E(n)-Equivariant cartesian tensor message passing interatomic potential

Machine learning potential (MLP) has been a popular topic in recent years for its capability to replace expensive first-principles calculations in some large systems. Meanwhile, message passing networks have gained significant attention due to their remarkable accuracy, and a wave of message passing networks based on Cartesian coordinates has emerged. However, the information of the node in these models is usually limited to scalars, and vectors. In this work, we propose High-order Tensor message Passing interatomic Potential (HotPP), an E(n) equivariant message passing neural network that extends the node embedding and message to an arbitrary order tensor. By performing some basic equivariant operations, high order tensors can be coupled very simply and thus the model can make direct predictions of high-order tensors such as dipole moments and polarizabilities without any modifications. The tests in several datasets show that HotPP not only achieves high accuracy in predicting target properties, but also successfully performs tasks such as calculating phonon spectra, infrared spectra, and Raman spectra, demonstrating its potential as a tool for future research.

Derivative learning of tensorial quantities-Predicting finite temperature infrared spectra from first principles

We develop a strategy that integrates machine learning and first-principles calculations to achieve technically accurate predictions of infrared spectra. In particular, the methodology allows one to predict infrared spectra for complex systems at finite temperatures. The method's effectiveness is demonstrated in challenging scenarios, such as the analysis of water and the organic-inorganic halide perovskite MAPbI3, where our results consistently align with experimental data. A distinctive feature of the methodology is the incorporation of derivative learning, which proves indispensable for obtaining accurate polarization data in bulk materials and facilitates the training of a machine learning surrogate model of the polarization adapted to rotational and translational symmetries. We achieve polarization prediction accuracies of about 1% for the water dimer by training only on the predicted Born effective charges.

Accuracy and limitations of the bond polarizability model in modeling of Raman scattering from molecular dynamics simulations

Calculation of Raman scattering from molecular dynamics (MD) simulations requires accurate modeling of the evolution of the electronic polarizability of the system along its MD trajectory. For large systems, this necessitates the use of atomistic models to represent the dependence of electronic polarizability on atomic coordinates. The bond polarizability model (BPM) is the simplest such model and has been used for modeling the Raman spectra of molecular systems but has not been applied to solid-state systems. Here, we systematically investigate the accuracy and limitations of the BPM parameterized from the density functional theory results for a series of simple molecules, such as CO2, SO2, H2S, H2O, NH3, and CH4; the more complex CH2O, CH3OH, CH3CH2OH, and thiophene molecules; and the BaTiO3 and CsPbBr3 perovskite solids. We find that BPM can reliably reproduce the overall features of the Raman spectra, such as shifts of peak positions. However, with the exception of highly symmetric systems, the assumption of non-interacting bonds limits the quantitative accuracy of the BPM; this assumption also leads to qualitatively inaccurate polarizability evolution and Raman spectra for systems where large deviations from the ground state structure are present.

Evidence of ferroelectric features in low-density supercooled water from ab initio deep neural-network simulations

Over the last decade, an increasing body of evidence has emerged, supporting the existence of a metastable liquid-liquid critical point in supercooled water whereby two distinct liquid phases of different densities coexist. Analyzing long molecular dynamics simulations performed using deep neural-network force fields trained to accurate quantum mechanical data, we demonstrate that the low-density liquid phase displays a strong propensity toward spontaneous polarization, as witnessed by large and long-lived collective dipole fluctuations. Our findings suggest that the dynamical stability of the low-density phase, and hence the transition from high-density to low-density liquid, is triggered by a collective process involving an accumulation of rotational angular jumps, which could ignite large dipole fluctuations. This dynamical transition involves subtle changes in the electronic polarizability of water molecules which affects their rotational mobility within the two phases. These findings hold the potential for catalyzing activity in the search for dielectric-based probes of the putative second critical point.

Advancing Force Fields Parameterization: A Directed Graph Attention Networks Approach

Force fields (FFs) are an established tool for simulating large and complex molecular systems. However, parametrizing FFs is a challenging and time-consuming task that relies on empirical heuristics, experimental data, and computational data. Recent efforts aim to automate the assignment of FF parameters using pre-existing databases and on-the-fly ab initio data. In this study, we propose a graph-based force field (GB-FFs) model to directly derive parameters for the Generalized Amber Force Field (GAFF) from chemical environments and research into the influence of functional forms. Our end-to-end parametrization approach predicts parameters by aggregating the basic information in directed molecular graphs, eliminating the need for expert-defined procedures and enhances the accuracy and transferability of GAFF across a broader range of molecular complexes. Simulation results are compared to the original GAFF parametrization. In practice, our results demonstrate an improved transferability of the model, showcasing its improved accuracy in modeling intermolecular and torsional interactions, as well as improved solvation free energies. The optimization approach developed in this work is fully applicable to other nonpolarizable FFs as well as to polarizable ones.

