial on basic models

In the last several years, there has been a surge in the development of machine learning potential (MLP) models for describing molecular systems. We are interested in a particular area of this field - the training of system-specific MLPs for reactive systems - with the goal of using these MLPs to accelerate free energy simulations of chemical and enzyme reactions. To help new members in our labs become familiar with the basic techniques, we have put together a self-guided Colab tutorial (https://cc-ats.github.io/mlp_tutorial/), which we expect to be also useful to other young researchers in the community. Our tutorial begins with the introduction of simple feedforward neural network (FNN) and kernel-based (using Gaussian process regression, GPR) models by fitting the two-dimensional Müller-Brown potential. Subsequently, two simple descriptors are presented for extracting features of molecular systems: symmetry functions (including the ANI variant) and embedding neural networks (such as DeepPot-SE). Lastly, these features will be fed into FNN and GPR models to reproduce the energies and forces for the molecular configurations in a Claisen rearrangement reaction.

Many-body interactions and deep neural network potentials for water

We present a detailed assessment of deep neural network potentials developed within the Deep Potential Molecular Dynamics (DeePMD) framework and trained on the MB-pol data-driven many-body potential energy function. Specific focus is directed at the ability of DeePMD-based potentials to correctly reproduce the accuracy of MB-pol across various water systems. Analyses of bulk and interfacial properties as well as many-body interactions characteristic of water elucidate inherent limitations in the transferability and predictive accuracy of DeePMD-based potentials. These limitations can be traced back to an incomplete implementation of the "nearsightedness of electronic matter" principle, which may be common throughout machine learning potentials that do not include a proper representation of self-consistently determined long-range electric fields. These findings provide further support for the "short-blanket dilemma" faced by DeePMD-based potentials, highlighting the challenges in achieving a balance between computational efficiency and a rigorous, physics-based representation of the properties of water. Finally, we believe that our study contributes to the ongoing discourse on the development and application of machine learning models in simulating water systems, offering insights that could guide future improvements in the field.

A New Ab Initio Potential Energy Surface and Rovibrational Spectra for the CO-N2O Complex

We constructed a new ab initio potential energy surface (PES) for CO-N2O which includes the intramolecular Q3 normal coordinate for the N2O ν3 antisymmetric stretching vibration. The intermolecular potential was evaluated employing the supermolecular method at the [CCSD(T)]-F12a level, with the aug-cc-pVTZ basis set plus bond functions. By integral over the intramolecular Q3 coordinate, we obtained the vibrationally averaged PESs for the CO-N2O system in the ground and ν3 excited states of N2O. Each PES features one nearly T-shaped global minimum and one skewed T-shaped local minimum. Based on these obtained PESs of CO-N2O, the radial discrete variable representation/angle finite base representation method and the Lanczos algorithm were applied for the calculations of bound states and rovibrational energy levels. The calculated ν3 vibrational band origin shift of the N2O monomer in CO-N2O is 2.7570 cm-1, matching well with the observed value of 2.9048 cm-1. The computed microwave and infrared transition frequencies, as well as the rotational parameters, are consistent with the experimental observations.

Active and Transfer Learning of High-Dimensional Neural Network Potentials for Transition Metals

Classical molecular dynamics (MD) simulations represent a very popular and powerful tool for materials modeling and design. The predictive power of MD hinges on the ability of the interatomic potential to capture the underlying physics and chemistry. There have been decades of seminal work on developing interatomic potentials, albeit with a focus predominantly on capturing the properties of bulk materials. Such physics-based models, while extensively deployed for predicting the dynamics and properties of nanoscale systems over the past two decades, tend to perform poorly in predicting nanoscale potential energy surfaces (PESs) when compared to high-fidelity first-principles calculations. These limitations stem from the lack of flexibility in such models, which rely on a predefined functional form. Machine learning (ML) models and approaches have emerged as a viable alternative to capture the diverse size-dependent cluster geometries, nanoscale dynamics, and the complex nanoscale PESs, without sacrificing the bulk properties. Here, we introduce an ML workflow that combines transfer and active learning strategies to develop high-dimensional neural networks (NNs) for capturing the cluster and bulk properties for several different transition metals with applications in catalysis, microelectronics, and energy storage, to name a few. Our NN first learns the bulk PES from the high-quality physics-based models in literature and subsequently augments this learning via retraining with a higher-fidelity first-principles training data set to concurrently capture both the nanoscale and bulk PES. Our workflow departs from status-quo in its ability to learn from a sparsely sampled data set that nonetheless covers a diverse range of cluster configurations from near-equilibrium to highly nonequilibrium as well as learning strategies that iteratively improve the fingerprinting depending on model fidelity. All the developed models are rigorously tested against an extensive first-principles data set of energies and forces of cluster configurations as well as several properties of bulk configurations for 10 different transition metals. Our approach is material agnostic and provides a methodology to transfer and build upon the learnings from decades of seminal work in molecular simulations on to a new generation of ML-trained potentials to accelerate materials discovery and design.

Comparing machine learning potentials for water: Kernel-based regression and Behler-Parrinello neural networks

In this paper, we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE + D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1500 structures, as well as a smaller dataset, about half the size, obtained using only on-the-fly learning. This study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, this study emphasizes the relevance of the database over the fitting method. Finally, this study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests.

