Model Potential Energy Surfaces Research Articles

Machine learning builds full-QM precision protein force fields in seconds.

Full-quantum mechanics (QM) calculations are extraordinarily precise but difficult to apply to large systems, such as biomolecules. Motivated by the massive demand for efficient calculations for large systems at the full-QM level and by the significant advances in machine learning, we have designed a neural network-based two-body molecular fractionation with conjugate caps (NN-TMFCC) approach to accelerate the energy and atomic force calculations of proteins. The results show very high precision for the proposed NN potential energy surface models of residue-based fragments, with energy root-mean-squared errors (RMSEs) less than 1.0kcal/mol and force RMSEs less than 1.3kcal/mol/Å for both training and testing sets. The proposed NN-TMFCC method calculates the energies and atomic forces of 15 representative proteins with full-QM precision in 10-100s, which is thousands of times faster than the full-QM calculations. The computational complexity of the NN-TMFCC method is independent of the protein size and only depends on the number of residue species, which makes this method particularly suitable for rapid prediction of large systems with tens of thousands or even hundreds of thousands of times acceleration. This highly precise and efficient NN-TMFCC approach exhibits considerable potential for performing energy and force calculations, structure predictions and molecular dynamics simulations of proteins with full-QM precision.

ParAMS: Parameter Optimization for Atomistic and Molecular Simulations.

This work introduces ParAMS-a versatile Python package that aims to make parametrization workflows in computational chemistry and physics more accessible, transparent, and reproducible. We demonstrate how ParAMS facilitates the parameter optimization for potential energy surface (PES) models, which can otherwise be a tedious specialist task. Because of the package's modular structure, various functionality can be easily combined to implement a diversity of parameter optimization protocols. For example, the choice of PES model and the parameter optimization algorithm can be selected independently. An illustration of ParAMS' strengths is provided in two case studies: (i) a density functional-based tight binding (DFTB) repulsive potential for the inorganic ionic crystal ZnO and (ii) a ReaxFF force field for the simulation of organic disulfides.

Crystal Structure Prediction of Binary Alloys via Deep Potential.

Predicting crystal structure has been a challenging problem in physics and materials science for a long time. A reliable energy calculation engine combined with an efficient global search algorithm, such as particle swarm optimization algorithm or genetic algorithm, is needed to conduct crystal structure prediction. In recent years, machine learning-based interatomic potential energy surface models have been proposed, potentially allowing us to perform crystal structure prediction for systems with the accuracy of density functional theory (DFT) and the speed of empirical force fields. In this paper, we employ a previously developed Deep Potential model to predict the intermetallic compound of the aluminum–magnesium system, and find six meta-stable phases with negative or nearly zero formation energy. In particular, Mg12Al8 shows excellent ductility and Mg5Al27 has a high Young's modulus. Based on our benchmark results, we propose a relatively robust structure screening criterion that selects potentially stable structures from the Deep Potential-based convex hull and performs DFT refinement. By using this criterion, the computational cost needed to construct the convex hull with ab initio accuracy can be dramatically reduced.

Unraveling the energetic significance of chemical events in enzyme catalysis via machine-learning based regression approach

The bacterial enzyme class of β-lactamases are involved in benzylpenicillin acylation reactions, which are currently being revisited using hybrid quantum mechanical molecular mechanical (QM/MM) chain-of-states pathway optimizations. Minimum energy pathways are sampled by reoptimizing pathway geometry under different representative protein environments obtained through constrained molecular dynamics simulations. Predictive potential energy surface models in the reaction space are trained with machine-learning regression techniques. Herein, using TEM-1/benzylpenicillin acylation reaction as the model system, we introduce two model-independent criteria for delineating the energetic contributions and correlations in the predicted reaction space. Both methods are demonstrated to effectively quantify the energetic contribution of each chemical process and identify the rate limiting step of enzymatic reaction with high degrees of freedom. The consistency of the current workflow is tested under seven levels of quantum chemistry theory and three non-linear machine-learning regression models. The proposed approaches are validated to provide qualitative compliance with experimental mutagenesis studies.

Gaussian process model of 51-dimensional potential energy surface for protonated imidazole dimer.