Nuclear Quantum Effects on the Electronic Structure of Water and Ice

The electronic properties and optical response of ice and water are intricately shaped by their molecular structure, including the quantum mechanical nature of the hydrogen atoms. Despite numerous previous studies, a comprehensive understanding of the nuclear quantum effects (NQEs) on the electronic structure of water and ice at finite temperatures remains elusive. Here, we utilize molecular simulations that harness efficient machine-learning potentials and many-body perturbation theory to assess how NQEs impact the electronic bands of water and hexagonal ice. By comparing path-integral and classical simulations, we find that NQEs lead to a larger renormalization of the fundamental gap of ice, compared to that of water, ultimately yielding similar bandgaps in the two systems, consistent with experimental estimates. Our calculations suggest that the increased quantum mechanical delocalization of protons in ice, relative to water, is a key factor leading to the enhancement of NQEs on the electronic structure of ice.

Raman Spectra of Amino Acids and Peptides from Machine Learning Polarizabilities

Raman spectroscopy is an important tool in the study of vibrational properties and composition of molecules, peptides, and even proteins. Raman spectra can be simulated based on the change of the electronic polarizability with vibrations, which can nowadays be efficiently obtained via machine learning models trained on first-principles data. However, the transferability of the models trained on small molecules to larger structures is unclear, and direct training on large structures is prohibitively expensive. In this work, we first train two machine learning models to predict the polarizabilities of all 20 amino acids. Both models are carefully benchmarked and compared to density functional theory (DFT) calculations, with the neural network method being found to offer better transferability. By combination of machine learning models with classical force field molecular dynamics, Raman spectra of all amino acids are also obtained and investigated, showing good agreement with experiments. The models are further extended to small peptides. We find that adding structures containing peptide bonds to the training set greatly improves predictions, even for peptides not included in training sets.

Impact of interfacial curvature on molecular properties of aqueous interfaces

The curvature of soft interfaces plays a crucial role in determining their mechanical and thermodynamic properties, both at macroscopic and microscopic scales. In the case of air/water interfaces, particular attention has recently focused on water microdroplets, due to their distinctive chemical reactivity. However, the specific impact of curvature on the molecular properties of interfacial water and interfacial reactivity has so far remained elusive. Here, we use molecular dynamics simulations to determine the effect of curvature on a broad range of structural, dynamical, and thermodynamical properties of the interface. For a droplet, a flat interface, and a cavity, we successively examine the structure of the hydrogen-bond network and its relation to vibrational spectroscopy, the dynamics of water translation, rotation, and hydrogen-bond exchanges, and the thermodynamics of ion solvation and ion-pair dissociation. Our simulations show that curvature predominantly impacts the hydrogen-bond structure through the fraction of dangling OH groups and the dynamics of interfacial water molecules. In contrast, curvature has a limited effect on solvation and ion-pair dissociation thermodynamics. For water microdroplets, this suggests that the curvature alone cannot fully account for the distinctive reactivity measured in these systems, which are of great importance for catalysis and atmospheric chemistry.

Confinement Effects on Proton Transfer in TiO2 Nanopores from Machine Learning Potential Molecular Dynamics Simulations

Improved understanding of proton transfer in nanopores is critical for a wide range of emerging applications, yet experimentally probing mechanisms and energetics of this process remains a significant challenge. To help reveal details of this process, we developed and applied a machine learning potential derived from first-principles calculations to examine water reactivity and proton transfer in TiO2 slit-pores. We find that confinement of water within pores smaller than 0.5 nm imposes strong and complex effects on water reactivity and proton transfer. Although the proton transfer mechanism is similar to that at a TiO2 interface with bulk water, confinement reduces the activation energy of this process, leading to more frequent proton transfer events. This enhanced proton transfer stems from the contraction of oxygen-oxygen distances dictated by the interplay between confinement and hydrophilic interactions. Our simulations also highlight the importance of the surface topology, where faster proton transport is found in the direction where a unique arrangement of surface oxygens enables the formation of an ordered water chain. In a broader context, our study demonstrates that proton transfer in hydrophilic nanopores can be enhanced by controlling pore size, surface chemistry, and topology.

