Sampling Of Configuration Space Research Articles

Methods for Classical-Mechanical Molecular Simulation in Chemistry: Achievements, Limitations, Perspectives.

More than a half century ago it became feasible to simulate, using classical-mechanical equations of motion, the dynamics of molecular systems on a computer. Since then classical-physical molecular simulation has become an integral part of chemical research. It is widely applied in a variety of branches of chemistry and has significantly contributed to the development of chemical knowledge. It offers understanding and interpretation of experimental results, semiquantitative predictions for measurable and nonmeasurable properties of substances, and allows the calculation of properties of molecular systems under conditions that are experimentally inaccessible. Yet, molecular simulation is built on a number of assumptions, approximations, and simplifications which limit its range of applicability and its accuracy. These concern the potential-energy function used, adequate sampling of the vast statistical-mechanical configurational space of a molecular system and the methods used to compute particular properties of chemical systems from statistical-mechanical ensembles. During the past half century various methodological ideas to improve the efficiency and accuracy of classical-physical molecular simulation have been proposed, investigated, evaluated, implemented in general simulation software or were abandoned. The latter because of fundamental flaws or, while being physically sound, computational inefficiency. Some of these methodological ideas are briefly reviewed and the most effective methods are highlighted. Limitations of classical-physical simulation are discussed and perspectives are sketched.

Comparing receptor binding properties of SARS-CoV-2 and of SARS-CoV virus by using unsupervised machine learning models

This work continues our recent molecular dynamics investigation of the three systems of the human ACE2 receptor interacting with the viral RBDs of SARS-CoV virus and two variants of SARS-CoV-2 viruses. The simulations are extended and analyzed using unsupervised machine learning models to give complementary descriptions of hidden features of the viral binding mechanism. Specifically, the principal component analysis (PCA) and the variational autoencoder (VAE) models are employed, both are classified as dimensionality reduction approaches with different focuses. The results support the molecular dynamics results that the two variants of SARS-CoV-2 bind stronger and more stable to the human ACE2 receptor than SARS-CoV virus does. Moreover, stronger bindings also affect the structure of the human receptor, making it fluctuate more, a sensitive feature which is hard to detect using standard analyses. Unexpectedly, it is found that the VAE model can learn and arrange randomly shuffled protein structures obtained from molecular dynamics in time order in the latent space representation. This result potentially has promising application in computational biomolecules. One could use this VAE model to jump forward in time during a molecular dynamics simulation, and to enhance the sampling of protein configuration space.

Collision-free Tool Motion Planning for 5-Axis CNC Machining with Toroidal Cutters

Collision detection is a crucial part of CNC machining, however, many state-of-the-art algorithms test collisions as a post-process, after the path-planning stage, or use conservative approaches that result in low machining accuracy in the neighborhood of the cutter’s contact paths. We propose a fast collision detection test that does not require a costly construction of the configuration space nor high-resolution sampling of the cutter’s axis and uses the information of the neighboring points to efficiently prune away points of the axis that cannot cause collisions. The proposed collision detection test is incorporated directly as a part of the tool motion-planning stage, enabling design of highly-accurate motions of a toroidal cutting tool along free-form geometries. We validate our algorithm on a variety of benchmark surfaces, showing that our results provide high-quality approximations with provably non-colliding motions.

Enhanced Sampling of Configuration and Path Space in a Generalized Ensemble by Shooting Point Exchange.

The computer simulation of many molecular processes is complicated by long timescales caused by rare transitions between long-lived states. Here, we propose a new approach to simulate such rare events, which combines transition path sampling with enhanced exploration of configuration space. The method relies on exchange moves between configuration and trajectory space, carried out based on a generalized ensemble. This scheme substantially enhances the efficiency of the transition path sampling simulations, particularly for systems with multiple transition channels, and yields information on thermodynamics, kinetics and reaction coordinates of molecular processes without distorting their dynamics. The method is illustrated using the isomerization of proline in the KPTP tetrapeptide.

Permutationally Invariant Networks for Enhanced Sampling (PINES): Discovery of Multimolecular and Solvent-Inclusive Collective Variables.