The goal of the present work is to obtain accurate potential energy surfaces (PESs) for high-dimensional molecular systems with a small number of ab initio calculations in a system-agnostic way. We use probabilistic modeling based on Gaussian processes (GPs). We illustrate that it is possible to build an accurate GP model of a 51-dimensional PES based on 5000 randomly distributed ab initio calculations with a global accuracy of <0.2 kcal/mol. Our approach uses GP models with composite kernels designed to enhance the Bayesian information content and represents the global PES as a sum of a full-dimensional GP and several GP models for molecular fragments of lower dimensionality. We demonstrate the potency of these algorithms by constructing the global PES for the protonated imidazole dimer, a molecular system with 19 atoms. We illustrate that GP models thus constructed can extrapolate the PES from low energies (<10 000 cm-1), yielding a PES at high energies (>20 000 cm-1). This opens the prospect for new applications of GPs, such as mapping out phase transitions by extrapolation or accelerating Bayesian optimization, for high-dimensional physics and chemistry problems with a restricted number of inputs, i.e., for high-dimensional problems where obtaining training data is very difficult.

Pathways for nicotinic receptor desensitization.

Nicotinic acetylcholine receptors (AChRs) are ligand-gated ion channels that generate transient currents by binding agonists and switching rapidly between closed- and open-channel conformations. Upon sustained exposure to ACh, the cell response diminishes slowly because of desensitization, a process that shuts the channel even with agonists still bound. In liganded receptors, the main desensitization pathway is from the open-channel conformation, but after agonists dissociate the main recovery pathway is to the closed-channel conformation. In this Viewpoint, I discuss two mechanisms that can explain the selection of different pathways, a question that has puzzled the community for 60 yr. The first is based on a discrete-state model (the "prism"), in which closed, open, and desensitized conformational states interconnect directly. This model predicts that 5% of unliganded AChRs are desensitized. Different pathways are taken with versus without agonists because ligands have different energy properties (φ values) at the transition states of the desensitization and recovery reactions. The second is a potential energy surface model (the "monkey saddle"), in which the states connect indirectly at a shared transition state region. Different pathways are taken because agonists shift the position of the gating transition state relative to the point where gating and desensitization conformational trajectories intersect. Understanding desensitization pathways appears to be a problem of kinetics rather than of thermodynamics. Other aspects of the two mechanisms are considered, as are experiments that may someday distinguish them.

Deep neural network for the dielectric response of insulators

We introduce a deep neural network to model in a symmetry preserving way the environmental dependence of the centers of the electronic charge. The model learns from ab-initio density functional theory, wherein the electronic centers are uniquely assigned by the maximally localized Wannier functions. When combined with the Deep Potential model of the atomic potential energy surface, the scheme predicts the dielectric response of insulators for trajectories inaccessible to direct ab-initio simulation. The scheme is non-perturbative and can capture the response of a mutating chemical environment. We demonstrate the approach by calculating the infrared spectra of liquid water at standard conditions, and of ice under extreme pressure, when it transforms from a molecular to an ionic crystal.

Thermophysical properties of supercritical [formula omitted] from Molecular Dynamics simulations

The ability to predict thermophysical properties of molecular hydrogen with high accuracy, especially at high pressures, is crucial to design and to operate processes involving compressed hydrogen. Molecular simulations comprise an adequate tool to investigate both thermodynamic and transport properties of different molecular systems using a single potential energy surface model. Such a potential is called a force field. Here we propose a new single-site force field for pure hydrogen using a Mie potential to describe the intermolecular interactions. The proposed force field yields better predictions of thermodynamic properties when compared to other available force fields that use Lennard-Jones interaction potential. The new force field is also able to predict transport properties with reasonable accuracy.

DP-GEN: A concurrent learning platform for the generation of reliable deep learning based potential energy models