Accelerating Molecular Vibrational Spectra Simulations with a Physically Informed Deep Learning Model

In recent years, machine learning (ML) surrogate models have emerged as an indispensable tool to accelerate simulations of physical and chemical processes. However, there is still a lack of ML models that can accurately predict molecular vibrational spectra. Here, we present a highly efficient multitask ML surrogate model termed Vibrational Spectra Neural Network (VSpecNN), to accurately calculate infrared (IR) and Raman spectra based on dipole moments and polarizabilities obtained on-the-fly via ML-enhanced molecular dynamics simulations. The methodology is applied to pyrazine, a prototypical polyatomic chromophore. The VSpecNN-predicted energies are well within the chemical accuracy (1 kcal/mol), and the errors for VSpecNN-predicted forces are only half of those obtained from a popular high-performance ML model. Compared to the ab initio reference, the VSpecNN-predicted frequencies of IR and Raman spectra differ only by less than 5.87 cm-1, and the intensities of IR spectra and the depolarization ratios of Raman spectra are well reproduced. The VSpecNN model developed in this work highlights the importance of constructing highly accurate neural network potentials for predicting molecular vibrational spectra.

Tensorial Properties via the Neuroevolution Potential Framework: Fast Simulation of Infrared and Raman Spectra

Infrared and Raman spectroscopy are widely used for the characterization of gases, liquids, and solids, as the spectra contain a wealth of information concerning, in particular, the dynamics of these systems. Atomic scale simulations can be used to predict such spectra but are often severely limited due to high computational cost or the need for strong approximations that limit the application range and reliability. Here, we introduce a machine learning (ML) accelerated approach that addresses these shortcomings and provides a significant performance boost in terms of data and computational efficiency compared with earlier ML schemes. To this end, we generalize the neuroevolution potential approach to enable the prediction of rank one and two tensors to obtain the tensorial neuroevolution potential (TNEP) scheme. We apply the resulting framework to construct models for the dipole moment, polarizability, and susceptibility of molecules, liquids, and solids and show that our approach compares favorably with several ML models from the literature with respect to accuracy and computational efficiency. Finally, we demonstrate the application of the TNEP approach to the prediction of infrared and Raman spectra of liquid water, a molecule (PTAF-), and a prototypical perovskite with strong anharmonicity (BaZrO3). The TNEP approach is implemented in the free and open source software package gpumd, which makes this methodology readily available to the scientific community.

Alkyne-tagged SERS nanoprobe for understanding Cu+ and Cu2+ conversion in cuproptosis processes

Simultaneously quantifying mitochondrial Cu+ and Cu2+ levels is crucial for evaluating the molecular mechanisms of copper accumulation-involved pathological processes. Here, a series of molecules containing various diacetylene derivatives as Raman reporters are designed and synthesized, and the alkyne-tagged SERS probe is created for determination Cu+ and Cu2+ with high selectivity and sensitivity. The developed SERS probe generates well-separated distinguishable Raman fingerprint peaks with built-in corrections in the cellular silent region, resulting in accurate quantification of Cu+ and Cu2+. The present probe demonstrates high tempo-spatial resolution for real-time imaging and simultaneously quantifying mitochondrial Cu+ and Cu2+ with long-term stability benefiting from the probe assembly with designed Au-C≡C groups. Using this powerful tool, it is found that mitochondrial Cu+ and Cu2+ increase during ischemia are associated with breakdown of proteins containing copper as well as conversion of Cu+ and Cu2+. Meanwhile, we observe that parts of Cu+ and Cu2+ are transported out of neurons by ATPase. More importantly, cuproptosis in neurons is found including the oxidative stress process caused by the conversion of Cu+ to Cu2+, which dominates at the early stage (<9 h), and subsequent proteotoxic stress. Both oxidative and proteotoxic stresses contribute to neuronal death.

Neural Network-Based Sum-Frequency Generation Spectra of Pure and Acidified Water Interfaces with Air

The affinity of hydronium ions (H3O+) for the air-water interface is a crucial question in environmental chemistry. While sum-frequency generation (SFG) spectroscopy has been instrumental in indicating the preference of H3O+ for the interface, key questions persist regarding the molecular origin of the SFG spectral changes in acidified water. Here we combine nanosecond long neural network (NN) reactive simulations of pure and acidified water slabs with NN predictions of molecular dipoles and polarizabilities to calculate SFG spectra of long reactive trajectories including proton transfer events. Our simulations show that H3O+ ions cause two distinct changes in phase-resolved SFG spectra: first, a low-frequency tail due to the vibrations of H3O+ and its first hydration shell, analogous to the bulk proton continuum, and second, an enhanced hydrogen-bonded band due to the ion-induced static field polarizing molecules in deeper layers. Our calculations confirm that changes in the SFG spectra of acidic solutions are caused by hydronium ions preferentially residing at the interface.