The typically rugged nature of molecular free-energy landscapes can frustrate efficient sampling of the thermodynamically relevant phase space due to the presence of high free-energy barriers. Enhanced sampling techniques can improve phase space exploration by accelerating sampling along particular collective variables (CVs). A number of techniques exist for the data-driven discovery of CVs parametrizing the important large-scale motions of the system. A challenge to CV discovery is learning CVs invariant to the symmetries of the molecular system, frequently rigid translation, rigid rotation, and permutational relabeling of identical particles. Of these, permutational invariance has proved a persistent challenge in frustrating the data-driven discovery of multimolecular CVs in systems of self-assembling particles and solvent-inclusive CVs for solvated systems. In this work, we integrate permutation invariant vector (PIV) featurizations with autoencoding neural networks to learn nonlinear CVs invariant to translation, rotation, and permutation and perform interleaved rounds of CV discovery and enhanced sampling to iteratively expand the sampling of configurational phase space and obtain converged CVs and free-energy landscapes. We demonstrate the permutationally invariant network for enhanced sampling (PINES) approach in applications to the self-assembly of a 13-atom argon cluster, association/dissociation of a NaCl ion pair in water, and hydrophobic collapse of a C45H92 n-pentatetracontane polymer chain. We make the approach freely available as a new module within the PLUMED2 enhanced sampling libraries.

Melting temperature prediction via first principles and deep learning

Melting is a high temperature process that requires extensive sampling of configuration space, thus making melting temperature prediction computationally very expensive and challenging. Over the past few years, I have built two methods to address this challenge, one via direct density functional theory (DFT) molecular dynamics (MD) simulations and the other via deep learning graph neural networks. The DFT approach is based on statistical analysis of small-size solid–liquid coexistence MD simulations. It eliminates the risk of metastable superheated solid in the fast-heating method, while also significantly reducing the computer cost relative to the traditional large-scale coexistence method. Being both accurate and efficient (at the speed of several days per material), it is considered as one of the best methods for direct DFT melting temperature calculation. The deep learning method is based on graph neural networks that effectively handles permutation invariance in chemical formula, which drastically improves efficiency and reduces cost. At the speed of milliseconds per material, the model is extremely fast, while being moderately accurate, especially within the composition space expanded by the dataset. I have implemented both methods into automated computer code packages, making them publicly available and free to download. The DFT and deep learning methods are highly complementary to each other, and hence they can be potentially well integrated into a framework for melting temperature prediction. I demonstrated examples of applying the methods to materials design and discovery of high-melting-point materials.

Comment on ‘Finite size effect on the existence of the liquid–vapour spinodal curve’

In a recent paper, Díaz-Herrera et al. [Mol. Phys. 122, e1989071 (2022)] have studied the condensation transition of spherical droplets in finite closed systems using large-scale Molecular Dynamics simulations. The authors find that the loci of discontinuities in the observed pressure–density isotherms do not converge to the bulk orthobaric curve, apparently at odds with results obtained previously using Monte Carlo simulations. The purpose of this comment is to point out that the Monte Carlo and Molecular Dynamics simulation results are actually mutually consistent, and the apparent differences are not related to the different sizes studied, but to the way each method implements sampling of configuration space.

High Efficiency Configuration Space Sampling -- probing the distribution of available states

Substantial acceleration of research and more efficient utilization of resources can be achieved in modelling investigated phenomena by identifying the limits of system's accessible states instead of tracing the trajectory of its evolution. The proposed strategy uses the Metropolis-Hastings Monte-Carlo sampling of the configuration space probability distribution coupled with physically-motivated prior probability distribution. We demonstrate this general idea by presenting a high performance method of generating configurations for lattice dynamics and other computational solid state physics calculations corresponding to non-zero temperatures. In contrast to the methods based on molecular dynamics, where only a small fraction of obtained data is used, the proposed scheme is distinguished by a considerably higher, reaching even 80%, acceptance ratio and much lower amount of computation required to obtain adequate sampling of the system in thermal equilibrium at non-zero temperature.

Machine learning of free energies in chemical compound space using ensemble representations: Reaching experimental uncertainty for solvation.