Chemistry-Informed Generative Model for Classical Dynamics Simulations

In this work, a chemistry-informed generative model was proposed, leading to the chemistry-informed generative adversarial network (CI-GAN) approach. To easily build the input database for complex molecular systems, an image-input algorithm is also implemented, leading to the capability to directly recognize the molecular image. Extensive test calculations and analysis on typical examples, H + H2, OH + HO2, and H2O/TiO2(110), find that the present CI-GAN approach generates distributions of geometry and energy. Calculations on the above examples show that the present CI-GAN approach is able to generate 50%-80% meaningful results among all of the generated data with chemistry constraints. Thus, it has the potential capability to predict classical dynamics simulations as well as ab initio calculations avoiding expensive calculations. These results and the power of CI-GANs in generating ab initio energies and MD trajectories are deeply discussed.

Degeneration of kernel regression with Matern kernels into low-order polynomial regression in high dimension

Kernel methods such as kernel ridge regression and Gaussian process regression with Matern-type kernels have been increasingly used, in particular, to fit potential energy surfaces (PES) and density functionals, and for materials informatics. When the dimensionality of the feature space is high, these methods are used with necessarily sparse data. In this regime, the optimal length parameter of a Matern-type kernel may become so large that the method effectively degenerates into a low-order polynomial regression and, therefore, loses any advantage over such regression. This is demonstrated theoretically as well as numerically in the examples of six- and fifteen-dimensional molecular PES using squared exponential and simple exponential kernels. The results shed additional light on the success of polynomial approximations such as PIP for medium-size molecules and on the importance of orders-of-coupling-based models for preserving the advantages of kernel methods with Matern-type kernels of on the use of physically motivated (reproducing) kernels.

Formation Mechanisms of Electronically Excited Nitrogen Molecules from N + N2 and N + N + N Collisions Revealed by Full-Dimensional Potential Energy Surfaces

This work reports six new full-dimensional adiabatic potential energy surfaces (PESs) of the N3 system (four 4A″ states and two 2A″ states) at the MRCI + Q/AVQZ level of theory that correlated to N2(X1Σg+) + N(4S), N2(X1Σg+) + N(2D), N2(A3Σu+) + N(4S), N2(B3Πg) + N(4S), N2(W3Δu) + N(4S), and N(4S) + N(4S) + N(4S) channels. The neural networks with a proper account of the nuclear permutation invariant symmetry of N3 were employed to fit the PESs based on about 4000 ab initio points. The accuracy of the PESs was validated by excellent agreement on the equilibrium bond length, vertical excitation energy, and dissociation energy with experimental values. Two possible mechanisms of the formation of N2(A) were found. One is that the collision occurs between N2(X) and N(4S) in the 14A″ state, followed by a nonadiabatic transition through the conical intersection with the 24A″ PES, resulting in the formation of the N2(A) + N(4S) product. The other takes place in the collision among three N(4S) atoms in the adiabatic 24A″ state, and then, N2(A) + N(4S) is formed. This is the first systematical research of the N3 system focusing on the formation of the excited states of N2 via both adiabatic and nonadiabatic pathways.

A new six-dimensional ab initio potential energy surface and rovibrational spectra for the N2-CO2 complex

New six-dimensional ab initio potential energy surfaces (PESs) for the N2-CO2 complex, which involve the stretching vibration of N2 and the Q3 normal mode for the ν3 asymmetric stretching vibration of CO2, were constructed using the CCSD(T)-F12/AVTZ method with midpoint bond functions. Two vibrational averaged 4D interaction potentials were obtained by integrating over the two intramolecular coordinates. It was found that both PESs possess two equivalent T-shaped global minima as well as two in-plane and one out-of-plane saddle points. Based on these PESs, rovibrational bound states and energy levels were calculated applying the radial discrete variable representation/angular finite basis representation method and the Lanczos algorithm. The splitting of the energy levels between oN2-CO2 and pN2-CO2 for the intermolecular vibrational ground state is determined to be only 0.000 09 cm-1 due to the higher barriers. The obtained band origin shift is about +0.471 74 cm-1 in the N2-CO2 infrared spectra with CO2 at the ν3 zone, which coincides with the experimental data of +0.483 74 cm-1. The frequencies of the in-plane geared-bending for N2-CO2 at the ν3 = 0 and 1 states of CO2 turn out to be 21.6152 and 21.4522 cm-1, the latter reproduces the available experimental 21.3793 cm-1 value with CO2 at the ν3 zone. The spectral parameters fitted from the rovibrational energy levels show that this dimer is a near prolate asymmetric rotor. The computed microwave transitions as well as the infrared fundamental and combination bands for the complex agree well with the observed data.

Unusual magnetic interaction in CrTe: insights from machine-learning and empirical models

Chromium telluride (CrTe) has received much attention due to its small magnetic anisotropy, which hosts the potential for complex magnetic structures. However, its magnetic properties have been relatively unexplored with numerical simulations, as the magnetic interactions inside are quite unusual. In this study, we employ both a machine-learning model and an empirical model to investigate the magnetic phase transitions of bulk and monolayer CrTe, revealing the existence of unusual magnetic interaction, which can be captured by the machine-learning model but not the simple empirical model. Furthermore, our results also demonstrate that magnetic moments further apart exhibit stronger interactions than those in closer proximity, deviating from typical behavior.