First-principles spectroscopy of aqueous interfaces using machine-learned electronic and quantum nuclear effects

Vibrational spectroscopy is a powerful approach to visualising interfacial phenomena. However, extracting structural and dynamical information from vibrational spectra is a challenge that requires first-principles simulations, including non-Condon and quantum nuclear effects. We address this challenge by developing a machine-learning enhanced first-principles framework to speed up predictive modelling of infrared, Raman, and sum-frequency generation spectra. Our approach uses machine learning potentials that encode quantum nuclear effects to generate quantum trajectories using simple molecular dynamics efficiently. In addition, we reformulate bulk and interfacial selection rules to express them unambiguously in terms of the derivatives of polarisation and polarisabilities of the whole system and predict these derivatives efficiently using fully-differentiable machine learning models of dielectric response tensors. We demonstrate our framework's performance by predicting the IR, Raman, and sum-frequency generation spectra of liquid water, ice and the water-air interface by achieving near quantitative agreement with experiments at nearly the same computational efficiency as pure classical methods. Finally, to aid the experimental discovery of new phases of nanoconfined water, we predict the temperature-dependent vibrational spectra of monolayer water across the solid-hexatic-liquid phases transition.

Raman Spectra of Electrified Si-Water Interfaces: First-Principles Simulations

We investigate the Raman spectra of liquid water in contact with a semiconductor surface using first-principles molecular dynamics simulations. We focus on a hydrogenated silicon-water interface and compute the Raman spectra from time correlation functions of the polarizability. We establish a relationship between Raman spectral signatures and structural properties of the liquid at the interface, and we identify the vibrational impacts of an applied electric field. We show that negative bias leads to a reduction of the number of hydrogen bonds (HBs) formed between the surface and the topmost water layer and an enhancement of the HB interactions between water molecules. Instead, positive bias leads to an enhancement of both the HB interactions between water and the surface and between water molecules, creating a semi-ordered interfacial layer. Our work provides molecular-level insights into electrified semiconductor/water interfaces and the identification of specific structural features through Raman spectroscopy.

Predicting the Raman Spectra of Liquid Water with a Monomer-Field Model

The Raman spectrum of liquid water is quite complex, reflecting its strong sensitivity to the local environment of the individual waters. The OH-stretch region of the spectrum, which captures the influence of hydrogen bonding, has only just begun to be unraveled. Here we develop a model for predicting the Raman spectra of the OH-stretch region by considering how local electric fields distort the energy surface of each water monomer. We find that our model is capable of reproducing the bimodal nature of the main peak, with the shoulder at 3250 cm-1 resulting almost entirely from Fermi resonance. Furthermore, we capture the temperature and polarization dependence of the shoulder, which has proven to be difficult to obtain with previous methods, and analyze the origin of this dependence. We expect our model to be generally useful for understanding and predicting how Raman spectra change under different conditions and with different probe reporters beyond water.

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.

Universal machine learning for the response of atomistic systems to external fields

Machine learned interatomic interaction potentials have enabled efficient and accurate molecular simulations of closed systems. However, external fields, which can greatly change the chemical structure and/or reactivity, have been seldom included in current machine learning models. This work proposes a universal field-induced recursively embedded atom neural network (FIREANN) model, which integrates a pseudo field vector-dependent feature into atomic descriptors to represent system-field interactions with rigorous rotational equivariance. This "all-in-one" approach correlates various response properties like dipole moment and polarizability with the field-dependent potential energy in a single model, very suitable for spectroscopic and dynamics simulations in molecular and periodic systems in the presence of electric fields. Especially for periodic systems, we find that FIREANN can overcome the intrinsic multiple-value issue of the polarization by training atomic forces only. These results validate the universality and capability of the FIREANN method for efficient first-principles modeling of complicated systems in strong external fields.

Accurate and Efficient Prediction of Post-Hartree-Fock Polarizabilities of Condensed-Phase Systems

To accurately and efficiently predict the molecular response properties (such as polarizability) at post-Hartree-Fock levels for condensed-phase systems under periodic boundary conditions (PBC) is still an unaccomplished and ongoing task. We demonstrate that static isotropic polarizabilities can be cost-effectively predicted at post-Hartree-Fock levels by combining the linear-scaling generalized energy-based fragmentation (GEBF) and information-theoretic approach (ITA) quantities. In PBC-GEBF, the total molecular polarizability of an extended system is obtained as a linear combination of the corresponding quantities of a series of small embedded subsystems of several monomers. Here, we show that in the PBC-GEBF-ITA framework, one can obtain the molecular polarizabilities and establish linear relations to ITA quantities. Once these relations are established for smaller subsystems, one can predict the polarizabilities of larger subsystems directly from the molecular wavefunction (or electron density) via ITA quantities. Alternatively, one can determine the total molecular polarizability via a linear combination equation in PBC-GEBF. We have corroborated that this newly proposed PBC-GEBF-ITA protocol is much more efficient than the original PBC-GEBF approach but is not much less accurate and that this conclusion holds for both many-body perturbation theory and the coupled cluster calculations. Good efficiency and transferability of the PBC-GEBF-ITA protocol are demonstrated for periodic systems with several hundred atoms in a unit cell.