Free energies govern the behavior of soft and liquid matter, and improving their predictions could have a large impact on the development of drugs, electrolytes, or homogeneous catalysts. Unfortunately, it is challenging to devise an accurate description of effects governing solvation such as hydrogen-bonding, van der Waals interactions, or conformational sampling. We present a Free energy Machine Learning (FML) model applicable throughout chemical compound space and based on a representation that employs Boltzmann averages to account for an approximated sampling of configurational space. Using the FreeSolv database, FML's out-of-sample prediction errors of experimental hydration free energies decay systematically with training set size, and experimental uncertainty (0.6 kcal/mol) is reached after training on 490 molecules (80% of FreeSolv). Corresponding FML model errors are on par with state-of-the art physics based approaches. To generate the input representation for a new query compound, FML requires approximate and short molecular dynamics runs. We showcase its usefulness through analysis of solvation free energies for 116k organic molecules (all force-field compatible molecules in the QM9 database), identifying the most and least solvated systems and rediscovering quasi-linear structure-property relationships in terms of simple descriptors such as hydrogen-bond donors, number of NH or OH groups, number of oxygen atoms in hydrocarbons, and number of heavy atoms. FML's accuracy is maximal when the temperature used for the molecular dynamics simulation to generate averaged input representation samples in training is the same as for the query compounds. The sampling time for the representation converges rapidly with respect to the prediction error.

Ergodic sampling of the topological charge using the density of states

In lattice calculations, the approach to the continuum limit is hindered by the severe freezing of the topological charge, which prevents ergodic sampling in configuration space. In order to significantly reduce the autocorrelation time of the topological charge, we develop a density of states approach with a smooth constraint and use it to study SU(3) pure Yang Mills gauge theory near the continuum limit. Our algorithm relies on simulated tempering across a range of couplings, which guarantees the decorrelation of the topological charge and ergodic sampling of topological sectors. Particular emphasis is placed on testing the accuracy, efficiency and scaling properties of the method. In their most conservative interpretation, our results provide firm evidence of a sizeable reduction of the exponent z related to the growth of the autocorrelation time as a function of the inverse lattice spacing.

Improving the Accuracy of Nearest-Neighbor Classification Using Principled Construction and Stochastic Sampling of Training-Set Centroids.

A conceptually simple way to classify images is to directly compare test-set data and training-set data. The accuracy of this approach is limited by the method of comparison used, and by the extent to which the training-set data cover configuration space. Here we show that this coverage can be substantially increased using coarse-graining (replacing groups of images by their centroids) and stochastic sampling (using distinct sets of centroids in combination). We use the MNIST and Fashion-MNIST data sets to show that a principled coarse-graining algorithm can convert training images into fewer image centroids without loss of accuracy of classification of test-set images by nearest-neighbor classification. Distinct batches of centroids can be used in combination as a means of stochastically sampling configuration space, and can classify test-set data more accurately than can the unaltered training set. On the MNIST and Fashion-MNIST data sets this approach converts nearest-neighbor classification from a mid-ranking- to an upper-ranking member of the set of classical machine-learning techniques.

Path Planning for Multi-Arm Manipulators Using Deep Reinforcement Learning: Soft Actor-Critic with Hindsight Experience Replay.

Since path planning for multi-arm manipulators is a complicated high-dimensional problem, effective and fast path generation is not easy for the arbitrarily given start and goal locations of the end effector. Especially, when it comes to deep reinforcement learning-based path planning, high-dimensionality makes it difficult for existing reinforcement learning-based methods to have efficient exploration which is crucial for successful training. The recently proposed soft actor–critic (SAC) is well known to have good exploration ability due to the use of the entropy term in the objective function. Motivated by this, in this paper, a SAC-based path planning algorithm is proposed. The hindsight experience replay (HER) is also employed for sample efficiency and configuration space augmentation is used in order to deal with complicated configuration space of the multi-arms. To show the effectiveness of the proposed algorithm, both simulation and experiment results are given. By comparing with existing results, it is demonstrated that the proposed method outperforms the existing results.

Robosample: A rigid-body molecular simulation program based on robot mechanics

BackgroundCompared with all-atom molecular dynamics (MD), constrained MD methods allow for larger time steps, potentially reducing computational cost. For this reason, there has been continued interest in improving constrained MD algorithms to increase configuration space sampling in molecular simulations. MethodsHere, we introduce Robosample, a software package that implements high-performance constrained dynamics algorithms, originally developed for robotics, and applies them to simulations of biomolecular systems. As in the gMolmodel package developed by Spiridon and Minh in 2017, Robosample uses Constrained Dynamics Hamiltonian Monte Carlo (CDHMC) as a Gibbs sampling move - a type of Monte Carlo move where a subset of coordinates is allowed to change. In addition to the previously described Cartesian and torsional dynamics moves, Robosample implements spherical and cylindrical joints that can be distributed along the molecule by the user. ResultsIn alanine dipeptide simulations, the free energy surface is recovered by mixing fully flexible with torsional, cylindrical, or spherical dynamics moves. Ramachandran dynamics, where only the two key torsions are mobile, accelerate the slowest transition by an order of magnitude. We also show that simulations of a complex glycan cover significantly larger regions of the configuration space when mixed with constrained dynamics. Major conclusionsRobosample is a tool of choice for efficient conformational sampling of large biomolecules. General significanceRobosample is intended as a reliable and user-friendly simulation package for fast biomolecular sampling that does not require extensive expertise in mechanical engineering or in the statistical mechanics of reduced coordinates.