Applications and Advances in Machine Learning Force Fields

Force fields (FFs) form the basis of molecular simulations and have significant implications in diverse fields such as materials science, chemistry, physics, and biology. A suitable FF is required to accurately describe system properties. However, an off-the-shelf FF may not be suitable for certain specialized systems, and researchers often need to tailor the FF that fits specific requirements. Before applying machine learning (ML) techniques to construct FFs, the mainstream FFs were primarily based on first-principles force fields (FPFF) and empirical FFs. However, the drawbacks of FPFF and empirical FFs are high cost and low accuracy, respectively, so there is a growing interest in using ML as an effective and precise tool for reconciling this trade-off in developing FFs. In this review, we introduce the fundamental principles of ML and FFs in the context of machine learning force fields (MLFF). We also discuss the advantages and applications of MLFF compared to traditional FFs, as well as the MLFF toolkits widely employed in numerous applications.

Effect of Framework Composition and NH3 on the Diffusion of Cu+ in Cu-CHA Catalysts Predicted by Machine-Learning Accelerated Molecular Dynamics

Cu-exchanged zeolites rely on mobile solvated Cu+ cations for their catalytic activity, but the role of the framework composition in transport is not fully understood. Ab initio molecular dynamics simulations can provide quantitative atomistic insight but are too computationally expensive to explore large length and time scales or diverse compositions. We report a machine-learning interatomic potential that accurately reproduces ab initio results and effectively generalizes to allow multinanosecond simulations of large supercells and diverse chemical compositions. Biased and unbiased simulations of [Cu(NH3)2]+ mobility show that aluminum pairing in eight-membered rings accelerates local hopping and demonstrate that increased NH3 concentration enhances long-range diffusion. The probability of finding two [Cu(NH3)2]+ complexes in the same cage, which is key for SCR-NOx reaction, increases with Cu content and Al content but does not correlate with the long-range mobility of Cu+. Supporting experimental evidence was obtained from reactivity tests of Cu-CHA catalysts with a controlled chemical composition.

Integrated Molecular Modeling and Machine Learning for Drug Design

Modern therapeutic development often involves several stages that are interconnected, and multiple iterations are usually required to bring a new drug to the market. Computational approaches have increasingly become an indispensable part of helping reduce the time and cost of the research and development of new drugs. In this Perspective, we summarize our recent efforts on integrating molecular modeling and machine learning to develop computational tools for modulator design, including a pocket-guided rational design approach based on AlphaSpace to target protein-protein interactions, delta machine learning scoring functions for protein-ligand docking as well as virtual screening, and state-of-the-art deep learning models to predict calculated and experimental molecular properties based on molecular mechanics optimized geometries. Meanwhile, we discuss remaining challenges and promising directions for further development and use a retrospective example of FDA approved kinase inhibitor Erlotinib to demonstrate the use of these newly developed computational tools.

Simulating the isotropic Raman spectra of O-H stretching mode in liquid H2O based on a machine learning potential: the influence of vibrational couplings

In this study, we trained a deep potential (DP) for H2O, an accurate machine learning (ML) potential. We performed molecular dynamics (MD) simulations of liquid water using the DP model (or DeePMD simulations). Our results showed that the DP model exhibits DFT-level accuracy, and the DeePMD simulation is a promising approach for modeling the structural properties of liquid water. Based on the DeePMD simulation trajectories, we calculated the isotropic Raman spectra of the O-H stretching mode using the surface-specific velocity-velocity correlation function (ssVVCF), showing that the DeePMD/ssVVCF approach can correctly capture the bimodal characteristics of the experimental Raman spectra, with one peak located near 3400 cm-1 and the other near 3250 cm-1. The success of the DeePMD/ssVVCF approach should be credited to (1) the DFT-level accuracy of the DP model for H2O, (2) the ssVVCF formulation considering the coupling between vibrational modes, and (3) non-Condon effects. Furthermore, the DeePMD simulations revealed that the anharmonic interactions between the coupled water molecules in the first and second hydration shells should play an essential role in the strong mixing of the H-O-H bending mode and the O-H stretching mode, leading to the delocalization of the O-H stretching band. In particular, increasing the strength of hydrogen bonds would enhance the bend-stretch coupling, leading to the red-shifting of the O-H vibrational spectra and the increase in the intensity of the shoulder around 3250 cm-1.

A Gaussian Process Based Δ-Machine Learning Approach to Reactive Potential Energy Surfaces

The Gaussian process (GP) is an efficient nonparametric machine learning (ML) method. A distinct advantage of the GP is its ability to provide an estimate of statistical uncertainties. This is particularly useful in constructing high-dimensional potential energy surfaces (PESs) from ab initio data as it offers an optimal way to add new geometries to reduce the overall error. In this work, GP is employed in the context of Δ-machine learning (Δ-ML), in which a correction PES to an inaccurate low-level PES is constructed using a small number of high-level ab initio calculations. This new method is tested in three prototypical reactive systems, namely, the H + H2 → H + H2, OH + H2 → H2O + H, and H + CH4 → H2 + CH3 reactions. The results show that the GP-based Δ-ML approach is more efficient than its direct application in constructing high-level PESs. We also compare the new method to a previously proposed neural-network-based Δ-ML approach [Liu and Li J. Phys. Chem. Lett. 2022, 13, 4729-4738]. The results indicate that the two Δ-ML methods have comparable efficiencies in constructing accurate PESs.