Fully First-Principles Surface Spectroscopy with Machine Learning

Our current understanding of the structure and dynamics of aqueous interfaces at the molecular level has grown substantially due to the continuous development of surface-specific spectroscopies, such as vibrational sum-frequency generation (VSFG). As in other vibrational spectroscopies, we must turn to atomistic simulations to extract all of the information encoded in the VSFG spectra. The high computational cost associated with existing methods means that they have limitations in representing systems with complex electronic structure or in achieving statistical convergence. In this work, we combine high-dimensional neural network interatomic potentials and symmetry-adapted Gaussian process regression to overcome these constraints. We show that it is possible to model VSFG signals with fully ab initio accuracy using machine learning and illustrate the versatility of our approach on the water/air interface. Our strategy allows us to identify the main sources of theoretical inaccuracy and establish a clear pathway toward the modeling of surface-sensitive spectroscopy of complex interfaces.

DeePMD-kit v2: A software package for deep potential models

DeePMD-kit is a powerful open-source software package that facilitates molecular dynamics simulations using machine learning potentials known as Deep Potential (DP) models. This package, which was released in 2017, has been widely used in the fields of physics, chemistry, biology, and material science for studying atomistic systems. The current version of DeePMD-kit offers numerous advanced features, such as DeepPot-SE, attention-based and hybrid descriptors, the ability to fit tensile properties, type embedding, model deviation, DP-range correction, DP long range, graphics processing unit support for customized operators, model compression, non-von Neumann molecular dynamics, and improved usability, including documentation, compiled binary packages, graphical user interfaces, and application programming interfaces. This article presents an overview of the current major version of the DeePMD-kit package, highlighting its features and technical details. Additionally, this article presents a comprehensive procedure for conducting molecular dynamics as a representative application, benchmarks the accuracy and efficiency of different models, and discusses ongoing developments.

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.

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

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

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.

Accurate and Interpretable Dipole Interaction Model-Based Machine Learning for Molecular Polarizability

Polarizabilities play significant roles in describing dispersive and inductive interactions of the atom and molecular systems. However, an accurate prediction of molecular polarizabilities from first principles is computationally prohibitive. Although physical models or statistical machine learning models have been proposed, either a lack of accurate description of local chemical environments or demanding a large number of samples for training has limited their practical applications. In this study, we combine a physically inspired dipole interaction model and an accurate neural network method for predicting the polarizability tensors of molecules. With the local chemical environment precisely described and the requirement of rotational covariance naturally fulfilled, this hybrid model is proven to give an accurate molecular polarizability prediction, essentially reducing the number of training samples. The atomic polarizabilities are physically interpretable and transferable to larger molecules unseen in the training set. This promising method may find its wide range of applications, such as spectroscopic simulations and the construction of polarizable force fields.

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.

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.

Prediction approach of larch wood density from visible-near-infrared spectroscopy based on parameter calibrating and transfer learning

Wood density, as a key indicator to measure wood properties, is of weighty significance in enhancing wood utilization and modifying wood properties in sustainable forest management. Visible-near-infrared (Vis-NIR) spectroscopy provides a feasible and efficient solution for obtaining wood density by the advantages of its efficiency and non-destructiveness. However, the spectral responses are different in wood products with different moisture content conditions, and changes in external factors may cause the regression model to fail. Although some calibration transfer methods and convolutional neural network (CNN)-based deep transfer learning methods have been proposed, the generalization ability and prediction accuracy of the models still need to be improved. For the prediction problem of Vis-NIR wood density in different moisture contents, a deep transfer learning hybrid method with automatic calibration capability (Resnet1D-SVR-TrAdaBoost.R2) was proposed in this study. The disadvantage of overfitting was avoided when CNN processes small sample data, which considered the complex exterior factors in actual production to enhance feature extraction and migration between samples. Density prediction of the method was performed on a larch dataset with different moisture content conditions, and the hybrid method was found to achieve the best prediction results under the calibration samples with different target domain calibration samples and moisture contents, and the performance of models was better than that of the traditional calibration transfer and migration learning methods. In particular, the hybrid model has achieved an improvement of about 0.1 in both R ² and root mean square error (RMSE) values compared to the support vector regression model transferred by piecewise direct standardization method (SVR+PDS), which has the best performance among traditional calibration methods. To further ascertain the generalizability of the hybrid model, the model was validated with samples collected from mixed moisture contents as the target domain. Various experiments demonstrated that the Resnet1D-SVR-TrAdaBoost.R2 model could predict larch wood density with a high generalization ability and accuracy effectively but was computation consuming. It showed the potential to be extended to predict other metrics of wood.