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.

Quantum Mechanics/Molecular Mechanics Density Functional Theory Simulations of the Optical Properties Fingerprinting the Ligand-Binding of Pentameric Formyl Thiophene Acetic Acid in Amyloid-β(1-42).

The binding pocket proposed by König [ Chem. Commun. 2018 , 54 , 3030 - 3033 ] for the biomarker pentameric formyl thiophene acetic acid (p-FTAA) in the fibrillar structure of amyloid-β(1-42) has been put to the test by the comparison of theoretical and experimental optical absorption and fluorescence spectra obtained in a water environment and inside the protein scaffold. The optical absorption/emission properties of this luminescent conjugated oligothiophene were studied by means of classical force field molecular dynamics simulations to account for the sampling of configuration space in conjunction with polarizable embedding time-dependent density functional theory calculations of spectra. The nuclear motions of residues in the β-sheet were found to be modest, and the time dependence of embedding parameters was shown to be negligible so that a time-independent parameter set could be derived and used for all 300 snapshots considered in the spectrum averaging. In regard to linear absorption spectra, the calculated red shift due to protein binding for the dominant S1 ← S0 transition in p-FTAA was found to be equal to 23 nm (0.17 eV), which is in excellent agreement with the corresponding experimental result of 18 nm and taken as corroborating evidence for having correctly identified the binding pocket of p-FTAA in the amyloid. The underlying mechanisms for the calculated red shift were disentangled, and it is shown that some 20 nm (0.15 eV) of the total 23 nm (0.17 eV) is associated with increased planarity of p-FTAA in the binding pocket, whereas a mere 3 nm (0.02 eV) is associated with changes in the environment. In regard to emission spectra, we demonstrate that intersystem crossing from the excited S1 state to the triplet manifold of states is a less likely event for p-FTAA in the binding pocket as compared to in the aqueous solution, and we thereby partly explain the much higher quantum yield of fluorescence for the more rigid p-FTAA in the binding pocket. Two-photon absorption in p-FTAA is shown to predominantly occur to an overall symmetric excited state and be more than twice as strong for the biomarker in the binding pocket as compared to in water. The corresponding red shift, on the other hand, is very small. Earlier experimental two-photon fluorescence imaging using p-FTAA is shown not to target the dominant two-photon state, and ways to reach a higher image quality (lower signal-to-noise ratio) are proposed in terms of tuning the laser wavelength toward the region of 600 nm or the synthesis of asymmetric ligands with S1 states that are both one- and two-photon allowed.

From ab initio data to high-dimensional potential energy surfaces: A critical overview and assessment of the development of permutationally invariant polynomial potential energy surfaces for single molecules.

The representation of high-dimensional potential energy surfaces by way of the many-body expansion and permutationally invariant polynomials has become a well-established tool for improving the resolution and extending the scope of molecular simulations. The high level of accuracy that can be attained by these potential energy functions (PEFs) is due in large part to their specificity: for each term in the many-body expansion, a species-specific training set must be generated at the desired level of theory and a number of fits attempted in order to obtain a robust and reliable PEF. In this work, we attempt to characterize the numerical aspects of the fitting problem, addressing questions which are of simultaneous practical and fundamental importance. These include concrete illustrations of the nonconvexity of the problem, the ill-conditionedness of the linear system to be solved and possible need for regularization, the sensitivity of the solutions to the characteristics of the training set, and limitations of the approach with respect to accuracy and the types of molecules that can be treated. In addition, we introduce a general approach to the generation of training set configurations based on the familiar harmonic approximation and evaluate the possible benefits to the use of quasirandom sequences for sampling configuration space in this context. Using sulfate as a case study, the findings are largely generalizable and expected to ultimately facilitate the efficient development of PIP-based many-body PEFs for general systems via automation.