Thermal transport across TiO2-H2O interface involving water dissociation: Ab initio-assisted deep potential molecular dynamics

Water dissociation on TiO2 surfaces has been known for decades and holds great potential in various applications, many of which require a proper understanding of thermal transport across the TiO2-H2O interface. Molecular dynamics (MD) simulations play an important role in characterizing complex systems' interfacial thermal transport properties. Nevertheless, due to the imprecision of empirical force field potentials, the interfacial thermal transport mechanism involving water dissociation remains to be determined. To cope with this, a deep potential (DP) model is formulated through the utilization of ab initio datasets. This model successfully simulates interfacial thermal transport accompanied by water dissociation on the TiO2 surfaces. The trained DP achieves a total energy accuracy of ∼238.8 meV and a force accuracy of ∼197.05 meV/Å. The DPMD simulations show that water dissociation induces the formation of hydrogen bonding networks and molecular bridges. Structural modifications further affect interfacial thermal transport. The interfacial thermal conductance estimated by DP is ∼8.54 × 109 W/m2 K, smaller than ∼13.17 × 109 W/m2 K by empirical potentials. The vibrational density of states (VDOS) quantifies the differences between the DP model and empirical potentials. Notably, the VDOS disparity between the adsorbed hydrogen atoms and normal hydrogen atoms demonstrates the influence of water dissociation on heat transfer processes. This work aims to understand the effect of water dissociation on thermal transport at the TiO2-H2O interface. The findings will provide valuable guidance for the thermal management of photocatalytic devices.

Reducing the Cost of Neural Network Potential Generation for Reactive Molecular Systems

Although machine learning potentials have recently had a substantial impact on molecular simulations, the construction of a robust training set can still become a limiting factor, especially due to the requirement of a reference ab initio simulation that covers all the relevant geometries of the system. Recognizing that this can be prohibitive for certain systems, we develop the method of transition tube sampling that mitigates the computational cost of training set and model generation. In this approach, we generate classical or quantum thermal geometries around a transition path describing a conformational change or a chemical reaction using only a sparse set of local normal mode expansions along this path and select from these geometries by an active learning protocol. This yields a training set with geometries that characterize the whole transition without the need for a costly reference trajectory. The performance of the method is evaluated on different molecular systems with the complexity of the potential energy landscape increasing from a single minimum to a double proton-transfer reaction with high barriers. Our results show that the method leads to training sets that give rise to models applicable in classical and path integral simulations alike that are on par with those based directly on ab initio calculations while providing the computational speedup we have come to expect from machine learning potentials.

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.

Graph-EAM: An Interpretable and Efficient Graph Neural Network Potential Framework

The development of deep learning interatomic potentials has enabled efficient and accurate computations in quantum chemistry and materials science, circumventing computationally expensive ab initio calculations. However, the huge number of learnable parameters in deep learning models and their complex architectures hinder physical interpretability and affect the robustness of the derived potential. In this work, we propose graph-EAM, a lightweight graph neural network (GNN) inspired by the empirical embedded atom method to model the interatomic potential of single-element structures. Four material systems: platinum, niobium, silicon, and amorphous-carbon, for which quantum simulation data sets are publicly available, are examined to demonstrate that graph-EAM can achieve high energy and force prediction accuracy─comparable or better than existing state-of-the-art machine learning models─with much fewer parameters. It is also shown that the explicit inclusion of the angular information via three-body atomic density increases the prediction accuracy. The accuracy and efficiency of potentials obtained from graph-EAM can help accelerate the molecular dynamics simulation.

Transferability evaluation of the deep potential model for simulating water-graphene confined system

Machine learning potentials (MLPs) are poised to combine the accuracy of ab initio predictions with the computational efficiency of classical molecular dynamics (MD) simulation. While great progress has been made over the last two decades in developing MLPs, there is still much to be done to evaluate their model transferability and facilitate their development. In this work, we construct two deep potential (DP) models for liquid water near graphene surfaces, Model S and Model F, with the latter having more training data. A concurrent learning algorithm (DP-GEN) is adopted to explore the configurational space beyond the scope of conventional ab initio MD simulation. By examining the performance of Model S, we find that an accurate prediction of atomic force does not imply an accurate prediction of system energy. The deviation from the relative atomic force alone is insufficient to assess the accuracy of the DP models. Based on the performance of Model F, we propose that the relative magnitude of the model deviation and the corresponding root-mean-square error of the original test dataset, including energy and atomic force, can serve as an indicator for evaluating the accuracy of the model prediction for a given structure, which is particularly applicable for large systems where density functional theory calculations are infeasible. In addition to the prediction accuracy of the model described above, we also briefly discuss simulation stability and its relationship to the former. Both are important aspects in assessing the transferability of the MLP model.

Gaussian process regression adaptive density-guided approach: Toward calculations of potential energy surfaces for larger molecules

We present a new program implementation of the Gaussian process regression adaptive density-guided approach [Schmitz et al., J. Chem. Phys. 153, 064105 (2020)] for automatic and cost-efficient potential energy surface construction in the MidasCpp program. A number of technical and methodological improvements made allowed us to extend this approach toward calculations of larger molecular systems than those previously accessible and maintain the very high accuracy of constructed potential energy surfaces. On the methodological side, improvements were made by using a Δ-learning approach, predicting the difference against a fully harmonic potential, and employing a computationally more efficient hyperparameter optimization procedure. We demonstrate the performance of this method on a test set of molecules of growing size and show that up to 80% of single point calculations could be avoided, introducing a root mean square deviation in fundamental excitations of about 3 cm-1. A much higher accuracy with errors below 1 cm-1 could be achieved with tighter convergence thresholds still reducing the number of single point computations by up to 68%. We further support our findings with a detailed analysis of wall times measured while employing different electronic structure methods. Our results demonstrate that GPR-ADGA is an effective tool, which could be applied for cost-efficient calculations of potential energy surfaces suitable for highly accurate vibrational spectra simulations.

