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Molecular dynamics simulations offer detailed insights into atomic motions but face timescale limitations. Enhanced sampling methods have addressed these challenges but even with machine learning, they often rely on pre-selected expert-based features. In this work, we present the Graph Neural Network-State Predictive Information Bottleneck (GNN-SPIB) framework, which combines graph neural networks and the State Predictive Information Bottleneck to automatically learn low-dimensional representations directly from atomic coordinates. Tested on three benchmark systems, our approach predicts essential structural, thermodynamic and kinetic information for slow processes, demonstrating robustness across diverse systems. The method shows promise for complex systems, enabling effective enhanced sampling without requiring pre-defined reaction coordinates or input features.

The recent surge in Generative Artificial Intelligence (AI) has introduced exciting possibilities for computational chemistry. Generative AI methods have made significant progress in sampling molecular structures across chemical species, developing force fields, and speeding up simulations. This Perspective offers a structured overview, beginning with the fundamental theoretical concepts in both Generative AI and computational chemistry. It then covers widely used Generative AI methods, including autoencoders, generative adversarial networks, reinforcement learning, flow models and language models, and highlights their selected applications in diverse areas including force field development, and protein/RNA structure prediction. A key focus is on the challenges these methods face before they become truly predictive, particularly in predicting emergent chemical phenomena. We believe that the ultimate goal of a simulation method or theory is to predict phenomena not seen before, and that Generative AI should be subject to these same standards before it is deemed useful for chemistry. We suggest that to overcome these challenges, future AI models need to integrate core chemical principles, especially from statistical mechanics.

The weighted ensemble (WE) method stands out as a widely used segment-based sampling technique renowned for its rigorous treatment of kinetics. The WE framework typically involves initially mapping the configuration space onto a low-dimensional collective variable (CV) space and then partitioning it into bins. The efficacy of WE simulations heavily depends on the selection of CVs and binning schemes. The recently proposed State Predictive Information Bottleneck (SPIB) method has emerged as a promising tool for automatically constructing CVs from data and guiding enhanced sampling through an iterative manner. In this work, we advance this data-driven pipeline by incorporating prior expert knowledge. Our hybrid approach combines SPIB-learned CVs to enhance sampling in explored regions with expert-based CVs to guide exploration in regions of interest, synergizing the strengths of both methods. Through benchmarking on alanine dipeptide and chignoin systems, we demonstrate that our hybrid approach effectively guides WE simulations to sample states of interest, and reduces run-to-run variances. Moreover, our integration of the SPIB model also enhances the analysis and interpretation of WE simulation data by effectively identifying metastable states and pathways, and offering direct visualization of dynamics.

In this study, we present a graph neural network-based learning approach using an autoencoder setup to derive low-dimensional variables from features observed in experimental crystal structures. These variables are then biased in enhanced sampling to observe state-to-state transitions and reliable thermodynamic weights. Our approach uses simple convolution and pooling methods. To verify the effectiveness of our protocol, we examined the nucleation of various allotropes and polymorphs of iron and glycine from their molten states. Our graph latent variables when biased in well-tempered metadynamics consistently show transitions between states and achieve accurate free energy calculations in agreement with experiments, both of which are indicators of dependable sampling. This underscores the strength and promise of our graph neural net variables for improved sampling. The protocol shown here should be applicable for other systems and with other sampling methods.

Ligand unbinding is mediated by the free energy change, which has intertwined contributions from both energy and entropy. It is important but not easy to quantify their individual contributions. We model hydrophobic ligand unbinding for two systems, a methane particle and a C60 fullerene, both unbinding from hydrophobic pockets in all-atom water. By using a modified deep learning framework, we learn a thermodynamically optimized reaction coordinate to describe hydrophobic ligand dissociation for both systems. Interpretation of these reaction coordinates reveals the roles of entropic and enthalpic forces as ligand and pocket sizes change. Irrespective of the contrasting roles of energy and entropy, we also find that for both the systems the transition from the bound to unbound states is driven primarily by solvation of the pocket and ligand, independent of ligand size. Our framework thus gives useful thermodynamic insight into hydrophobic ligand dissociation problems that are otherwise difficult to glean., Comment: 27 pages; 5 figures

Kinases compose one of the largest fractions of the human proteome, and their misfunction is implicated in many diseases, in particular cancers. The ubiquitousness and structural similarities of kinases makes specific and effective drug design difficult. In particular, conformational variability due to the evolutionarily conserved DFG motif adopting in and out conformations and the relative stabilities thereof are key in structure-based drug design for ATP competitive drugs. These relative conformational stabilities are extremely sensitive to small changes in sequence, and provide an important problem for sampling method development. Since the invention of AlphaFold2, the world of structure-based drug design has noticably changed. In spite of it being limited to crystal-like structure prediction, several methods have also leveraged its underlying architecture to improve dynamics and enhanced sampling of conformational ensembles, including AlphaFold2-RAVE. Here, we extend AlphaFold2-RAVE and apply it to a set of kinases: the wild type DDR1 sequence and three mutants with single point mutations that are known to behave drastically differently. We show that AlphaFold2-RAVE is able to efficiently recover the changes in relative stability using transferable learnt order parameters and potentials, thereby supplementing AlphaFold2 as a tool for exploration of Boltzmann-weighted protein conformations.