Machine Learning Stability and Bandgaps of Lead‐Free Perovskites for Photovoltaics

AbstractCompositional engineering of perovskites has enabled the precise control of material properties required for their envisioned applications in photovoltaics. However, challenges remain to address efficiency, stability, and toxicity simultaneously. Mixed lead‐free and inorganic perovskites have recently demonstrated potential for resolving such issues but their composition space is gigantic, making it difficult to discover promising candidates even using high‐throughput methods. A machine learning approach employing a generalized element‐agnostic fingerprint is shown to rapidly and accurately predict key properties using a new database of 344 perovskites generated with density functional theory. Bandgap, formation energy, and convex hull distance are predicted using validation subsets to within 146 meV, 15 meV per atom, and 11 meV per atom, respectively. The resulting model is used to predict trends in entirely different chemical spaces, and perform rapid composition and configuration space sampling without the need for expensive ab initio simulations.

Isotope effects in liquid water via deep potential molecular dynamics

A comprehensive microscopic understanding of ambient liquid water is a major challenge for ab initio simulations as it simultaneously requires an accurate quantum mechanical description of the underlying potential energy surface (PES) as well as extensive sampling of configuration space. Due to the presence of light atoms (e.g. or ), nuclear quantum fluctuations lead to observable changes in the structural properties of liquid water (e.g. isotope effects), and therefore provide yet another challenge for ab initio approaches. In this work, we demonstrate that the combination of dispersion-inclusive hybrid density functional theory (DFT), the Feynman discretised path-integral (PI) approach, and machine learning (ML) constitutes a versatile ab initio based framework that enables extensive sampling of both thermal and nuclear quantum fluctuations on a quite accurate underlying PES. In particular, we employ the recently developed deep potential molecular dynamics (DPMD) model – a neural-network representation of the ab initio PES – in conjunction with a PI approach based on the generalised Langevin equation (PIGLET) to investigate how isotope effects influence the structural properties of ambient liquid and . Through a detailed analysis of the interference differential cross sections as well as several radial and angular distribution functions, we demonstrate that this approach can furnish a semi-quantitative prediction of these subtle isotope effects.

Redox Potentials of Small Inorganic Radicals and Hexa-Aquo Complexes of First-Row Transition Metals in Water: A DFT Study Based on the Grand Canonical Ensemble.

The potentials of redox systems involving nitrogen, oxygen, and metal ions of the first-row transition series have been computed according to the general approach of the grand canonical ensemble, which leads to the equilibrium value of the reduction potential via a (complete) sampling of configuration space at a given temperature. The approach is a single configuration approach in the sense that identical molecular structures are sampled for both the oxidized and reduced species considered in water solution. In this study, the solute and a cluster of 11-12 water molecules are treated explicitly at the same level of theory and embedded in a continuum solvent. The molecular energies are computed in the framework of the density functional theory. Our approach is basically different from the approach based on the ThermoDynamic Cycle involving gas-phase calculations of the electron affinity of the oxidized species, corrected by the differential hydration energy (obtained from continuum solvent models only) between oxidized and reduced forms. The calculated redox potentials are in agreement with the available experimental data much closer than other results so far presented in the literature. Our results are very satisfactory also in the case of the 3+/2+ redox states of the first-row transition metals, i.e., systems with a high positive charge for which enhanced effects of the solvent are expected.

Dual approach for effective potentials that accurately model structure and energetics.

Because they eliminate unnecessary degrees of freedom, coarse-grained (CG) models enable studies of phenomena that are intractable with more detailed models. For the same reason, the effective potentials that govern CG degrees of freedom incorporate entropic contributions from the eliminated degrees of freedom. Consequently, these effective potentials demonstrate limited transferability and provide a poor estimate of atomic energetics. Here, we propose a simple dual-potential approach that combines "structure-based" and "energy-based" variational principles to determine effective potentials that model free energies and potential energies, respectively, as a function of the CG configuration. We demonstrate this approach for 1-site CG models of water and methanol. We accurately sample configuration space by performing simulations with the structure-based potential. We accurately estimate average atomic energies by postprocessing the sampled configurations with the energy-based potential. Finally, the difference between the two potentials predicts a qualitatively accurate estimate for the temperature dependence of the structure-based potential.