Machine Learning for Bridging the Gap between Density Functional Theory and Coupled Cluster Energies

Accurate electronic energies and properties are crucial for successful reaction design and mechanistic investigations. Computing energies and properties of molecular structures has proven extremely useful, and, with increasing computational power, the limits of high-level approaches (such as coupled cluster theory) are expanding to ever larger systems. However, because scaling is highly unfavorable, these methods are still not universally applicable to larger systems. To address the need for fast and accurate electronic energies of larger systems, we created a database of around 8000 small organic monomers (2000 dimers) optimized at the B3LYP-D3(BJ)/cc-pVTZ level of theory. This database also includes single-point energies computed at various levels of theory, including PBE1PBE, ωΒ97Χ, M06-2X, revTPSS, B3LYP, and BP86, for density functional theory as well as DLPNO-CCSD(T) and CCSD(T) for coupled cluster theory, all in conjunction with a cc-pVTZ basis. We used this database to train machine learning models based on graph neural networks using two different graph representations. Our models are able to make energy predictions from B3LYP-D3(BJ)/cc-pVTZ inputs to CCSD(T)/cc-pVTZ outputs with a mean absolute error of 0.78 and to DLPNO-CCSD(T)/cc-pVTZ with an mean absolute error of 0.50 and 0.18 kcal mol^-1 for monomers and dimers, respectively. The model for dimers was further validated on the S22 database, and the monomer model was tested on challenging systems, including those with highly conjugated or functionally complex molecules.

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.

Atomistic modeling of the mechanical properties: the rise of machine learning interatomic potentials

Since the birth of the concept of machine learning interatomic potentials (MLIPs) in 2007, a growing interest has been developed in the replacement of empirical interatomic potentials (EIPs) with MLIPs, in order to conduct more accurate and reliable molecular dynamics calculations. As an exciting novel progress, in the last couple of years the applications of MLIPs have been extended towards the analysis of mechanical and failure responses, providing novel opportunities not heretofore efficiently achievable, neither by EIPs nor by density functional theory (DFT) calculations. In this minireview, we first briefly discuss the basic concepts of MLIPs and outline popular strategies for developing a MLIP. Next, by considering several examples of recent studies, the robustness of MLIPs in the analysis of the mechanical properties will be highlighted, and their advantages over EIP and DFT methods will be emphasized. MLIPs furthermore offer astonishing capabilities to combine the robustness of the DFT method with continuum mechanics, enabling the first-principles multiscale modeling of mechanical properties of nanostructures at the continuum level. Last but not least, the common challenges of MLIP-based molecular dynamics simulations of mechanical properties are outlined and suggestions for future investigations are proposed.

Constructing Diabatic Potential Energy Matrices with Neural Networks Based on Adiabatic Energies and Physical Considerations: Toward Quantum Dynamic Accuracy

A permutation invariant polynomial-neural network (PIP-NN) approach for constructing the global diabatic potential energy matrices (PEMs) of the coupled states of molecules is proposed. Specifically, the diabatization scheme is based merely on the adiabatic energy data of the system, which is ideally a most convenient way due to not requiring additional ab initio calculations for the data of the derivative coupling or any other physical properties of the molecule. Considering the permutation and coupling characteristics of the system, particularly in the presence of conical intersections, some vital treatments for the off-diagonal terms in diabatic PEM are essentially needed. Taking the photodissociation of H₂O(X~/B~)/NH₃(X~/A~) and nonadiabatic reaction Na(3p) + H₂ → NaH(Σ⁺) + H for example, this PIP-NN method is shown to build up the global diabatic PEMs effectively and accurately. The root-mean-square errors of the adiabatic potential energies in the fitting for three different systems are all small (<10 meV). Further quantum dynamic calculations show that the absorption spectra and product branching ratios in both H₂O(X~/B~) and NH₃(X~/A~) nonadiabatic photodissociation are well reproduced on the new diabatic PEMs, and the nonadiabatic reaction probability of Na(3p) + H₂ → NaH(Σ⁺) + H obtained on the new diabatic PEMs of the 1²A₁ and 1²B₂ states is in reasonably good agreement with previous theoretical result as well, validating this new PIP-NN method.

Is Unified Understanding of Vibrational Coupling of Water Possible? Hyper-Raman Measurement and Machine Learning Spectra

The impact of the vibrational coupling of the OH stretch mode on the spectra differs significantly between IR and Raman spectra of water. Unified understanding of the vibrational couplings is not yet achieved. By using a different class of vibrational spectroscopy, hyper-Raman (HR) spectroscopy, together with machine-learning-assisted HR spectra calculation, we examine the impact of the vibrational couplings of water through the comparison of isotopically diluted H₂O and pure H₂O. We found that the isotopic dilution reduces the HR bandwidths, but the impact of the vibrational coupling is smaller than in the IR and parallel-polarized Raman. Machine learning HR spectra indicate that the intermolecular coupling plays a major role in broadening the bandwidth, while the intramolecular coupling is negligibly small, which is consistent with the IR and Raman spectra. Our result clearly demonstrates a limited impact of the intramolecular vibration, independent of the selection rules of vibrational spectroscopies.