Homogeneous ice nucleation in an ab initio machine-learning model of water

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine-learning model trained on density-functional theory energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation), which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates.

DP Compress: A Model Compression Scheme for Generating Efficient Deep Potential Models

Machine-learning-based interatomic potential energy surface (PES) models are revolutionizing the field of molecular modeling. However, although much faster than electronic structure schemes, these models suffer from costly computations via deep neural networks to predict the energy and atomic forces, resulting in lower running efficiency as compared to the typical empirical force fields. Herein, we report a model compression scheme for boosting the performance of the Deep Potential (DP) model, a deep learning-based PES model. This scheme, we call DP Compress, is an efficient postprocessing step after the training of DP models (DP Train). DP Compress combines several DP-specific compression techniques, which typically speed up DP-based molecular dynamics simulations by an order of magnitude faster and consume an order of magnitude less memory. We demonstrate that DP Compress is sufficiently accurate by testing a variety of physical properties of Cu, H₂O, and Al-Cu-Mg systems. DP Compress applies to both CPU and GPU machines and is publicly available online.

Permutationally invariant polynomial representation of polarizability tensor surfaces for linear regression analysis

A linearly parameterized functional form for a Cartesian representation of molecular dipole polarizability tensor surfaces (PTS) is described. The proposed expression for the PTS is a linearization of the recently reported power series ansatz of the original Applequist model, which by construction is non-linear in parameter space. This new approach possesses (i) a unique solution to the least-squares fitting problem; (ii) a low level of the computational complexity of the resulting linear regression procedure, comparable to those of the potential energy and dipole moment surfaces; and (iii) a competitive level of accuracy compared to the non-linear PTS model. Calculations of CH₄ PTS, with polarizabilities fitted to 9000 training set points with the energies up to 14,000 cm^-1 show an impressive level of accuracy of the linear PTS model obtained with ~1600 parameters: ~1% versus 0.3% RMSE for the non-linear vs. linear model on a test set of 1000 configurations.

Completely Computational Model Setup for Spectroscopic Techniques: The Ab Initio Molecular Dynamics Indirect Hard Modeling Approach

The spectroscopic quantification of mixture compositions usually requires pure compounds and mixtures of known compositions for calibration. Since they are not always available, methods to fill such gaps have evolved, which are, however, not generally applicable. Therefore, calibration can be extremely challenging, especially when multiple unstable species, for example, intermediates, exist in a system. This study presents a new calibration approach that uses ab initio molecular dynamics (AIMD)-simulated spectra to set up and calibrate models for the physics-based spectral analysis method indirect hard modeling (IHM). To demonstrate our approach called AIMD-IHM, we analyze Raman spectra of ternary hydrogen-bonding mixtures of acetone, methanol, and ethanol. The derived AIMD-IHM pure-component models and calibration coefficients are in good agreement with conventionally generated experimental results. The method yields compositions with prediction errors of less than 5% without any experimental calibration input. Our approach can be extended, in principle, to infrared and NMR spectroscopy and allows for the analysis of systems that were hitherto inaccessible to quantitative spectroscopic analysis.

Machine learning recognition of protein secondary structures based on two-dimensional spectroscopic descriptors

Protein secondary structure discrimination is crucial for understanding their biological function. It is not generally possible to invert spectroscopic data to yield the structure. We present a machine learning protocol which uses two-dimensional UV (2DUV) spectra as pattern recognition descriptors, aiming at automated protein secondary structure determination from spectroscopic features. Accurate secondary structure recognition is obtained for homologous (97%) and nonhomologous (91%) protein segments, randomly selected from simulated model datasets. The advantage of 2DUV descriptors over one-dimensional linear absorption and circular dichroism spectra lies in the cross-peak information that reflects interactions between local regions of the protein. Thanks to their ultrafast (∼200 fs) nature, 2DUV measurements can be used in the future to probe conformational variations in the course of protein dynamics.

A deep potential model with long-range electrostatic interactions

Machine learning models for the potential energy of multi-atomic systems, such as the deep potential (DP) model, make molecular simulations with the accuracy of quantum mechanical density functional theory possible at a cost only moderately higher than that of empirical force fields. However, the majority of these models lack explicit long-range interactions and fail to describe properties that derive from the Coulombic tail of the forces. To overcome this limitation, we extend the DP model by approximating the long-range electrostatic interaction between ions (nuclei + core electrons) and valence electrons with that of distributions of spherical Gaussian charges located at ionic and electronic sites. The latter are rigorously defined in terms of the centers of the maximally localized Wannier distributions, whose dependence on the local atomic environment is modeled accurately by a deep neural network. In the DP long-range (DPLR) model, the electrostatic energy of the Gaussian charge system is added to short-range interactions that are represented as in the standard DP model. The resulting potential energy surface is smooth and possesses analytical forces and virial. Missing effects in the standard DP scheme are recovered, improving on accuracy and predictive power. By including long-range electrostatics, DPLR correctly extrapolates to large systems the potential energy surface learned from quantum mechanical calculations on smaller systems. We illustrate the approach with three examples: the potential energy profile of the water dimer, the free energy of interaction of a water molecule with a liquid water slab, and the phonon dispersion curves of the NaCl crystal.