Phase transitions are ubiquitous across life, yet hard to quantify and describe accurately. In this work, we develop an approach for characterizing generic attributes of phase transitions from very limited observations made deep within different phases' domains of stability. Our approach is called Thermodynamic Maps, which combines statistical mechanics and molecular simulations with score-based generative models. Thermodynamic Maps enable learning the temperature dependence of arbitrary thermodynamic observables across a wide range of temperatures. We show its usefulness by calculating phase transition attributes such as melting temperature, temperature-dependent heat capacities, and critical exponents. For instance, we demonstrate the ability of thermodynamic maps to infer the ferromagnetic phase transition of the Ising model, including temperature-dependent heat capacity and critical exponents, despite never having seen samples from the transition region. In addition, we efficiently characterize the temperature-dependent conformational ensemble and compute melting curves of the two RNA systems GCAA tetraloop and HIV-TAR, which are notoriously hard to sample due to glassy-like landscapes.

Understanding nucleation from aqueous solutions is of fundamental importance in a multitude of fields, ranging from materials science to biophysics. The complex solvent-mediated interactions in aqueous solutions hamper the development of a simple physical picture elucidating the roles of different interactions in nucleation processes. In this work we make use of three complementary techniques to disentangle the role played by short and long-range interactions in solvent mediated nucleation. Specifically, the first approach we utilize is the local molecular field (LMF) theory to renormalize long-range Coulomb electrostatics. Secondly, we use well-tempered metadynamics to speed up rare events governed by short-range interactions. Thirdly, deep learning-based State Predictive Information Bottleneck approach is employed in analyzing the reaction coordinate of the nucleation processes obtained from LMF treatment coupled with well-tempered metadynamics. We find that the two-step nucleation mechanism can largely be captured by the short-range interactions, while the long-range interactions further contribute to the stability of the primary crystal state at ambient conditions. Furthermore, by analyzing the reaction coordinate obtained from combined LMF-metadynamics treatment, we discern the fluctuations on different time scales, highlighting the need for long-range interactions when accounting for metastability.

Molecular dynamics (MD) enables the study of physical systems with excellent spatiotemporal resolution but suffers from severe time-scale limitations. To address this, enhanced sampling methods have been developed to improve exploration of configurational space. However, implementing these is challenging and requires domain expertise. In recent years, integration of machine learning (ML) techniques in different domains has shown promise, prompting their adoption in enhanced sampling as well. Although ML is often employed in various fields primarily due to its data-driven nature, its integration with enhanced sampling is more natural with many common underlying synergies. This review explores the merging of ML and enhanced MD by presenting different shared viewpoints. It offers a comprehensive overview of this rapidly evolving field, which can be difficult to stay updated on. We highlight successful strategies like dimensionality reduction, reinforcement learning, and flow-based methods. Finally, we discuss open problems at the exciting ML-enhanced MD interface., Comment: Submitted as invited article to Annual Review of Physical Chemistry vol 75; updated formatting issues

With the advent of faster computer processors and especially graphics processing units (GPUs) over the last few decades, the use of data-intensive machine learning (ML) and artificial intelligence (AI) has increased greatly, and the study of crystal nucleation has been one of the beneficiaries. In this review, we outline how ML and AI have been applied to address four outstanding difficulties of crystal nucleation: how to discover better reaction coordinates (RCs) for describing accurately non-classical nucleation situations; the development of more accurate force fields for describing the nucleation of multiple polymorphs or phases for a single system; more robust identification methods for determining crystal phases and structures; and as a method to yield improved course-grained models for studying nucleation., Comment: 15 pages; 1 figure

Crystal nucleation is relevant across the domains of fundamental and applied sciences. However, in many cases its mechanism remains unclear due to a lack of temporal or spatial resolution. To gain insights to the molecular details of nucleation, some form of molecular dynamics simulations is typically performed; these simulations, in turn, are limited by their ability to run long enough to sample the nucleation event thoroughly. To overcome the timescale limits in typical molecular dynamics simulations in a manner free of prior human bias, here we employ the machine learning augmented molecular dynamics framework ``Reweighted Autoencoded Variational Bayes for enhanced sampling (RAVE)". We study two molecular systems, urea and glycine in explicit all-atom water, due to their enrichment in polymorphic structures and common utility in commercial applications. From our simulations, we observe multiple back-and-forth liquid-solid transitions of different polymorphs and from these trajectories calculate the polymorph stability relative to the dissolved liquid state. We further observe that the obtained reaction coordinates and transitions are highly non-classical., Comment: 12 pages, 7 figures