Active sampling for neural network potentials: Accelerated simulations of shear-induced deformation in Cu-Ni multilayers

Neural network potentials (NNPs) can greatly accelerate atomistic simulations relative to ab initio methods, allowing one to sample a broader range of structural outcomes and transformation pathways. In this work, we demonstrate an active sampling algorithm that trains an NNP that is able to produce microstructural evolutions with accuracy comparable to those obtained by density functional theory, exemplified during structure optimizations for a model Cu-Ni multilayer system. We then use the NNP, in conjunction with a perturbation scheme, to stochastically sample structural and energetic changes caused by shear-induced deformation, demonstrating the range of possible intermixing and vacancy migration pathways that can be obtained as a result of the speedups provided by the NNP. The code to implement our active learning strategy and NNP-driven stochastic shear simulations is openly available at https://github.com/pnnl/Active-Sampling-for-Atomistic-Potentials.

Semiclassical Dynamics on Machine-Learned Coupled Multireference Potential Energy Surfaces: Application to the Photodissociation of the Simplest Criegee Intermediate

Determination of high-dimensional potential energy surfaces (PESs) and nonadiabatic couplings have always been quite challenging. To this end, machine learning (ML) models, trained with a finite set of ab initio data, allow accurate prediction of such properties. To express the PESs in terms of atomic contributions is the cornerstone of any ML based technique because it can be easily scaled to large systems. In this work, we have constructed high fidelity PESs and nonadiabatic coupling terms at the CASSCF level of ab initio data using a machine learning technique, namely, kernel-ridge regression. Additional MRCI-level calculations were carried out to assess the quality of the PESs. We use these machine-learned PESs and nonadiabatic couplings to simulate excited-state molecular dynamics based on Tully's fewest-switches surface hopping method (FSSH). FSSH is a semiclassical method in which nuclei move on the PESs due to the electrons according to the laws of classical mechanics. Nonadiabatic effects are taken into account in terms of transitions between PESs. We apply this scheme to study the O-O photodissociation of the simplest Criegee intermediate (CH₂OO). The FSSH trajectories were initiated on the lowest optically bright singlet excited state (S₂) and propagated along the three most important internal coordinates, namely, O-O and C-O bond distances and the COO bond angle. Some of the trajectories end up on energetically lower PESs as a result of radiationless transfer through conical intersections. All of the trajectories lead to the dissociation of the O-O bond due to the dissociative nature of the excited PESs through one of the two dissociative channels. The simulation reveals that there is about 88.4% probability of dissociation through the lower channel leading to the H₂CO (X¹A₁) and O (¹D) products, whereas there is only 11.6% probability of dissociation through the upper channel leading to H₂CO (a³A″) and O (³P) products.

MLRNet: Combining the Physics-Motivated Potential Models with Neural Networks for Intermolecular Potential Energy Surface Construction

A physics-based machine learning model called MLRNet has been developed to construct the high-accuracy two-body intermolecular potential energy surface (IPES). The outputs of the neural network are integrated into the physically realistic Morse/long-range (MLR) function, which ensures that the MLRNet has meaningful extrapolation at both short and long ranges and solves the asymptotic problem in common neural network potential (NNP) models. The neural network representation of the MLR parameters is more flexible and more efficient than the polynomial expansion in the conventional mdMLR model, especially for systems containing nonrigid monomer(s). The present work illustrates the basic framework of the current MLRNet model, including (i) how to combine the physically meaningful MLR function with different possible NN structures, (ii) the preservation of permutation symmetry, and (iii) the predetermination of the long-range function u_LR. We choose two realistic systems to demonstrate the performance of MLRNet: the three-dimensional IPES of CO₂-He including the CO₂ antisymmetric vibration Q₃ and the six-dimensional IPES of the H₂O-Ar system. In both cases, the fitting errors of the MLRNet are several times smaller than those of the conventional mdMLR model. Both short-range and long-range extrapolation tests were performed to illustrate the extrapolation ability of the MLRNet and its damping function version. Moreover, for the 6-D H₂O-Ar system, the MLRNet only needs 1596 trainable parameters, which is almost equal to the number needed for the 5-D mdMLR model (1509) and half that needed for the PIP-NN model (3501) within similar accuracy, which illustrates the model efficiency in high-dimensional IPES fitting.

Storage and diffusion of CO2 in covalent organic frameworks—A neural network-based molecular dynamics simulation approach

As a consequence of the accelerated climate change, solutions to capture, store and potentially activate carbon dioxide received increased interest in recent years. Herein, it is demonstrated, that the neural network potential ANI-2x is able to describe nanoporous organic materials at approx. density functional theory accuracy and force field cost, using the example of the recently published two- and three-dimensional covalent organic frameworks HEX-COF1 and 3D-HNU5 and their interaction with CO2 guest molecules. Along with the investigation of the diffusion behaviour, a wide range of properties of interest is analyzed, such as the structure, pore size distribution and host-guest distribution functions. The workflow developed herein facilitates the estimation of the maximum CO2 adsorption capacity and is easily generalizable to other systems. Additionally, this work illustrates, that minimum distance distribution functions can be a highly useful tool in understanding the nature of interactions in host-gas systems at the atomic level.