REANN: A PyTorch-based end-to-end multi-functional deep neural network package for molecular, reactive, and periodic systems

In this work, we present a general purpose deep neural network package for representing energies, forces, dipole moments, and polarizabilities of atomistic systems. This so-called recursively embedded atom neural network model takes advantages of both the physically inspired atomic descriptor based neural networks and the message-passing based neural networks. Implemented in the PyTorch framework, the training process is parallelized on both the central processing unit and the graphics processing unit with high efficiency and low memory in which all hyperparameters can be optimized automatically. We demonstrate the state-of-the-art accuracy, high efficiency, scalability, and universality of this package by learning not only energies (with or without forces) but also dipole moment vectors and polarizability tensors in various molecular, reactive, and periodic systems. An interface between a trained model and LAMMPs is provided for large scale molecular dynamics simulations. We hope that this open-source toolbox will allow for future method development and applications of machine learned potential energy surfaces and quantum-chemical properties of molecules, reactions, and materials.

Accurate Machine Learning Prediction of Protein Circular Dichroism Spectra with Embedded Density Descriptors

A data-driven approach to simulate circular dichroism (CD) spectra is appealing for fast protein secondary structure determination, yet the challenge of predicting electric and magnetic transition dipole moments poses a substantial barrier for the goal. To address this problem, we designed a new machine learning (ML) protocol in which ordinary pure geometry-based descriptors are replaced with alternative embedded density descriptors and electric and magnetic transition dipole moments are successfully predicted with an accuracy comparable to first-principle calculation. The ML model is able to not only simulate protein CD spectra nearly 4 orders of magnitude faster than conventional first-principle simulation but also obtain CD spectra in good agreement with experiments. Finally, we predicted a series of CD spectra of the Trp-cage protein associated with continuous changes of protein configuration along its folding path, showing the potential of our ML model for supporting real-time CD spectroscopy study of protein dynamics.

Antibodies Processed Using High Dilution Technology Distantly Change Structural Properties of IFNγ Aqueous Solution

Terahertz spectroscopy allows for the analysis of vibrations corresponding to the large-scale structural movements and collective dynamics of hydrogen-bonded water molecules. Previously, differences had been detected in the emission spectra of interferon-gamma (IFNγ) solutions surrounded by extremely diluted solutions of either IFNγ or antibodies to IFNγ without direct contact compared to a control. Here we aimed to analyse the structural properties of water in a sample of an aqueous solution of IFNγ via terahertz time-domain spectroscopy (THz-TDS). Tubes with the IFNγ solution were immersed in fluidised lactose saturated with test samples (dilutions of antibodies to IFNγ or control) and incubated at 37 °C for 1, 1.5-2, 2.5-3, or 3.5-4 h. Fluidised lactose was chosen since it is an excipient in the manufacture of drugs based on diluted antibodies to IFNγ. After incubation, spectra were recorded within a wavenumber range of 10 to 110 cm-1 with a resolution of 4 cm-1. Lactose saturated with dilutions of antibodies to IFNγ (incubated for more than 2.5 h) changed the structural properties of an IFNγ aqueous solution without direct contact compared to the control. Terahertz spectra revealed stronger intermolecular hydrogen bonds and an increase in the relaxation time of free and weakly bound water molecules. The methodology developed on the basis of THz-TDS could potentially be applied to quality control of pharmaceuticals based on extremely diluted antibodies.

Condensed Phase Water Molecular Multipole Moments from Deep Neural Network Models Trained on Ab Initio Simulation Data

Ionic solvation phenomena in liquids involve intense interactions in the inner solvation shell. For interactions beyond the first shell, the ion-solvent interaction energies result from the sum of many smaller-magnitude contributions that can still include polarization effects. Deep neural network (DNN) methods have recently found wide application in developing efficient molecular models that maintain near-quantum accuracy. Here we extend the DeePMD-kit code to produce accurate molecular multipole moments in the bulk and near interfaces. The new method is validated by comparing the DNN moments with those generated by ab initio simulations. The moments are used to compute the electrostatic potential at the center of a molecular-sized hydrophobic cavity in water. The results show that the fields produced by the DNN models are in quantitative agreement with the AIMD-derived values. These efficient methods will open the door to more accurate solvation models for large solutes such as proteins.