In recent years, promising deep learning based interatomic potential energy surface (PES) models have been proposed that can potentially allow us to perform molecular dynamics simulations for large scale systems with quantum accuracy. However, making these models truly reliable and practically useful is still a very non-trivial task. A key component in this task is the generation of datasets used in model training. In this paper, we introduce the Deep Potential GENerator (DP-GEN), an open-source software platform that implements the recently proposed ”on-the-fly” learning procedure (Zhang et al. 2019) and is capable of generating uniformly accurate deep learning based PES models in a way that minimizes human intervention and the computational cost for data generation and model training. DP-GEN automatically and iteratively performs three steps: exploration, labeling, and training. It supports various popular packages for these three steps: LAMMPS for exploration, Quantum Espresso, VASP, CP2K, etc. for labeling, and DeePMD-kit for training. It also allows automatic job submission and result collection on different types of machines, such as high performance clusters and cloud machines, and is adaptive to different job management tools, including Slurm, PBS, and LSF. As a concrete example, we illustrate the details of the process for generating a general-purpose PES model for Cu using DP-GEN. Program summaryProgram Title: DP-GENProgram Files doi:http://dx.doi.org/10.17632/sxybkgc5xc.1Licensing provisions: LGPLProgramming language: PythonNature of problem: Generating reliable deep learning based potential energy models with minimal human intervention and computational cost.Solution method: The concurrent learning scheme is implemented. Supports for sampling configuration space with LAMMPS, generating ab initio data with Quantum Espresso, VASP, CP2K and training potential models with DeePMD-kit are provided. Supports for different machines including workstations, high performance clusters and cloud machines are provided. Supports for job management tools including Slurm, PBS, LSF are provided.

A Method for Dimensionally Adaptive Sparse Trigonometric Interpolation of Periodic Functions

We present a method for dimensionally adaptive sparse trigonometric interpolation of multidimensional periodic functions belonging to a smoothness class of finite order. This method targets applications where periodicity must be preserved and the precise anisotropy is not known a priori. To the authors' knowledge, this is the first instance of a dimensionally adaptive sparse interpolation algorithm that uses a trigonometric interpolation basis. The motivating application behind this work is the adaptive approximation of a multi-input model for a molecular potential energy surface (PES) where each input represents an angle of rotation. Our method is based on an anisotropic quasi-optimal estimate for the decay rate of the Fourier coefficients of the model; a least-squares fit to the coefficients of the interpolant is used to estimate the anisotropy. Thus, our adaptive approximation strategy begins with a coarse isotropic interpolant, which is gradually refined using the estimated anisotropic rates. The procedure takes several iterations where ever-more accurate interpolants are used to generate ever-improving anisotropy rates. We present several numerical examples of our algorithm where the adaptive procedure successfully recovers the theoretical "best" convergence rate, including an application to a periodic PES approximation. An open-source implementation of our algorithm resides in the Tasmanian UQ library developed at Oak Ridge National Laboratory.

Equation of State of Fluid Methane from First Principles with Machine Learning Potentials.

The predictive simulation of molecular liquids requires potential energy surface (PES) models that are not only accurate but also computationally efficient enough to handle the large systems and long time scales required for reliable prediction of macroscopic properties. We present a new approach to the systematic approximation of the first-principles PES of molecular liquids using the GAP (Gaussian Approximation Potential) framework. The approach allows us to create potentials at several different levels of accuracy in reproducing the true PES and thus to determine the level of quantum chemistry that is necessary to accurately predict macroscopic properties. We test the approach by building a series of many-body potentials for liquid methane (CH4), which is difficult to model from first principles because its behavior is dominated by weak dispersion interactions with a significant many-body component. The increasing accuracy of the potentials in predicting the bulk density correlates with their fidelity to the true PES, whereas the trend with the empirical potentials tested is surprisingly the opposite. We conclude that an accurate, consistent prediction of its bulk density across wide ranges of temperature and pressure requires not only many-body dispersion but also quantum nuclear effects to be modeled accurately.

Reaction force surface for the hydrogen transfer reaction in malonaldehyde: A classical wavefront-based formulation

This paper investigates the simulation of a modified Hamilton–Jacobi equation in order to provide a classical wavefront-based formulation of reaction dynamics. Here, the wavefront is interpreted as minimizing a particular action functional. The method is rooted in the geometric optics and an eikonal equation is typically used for describing the light wave propagation. We have introduced a general formulation for reaction force surface (RFS) and a host of several force-based properties, which offer a reinvigorated understanding of the occurrence of a reaction event at molecular level. The calculation is performed on a model potential energy surface representing the hydrogen transfer reaction in malonaldehyde.

Neural network diabatization: A new ansatz for accurate high-dimensional coupled potential energy surfaces.