Adaptive regularized Gaussian process regression for application in the context of hydrogen adsorption on graphene sheets

We present a Gaussian process regression (GPR) scheme with an adaptive regularization scheme applied to the QM7 and QM9 test set, several protonated water clusters and specifically to the problem of atomic hydrogen adsorption on graphene sheets. For the last system our goal is to achieve good predictive accuracy with only a few training points. Therefore, we assess for these systems a self-correcting multilayer GPR model, in which the prediction is corrected by a chain of additional GPR models. In our adaptive regularization scheme, we impose no noise on the training data, but use an approach based on the data itself to account for its impurity. The strength of this strategy is that the data points are treated differently based on their importance and that the regularization can still be controlled by a single parameter. We assess how the accuracy of the prediction depends on this parameter. We can show that the new regularization scheme as well as the multilayer approach results in more robust predictors. Furthermore, we demonstrate that the predictor can be in good agreement with the density-functional theory results.

Thermal transport across copper-water interfaces according to deep potential molecular dynamics

Nanoscale thermal transport at solid-liquid interfaces plays an essential role in many engineering fields. This work performs deep potential molecular dynamics (DPMD) simulations to investigate thermal transport across copper-water interfaces. Unlike traditional classical molecular dynamics (CMD) simulations, we independently train a deep learning potential (DLP) based on density functional theory (DFT) calculations and demonstrated its high computational efficiency and accuracy. The trained DLP predicts radial distribution functions (RDFs), vibrational densities of states (VDOS), density curves, and thermal conductivity of water confined in the nanochannel at a DFT accuracy. The thermal conductivity decreases slightly with an increase in the channel height, while the influence of the cross-sectional area is negligible. Moreover, the predicted interfacial thermal conductance (ITC) across the copper-water interface by DPMD is 2.505 × 10⁸ W m^-2 K^-1, the same order of magnitude as the CMD and experimental results but with a high computational accuracy. This work seeks to simulate the thermal transport properties of solid-liquid interfaces with DFT accuracy at large-system and long-time scales.

A "short blanket" dilemma for a state-of-the-art neural network potential for water: Reproducing experimental properties or the physics of the underlying many-body interactions?

Deep neural network (DNN) potentials have recently gained popularity in computer simulations of a wide range of molecular systems, from liquids to materials. In this study, we explore the possibility of combining the computational efficiency of the DeePMD framework and the demonstrated accuracy of the MB-pol data-driven, many-body potential to train a DNN potential for large-scale simulations of water across its phase diagram. We find that the DNN potential is able to reliably reproduce the MB-pol results for liquid water, but provides a less accurate description of the vapor-liquid equilibrium properties. This shortcoming is traced back to the inability of the DNN potential to correctly represent many-body interactions. An attempt to explicitly include information about many-body effects results in a new DNN potential that exhibits the opposite performance, being able to correctly reproduce the MB-pol vapor-liquid equilibrium properties, but losing accuracy in the description of the liquid properties. These results suggest that DeePMD-based DNN potentials are not able to correctly "learn" and, consequently, represent many-body interactions, which implies that DNN potentials may have limited ability to predict the properties for state points that are not explicitly included in the training process. The computational efficiency of the DeePMD framework can still be exploited to train DNN potentials on data-driven many-body potentials, which can thus enable large-scale, "chemically accurate" simulations of various molecular systems, with the caveat that the target state points must have been adequately sampled by the reference data-driven many-body potential in order to guarantee a faithful representation of the associated properties.

Accelerated Quantum Mechanics/Molecular Mechanics Simulations via Neural Networks Incorporated with Mechanical Embedding Scheme

A powerful tool to study the mechanism of reactions in solutions or enzymes is to perform the ab initio quantum mechanical/molecular mechanical (QM/MM) molecular dynamics (MD) simulations. However, the computational cost is too high due to the explicit electronic structure calculations at every time step of the simulation. A neural network (NN) method can accelerate the QM/MM-MD simulations, but it has long been a problem to accurately describe the QM/MM electrostatic coupling by NN in the electrostatic embedding (EE) scheme. In this work, we developed a new method to accelerate QM/MM calculations in the mechanic embedding (ME) scheme. The potentials and partial point charges of QM atoms are first learned in vacuo by the embedded atom neural networks (EANN) approach. MD simulations are then performed on this EANN/MM potential energy surface (PES) to obtain free energy (FE) profiles for reactions, in which the QM/MM electrostatic coupling is treated in the mechanic embedding (ME) scheme. Finally, a weighted thermodynamic perturbation (wTP) corrects the FE profiles in the ME scheme to the EE scheme. For two reactions in water and one in methanol, our simulations reproduced the B3LYP/MM free energy profiles within 0.5 kcal/mol with a speed-up of 30-60-fold. The results show that the strategy of combining EANN potential in the ME scheme with the wTP correction is efficient and reliable for chemical reaction simulations in liquid. Another advantage of our method is that the QM PES is independent of the MM subsystem, so it can be applied to various MM environments as demonstrated by an S_N2 reaction studied in water and methanol individually, which used the same EANN PES. The free energy profiles are in excellent accordance with the results obtained from B3LYP/MM-MD simulations. In future, this method will be applied to the reactions of enzymes and their variants.

Neural network potentials for chemistry: concepts, applications and prospects

Artificial Neural Networks (NN) are already heavily involved in methods and applications for frequent tasks in the field of computational chemistry such as representation of potential energy surfaces (PES) and spectroscopic predictions. This perspective provides an overview of the foundations of neural network-based full-dimensional potential energy surfaces, their architectures, underlying concepts, their representation and applications to chemical systems. Methods for data generation and training procedures for PES construction are discussed and means for error assessment and refinement through transfer learning are presented. A selection of recent results illustrates the latest improvements regarding accuracy of PES representations and system size limitations in dynamics simulations, but also NN application enabling direct prediction of physical results without dynamics simulations. The aim is to provide an overview for the current state-of-the-art NN approaches in computational chemistry and also to point out the current challenges in enhancing reliability and applicability of NN methods on a larger scale.