Machine learning of solvent effects on molecular spectra and reactions

Fast and accurate simulation of complex chemical systems in environments such as solutions is a long standing challenge in theoretical chemistry. In recent years, machine learning has extended the boundaries of quantum chemistry by providing highly accurate and efficient surrogate models of electronic structure theory, which previously have been out of reach for conventional approaches. Those models have long been restricted to closed molecular systems without accounting for environmental influences, such as external electric and magnetic fields or solvent effects. Here, we introduce the deep neural network FieldSchNet for modeling the interaction of molecules with arbitrary external fields. FieldSchNet offers access to a wealth of molecular response properties, enabling it to simulate a wide range of molecular spectra, such as infrared, Raman and nuclear magnetic resonance. Beyond that, it is able to describe implicit and explicit molecular environments, operating as a polarizable continuum model for solvation or in a quantum mechanics/molecular mechanics setup. We employ FieldSchNet to study the influence of solvent effects on molecular spectra and a Claisen rearrangement reaction. Based on these results, we use FieldSchNet to design an external environment capable of lowering the activation barrier of the rearrangement reaction significantly, demonstrating promising venues for inverse chemical design.

Gaussian Process Regression for Materials and Molecules

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

Machine Learning Force Fields

In recent years, the use of machine learning (ML) in computational chemistry has enabled numerous advances previously out of reach due to the computational complexity of traditional electronic-structure methods. One of the most promising applications is the construction of ML-based force fields (FFs), with the aim to narrow the gap between the accuracy of ab initio methods and the efficiency of classical FFs. The key idea is to learn the statistical relation between chemical structure and potential energy without relying on a preconceived notion of fixed chemical bonds or knowledge about the relevant interactions. Such universal ML approximations are in principle only limited by the quality and quantity of the reference data used to train them. This review gives an overview of applications of ML-FFs and the chemical insights that can be obtained from them. The core concepts underlying ML-FFs are described in detail, and a step-by-step guide for constructing and testing them from scratch is given. The text concludes with a discussion of the challenges that remain to be overcome by the next generation of ML-FFs.

Perspective on integrating machine learning into computational chemistry and materials science

Machine learning (ML) methods are being used in almost every conceivable area of electronic structure theory and molecular simulation. In particular, ML has become firmly established in the construction of high-dimensional interatomic potentials. Not a day goes by without another proof of principle being published on how ML methods can represent and predict quantum mechanical properties-be they observable, such as molecular polarizabilities, or not, such as atomic charges. As ML is becoming pervasive in electronic structure theory and molecular simulation, we provide an overview of how atomistic computational modeling is being transformed by the incorporation of ML approaches. From the perspective of the practitioner in the field, we assess how common workflows to predict structure, dynamics, and spectroscopy are affected by ML. Finally, we discuss how a tighter and lasting integration of ML methods with computational chemistry and materials science can be achieved and what it will mean for research practice, software development, and postgraduate training.

Phase Diagram of a Deep Potential Water Model

Using the Deep Potential methodology, we construct a model that reproduces accurately the potential energy surface of the SCAN approximation of density functional theory for water, from low temperature and pressure to about 2400 K and 50 GPa, excluding the vapor stability region. The computational efficiency of the model makes it possible to predict its phase diagram using molecular dynamics. Satisfactory overall agreement with experimental results is obtained. The fluid phases, molecular and ionic, and all the stable ice polymorphs, ordered and disordered, are predicted correctly, with the exception of ice III and XV that are stable in experiments, but metastable in the model. The evolution of the atomic dynamics upon heating, as ice VII transforms first into ice VII^{''} and then into an ionic fluid, reveals that molecular dissociation and breaking of the ice rules coexist with strong covalent fluctuations, explaining why only partial ionization was inferred in experiments.

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

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

Machine learning phase space quantum dynamics approaches

Derived from phase space expressions of the quantum Liouville theorem, equilibrium continuity dynamics is a category of trajectory-based phase space dynamics methods, which satisfies the two critical fundamental criteria: conservation of the quantum Boltzmann distribution for the thermal equilibrium system and being exact for any thermal correlation functions (even of nonlinear operators) in the classical and harmonic limits. The effective force and effective mass matrix are important elements in the equations of motion of equilibrium continuity dynamics, where only the zeroth term of an exact series expansion of the phase space propagator is involved. We introduce a machine learning approach for fitting these elements in quantum phase space, leading to a much more efficient integration of the equations of motion. Proof-of-concept applications to realistic molecules demonstrate that machine learning phase space dynamics approaches are possible as well as competent in producing reasonably accurate results with a modest computation effort.