A new diabatization method based on artificial neural networks (ANNs) is presented, which is capable of reproducing high-quality ab initio data with excellent accuracy for use in quantum dynamics studies. The diabatic potential matrix is expanded in terms of a set of basic coupling matrices and the expansion coefficients are made geometry-dependent by the output neurons of the ANN. The ANN is trained with respect to ab initio data using a modified Marquardt-Levenberg back-propagation algorithm. Due to its setup, this approach combines the stability and straightforwardness of a standard low-order vibronic coupling model with the accuracy by the ANN, making it particularly advantageous for problems with a complicated electronic structure. This approach combines the stability and straightforwardness of a standard low-order vibronic coupling model with the accuracy by the ANN, making it particularly advantageous for problems with a complicated electronic structure. This novel ANN diabatization approach has been applied to the low-lying electronic states of NO3 as a prototypical and notoriously difficult Jahn-Teller system in which the accurate description of the very strong non-adiabatic coupling is of paramount importance. Thorough tests show that an ANN with a single hidden layer is sufficient to achieve excellent results and the use of a "deeper" layering shows no clear benefit. The newly developed diabatic ANN potential energy surface (PES) model accurately reproduces a set of more than 90 000 Multi-configuration Reference Singles and Doubles Configuration Interaction (MR-SDCI) energies for the five lowest PES sheets.

On the impossibility of localised states for molecular rotors with cyclic potentials

We discover a surprising property of an important class of molecular rotors. These rotors have one (e.g. a methyl group) or two (e.g. the planar boron rotor ) moieties that consist of identical nuclei rotating in cyclic model potential energy surfaces with equivalent potential wells (e.g. for CH, for ). The familiar semiclassical picture of this contorsion assumes that the potential wells support equivalent global minimum structures with corresponding localised wave functions being embedded in the individual potential wells. In contrast, we show that the wave functions of these rotors can never be squeezed into a single potential well, and hence, global minimum structures do not exist. Our quantum mechanical derivation describes the rotors in the frame of the proper cyclic molecular symmetry group and makes use of the spin-statistics theorem and the hypothesis of nuclear spin isomers. We show that if the identical nuclei have zero spins, then a hypothetical localised state would violate the spin-statistic theorem. Otherwise, the hypothetical localised state is ruled out as unphysical superposition of different nuclear spin isomers of the molecular rotors.

Exploring potential energy surfaces with gentlest ascent dynamics in combination with the shrinking dimer method and Newtonian dynamics

We revisit the so-called gentlest ascent dynamics reaction path model for finding saddle points of any index in multidimensional potential energy surfaces. The variational nature of the method is analyzed in detail, and an algorithm for the integration of its equations of motion is proposed based on the optimization-based shrinking dimer method. By means of three different two-dimensional model potential energy surfaces, we argue that the combination of the proposed method with Newtonian (dissipative) dynamics could lead to a practical scheme for the exhaustive exploration of potential energy landscapes.

Extension of the effective relativistic coupling by asymptotic representation (ERCAR) approach to multi-dimensional potential energy surfaces: 3D model for CH3I

The Effective Relativistic Coupling by Asymptotic Representation (ERCAR) approach is a new method developed by us over the past few years that allows for the accurate diabatic representation of a molecular Coulomb and spin-orbit Hamiltonian and yields an analytic potential energy surface (PES) model for use in quantum dynamics simulations. So far, we focused on the single one dissociation coordinate defining the asymptote for diabatic representation and corresponding to removing a single, strongly relativistic atom from the remaining fragment. In the present study, we extend this approach to multiple dimensions for the first time. To this end, a 3D PES model is developed for the methyl iodide (CH3I) system accounting for all totally symmetric coordinates (C–I stretch, CH3 umbrella, and CH3 breathing modes). The model parameters are fitted with respect to high-level ab initio reference data for the spin space (“spin-free”) states which are reproduced with very good accuracy. The ERCAR method also yields the fine structure states and energies which are not computed ab initio. This is particularly important for the 1Q1 and 3Q0 fine structure states of CH3I which form an intersection that is considered key for the photodissociation dynamics of the system. Our new model shows that this intersection is considerably curved in the 2D subspace of the C–I stretch and CH3 umbrella coordinate. This will certainly affect the complicated nonadiabatic photodissociation dynamics of CH3I. The construction of a full 9D diabatic PES model is currently in progress.