Low-cost machine learning prediction of excited state properties of iridium-centered phosphors

Prediction of the excited state properties of photoactive iridium complexes challenges ab initio methods such as time-dependent density functional theory (TDDFT) both from the perspective of accuracy and of computational cost, complicating high-throughput virtual screening (HTVS). We instead leverage low-cost machine learning (ML) models and experimental data for 1380 iridium complexes to perform these prediction tasks. We find the best-performing and most transferable models to be those trained on electronic structure features from low-cost density functional tight binding calculations. Using artificial neural network (ANN) models, we predict the mean emission energy of phosphorescence, the excited state lifetime, and the emission spectral integral for iridium complexes with accuracy competitive with or superseding that of TDDFT. We conduct feature importance analysis to determine that high cyclometalating ligand ionization potential correlates to high mean emission energy, while high ancillary ligand ionization potential correlates to low lifetime and low spectral integral. As a demonstration of how our ML models can be used for HTVS and the acceleration of chemical discovery, we curate a set of novel hypothetical iridium complexes and use uncertainty-controlled predictions to identify promising ligands for the design of new phosphors while retaining confidence in the quality of the ANN predictions.

Machine Learned Composite Methods for Electronic Structure Theory

Because of the prohibitive scaling of ab initio techniques for modeling chemical species with high accuracy, they are not generally tractable for large systems. It is therefore of considerable interest to develop high-accuracy computational models with low computational cost that can afford predictions of electronic structure and properties of macromolecular species. Composite methods, as first introduced by Pople [Pople, J. A.; Head-Gordon, M.; Fox, D. J.; Raghavachari, K.; Curtiss, L. A. J. Chem. Phys.1989, 90, 5622.], are an intuitive solution to this problem as they seek to systematically increase accuracy in model chemistries by taking advantage of favorable error cancellation among reasonably low-cost models. By linearly combining a series of carefully chosen model chemistries, the result of a prohibitive-scaling correlated model chemistry with a large basis set may be approximated with relatively good fidelity. However, the full extent to which the choice of low-cost models dictates the predictive accuracy of composite methods is not known, and a full exploration of all model chemistries would be advantageous for the design and validation of a generalizable composite method for widespread application. Here, we show that remarkable accuracy can be generally achieved with composite methods that are more judiciously constructed, leading to increased accuracy with significantly reduced computational cost. By designing a systematic procedure for the automated generation and assessment of over 10 billion unique composite methods, we have extensively explored the space of modern model chemistries to elucidate important design principles in the construction of reliable composite procedures. We anticipate our work to be the starting point in the pursuit of creative approaches to modeling large chemical systems with high accuracy by using novel combinatorial modeling.

Multitask Deep Ensemble Prediction of Molecular Energetics in Solution: From Quantum Mechanics to Experimental Properties

The past few years have witnessed significant advances in developing machine learning methods for molecular energetics predictions, including calculated electronic energies with high-level quantum mechanical methods and experimental properties, such as solvation free energy and logP. Typically, task-specific machine learning models are developed for distinct prediction tasks. In this work, we present a multitask deep ensemble model, sPhysNet-MT-ens5, which can simultaneously and accurately predict electronic energies of molecules in gas, water, and octanol phases, as well as transfer free energies at both calculated and experimental levels. On the calculated data set Frag20-solv-678k, which is developed in this work and contains 678,916 molecular conformations, up to 20 heavy atoms, and their properties calculated at B3LYP/6-31G* level of theory with continuum solvent models, sPhysNet-MT-ens5 predicts density functional theory (DFT)-level electronic energies directly from force field-optimized geometry within chemical accuracy. On the experimental data sets, sPhysNet-MT-ens5 achieves state-of-the-art performances, which predict both experimental hydration free energy with a RMSE of 0.620 kcal/mol on the FreeSolv data set and experimental logP with a RMSE of 0.393 on the PHYSPROP data set. Furthermore, sPhysNet-MT-ens5 also provides a reasonable estimation of model uncertainty which shows correlations with prediction error. Finally, by analyzing the atomic contributions of its predictions, we find that the developed deep learning model is aware of the chemical environment of each atom by assigning reasonable atomic contributions consistent with our chemical knowledge.

High-dimensional neural network potentials for accurate vibrational frequencies: the formic acid dimer benchmark

In recent years, machine learning potentials (MLP) for atomistic simulations have attracted a lot of attention in chemistry and materials science. Many new approaches have been developed with the primary aim to transfer the accuracy of electronic structure calculations to large condensed systems containing thousands of atoms. In spite of these advances, the reliability of modern MLPs in reproducing the subtle details of the multi-dimensional potential-energy surface is still difficult to assess for such systems. On the other hand, moderately sized systems enabling the application of tools for thorough and systematic quality-control are nowadays rarely investigated. In this work we use benchmark-quality harmonic and anharmonic vibrational frequencies as a sensitive probe for the validation of high-dimensional neural network potentials. For the case of the formic acid dimer, a frequently studied model system for which stringent spectroscopic data became recently available, we show that high-quality frequencies can be obtained from state-of-the-art calculations in excellent agreement with coupled cluster theory and experimental data.