NO3 full-dimensional potential energy surfaces and ground state vibrational levels revisited

A new full-dimensional (6D) diabatic potential energy surface (PES) model is presented representing the five lowest PESs corresponding to the X̃2A2′,Ã2E″, and B̃2E′ electronic states of the nitrate radical (NO3). It is based on high-level ab initio calculations of roughly 90000 energy data over a wide range of nuclear configurations and represents the energies with a root mean-squares (rms) error of about 100 cm−1. An accurate dipole surface was developed for the X̃ state as well. The new PES model is used to re-investigate the infra-red (IR) spectrum corresponding to the electronic ground state by full dimensional quantum dynamics simulations. Vibrational eigenstates, IR transition probabilities, and isotopic shifts are computed and analyzed. Levels up to 2000 cm−1 are obtained and show good to excellent agreement with known experimental values. Some larger deviations are observed and discussed as well. The new results are in agreement with previous theoretical studies that the disputed ν3 fundamental corresponds to a frequency of roughly 1022 cm−1 and that the prominent experimental feature observed at 1492 cm−1 is due to the 3141 (e′) combination mode. Observed discrepancies in the IR intensities may be explained by coupling to the B̃ state which is also analysed by diabatic decomposition of the eigenstates.

Photodissociation of van der Waals complexes of iodine X-I2 (X = I2, C2H4) via charge-transfer state: A velocity map imaging investigation.

The photodissociation of van der Waals complexes of iodine X-I2 (X = I2, C2H4) excited via Charge-Transfer (CT) band has been studied with the velocity map imaging technique. Photodissociation of both complexes gives rise to translationally "hot" molecular iodine I2 via channels differing by kinetic energy and angular distribution of the recoil directions. These measured characteristics together with the analysis of the model potential energy surface for these complexes allow us to infer the back-electron-transfer (BET) in the CT state to be a source of observed photodissociation channels and to make conclusions on the location of conical intersections where the BET process takes place. The BET process is concluded to provide an I2 molecule in the electronic ground state with moderate vibrational excitation as well as X molecule in the electronic excited state. In the case of X = I2, the BET process converts anion I2- of the CT state into the neutral I2 in the repulsive excited electronic state which then dissociates promptly giving rise to a pair of I atoms in the fine states 2P1/2. In the case of C2H4-I2, the C2H4 molecules appear in the triplet T1 electronic state. Conical intersection for corresponding BET process becomes energetically accessible after partial twisting of C2H4+ frame in the excited CT state of complex. The C2H4(T)-I2 complex gives rise to triplet ethylene as well as singlet ethylene via the T-S conversion.

Discontinuity in Fast Dynamics at the Glass Transition of ortho-Terphenyl.

The dynamics of the molecular glass former ortho-terphenyl through the glass transition were observed with two-dimensional infrared vibrational spectroscopy measurements of spectral diffusion using the small probe molecule phenylselenocyanate. Although the slow diffusive motions were not visible on the experimental time scale, a picosecond-scale exponential relaxation was observed at temperatures from above to well below the glass transition temperature. The characteristic time scale has a smooth temperature dependence from the liquid into the glass phase, but the range of vibrational frequencies the probe samples displayed a discontinuity at the glass transition temperature. Complementary pump-probe experiments associate the observed motion with density fluctuations. The key features of the dynamics are reproduced with a simple corrugated well potential energy surface model. In addition, the temperature dependence of the homogeneous vibrational dephasing was found to have a T2 functional form, where T is the absolute temperature.

Dimension reduction in conformational analysis: a two-rotor mathematical model of amino acid diamide conformational potential energy surface

The conformational potential energy surface (PES) of a molecule provides insights into the relative stability of the possible foldamers. However, the time and space complexity of electronic structure calculations, commonly used to generate PES, increases exponentially with an increasing number of atoms. The use of mathematical functions to model the topology of conformational PES is an alternative to more computer-intensive quantum chemical calculations, but the choice and complexity of functions used are crucial in achieving more accurate results. This paper presents a method to illustrate the topology of amino acid diamide PESs through a linear combination of a Fourier series and a mixture of Gaussian functions. Results yield a significantly small error, with an average RMSE of 4.9946 kJ mol−1 for all fits, which suggest that these functions may be used to represent the topology of the PESs, with around twofold order of magnitude decrease in computational time, with respect to DFT electronic structure calculations. This study ultimately aims to provide a foundation for a framework on building polypeptide PES from individual amino acid PESs.