While representation learning has been central to the rise of machine learning and artificial intelligence, a key problem remains in making the learned representations meaningful. For this, the typical approach is to regularize the learned representation through prior probability distributions. However, such priors are usually unavailable or are ad hoc. To deal with this, recent efforts have shifted towards leveraging the insights from physical principles to guide the learning process. In this spirit, we propose a purely dynamics-constrained representation learning framework. Instead of relying on predefined probabilities, we restrict the latent representation to follow overdamped Langevin dynamics with a learnable transition density - a prior driven by statistical mechanics. We show this is a more natural constraint for representation learning in stochastic dynamical systems, with the crucial ability to uniquely identify the ground truth representation. We validate our framework for different systems including a real-world fluorescent DNA movie dataset. We show that our algorithm can uniquely identify orthogonal, isometric and meaningful latent representations.

The study of phenomena such as protein folding and conformational changes in molecules is a central theme in chemical physics. Molecular dynamics (MD) simulation is the primary tool for the study of transition processes in biomolecules, but it is hampered by a huge timescale gap between the processes of interest and atomic vibrations which dictate the time step size. Therefore, it is imperative to combine MD simulations with other techniques in order to quantify the transition processes taking place on large timescales. In this work, the diffusion map with Mahalanobis kernel, a meshless approach for approximating the Backward Kolmogorov Operator (BKO) in collective variables, is upgraded to incorporate standard enhanced sampling techniques such as metadynamics. The resulting algorithm, which we call the "target measure Mahalanobis diffusion map" (tm-mmap), is suitable for a moderate number of collective variables in which one can approximate the diffusion tensor and free energy. Imposing appropriate boundary conditions allows use of the approximated BKO to solve for the committor function and utilization of transition path theory to find the reactive current delineating the transition channels and the transition rate. The proposed algorithm, tm-mmap, is tested on the two-dimensional Moro-Cardin two-well system with position-dependent diffusion coefficient and on alanine dipeptide in two collective variables where the committor, the reactive current, and the transition rate are compared to those computed by the finite element method (FEM). Finally, tm-mmap is applied to alanine dipeptide in four collective variables where the use of finite elements is infeasible., Comment: Restructured introduction, improved explanation of key algorithms and formulas (Section II.C and III.B,C). Streamlined presentation and proof of Theorem 1

In recent years, predictive machine learning methods have gained prominence in various scientific domains. However, due to their black-box nature, it is essential to establish trust in these models before accepting them as accurate. One promising strategy for assigning trust involves employing explanation techniques that elucidate the rationale behind a black-box model's predictions in a manner that humans can understand. However, assessing the degree of human interpretability of the rationale generated by such methods is a nontrivial challenge. In this work, we introduce interpretation entropy as a universal solution for assessing the degree of human interpretability associated with any linear model. Using this concept and drawing inspiration from classical thermodynamics, we present Thermodynamics-inspired Explainable Representations of AI and other black-box Paradigms (TERP), a method for generating accurate, and human-interpretable explanations for black-box predictions in a model-agnostic manner. To demonstrate the wide-ranging applicability of TERP, we successfully employ it to explain various black-box model architectures, including deep learning Autoencoders, Recurrent Neural Networks, and Convolutional Neural Networks, across diverse domains such as molecular simulations, text, and image classification., Comment: revised theory and examples

An effective implementation of enhanced sampling algorithms for molecular dynamics simulations requires a priori knowledge of the approximate reaction coordinate describing the relevant mechanisms in the system. Here we demonstrate how the artificial intelligence based recent State Predictive Information Bottleneck (SPIB) approach can learn such a reaction coordinate as a deep neural network even from under-sampled trajectories. We demonstrate its usefulness by achieving more than 40 magnitudes of acceleration in simulating two test-piece biophysical systems through well-tempered metadynamics performed by biasing along the SPIB learned reaction coordinate. These include left- to right- handed chirality transitions in a synthetic protein (Aib)_9, and permeation of a small, asymmetric molecule benzoic acid through a synthetic, symmetric phospholipid bilayer. In addition to significantly accelerating the dynamics and achieving back-and-forth movement between different metastable states, the SPIB based reaction coordinate gives mechanistic insight into the processes driving these two important problems.

We study NaCl ion-pair dissociation in a dilute aqueous solution using computer simulations both for the full system with long range Coulomb interactions and for a well chosen reference system with short range intermolecular interactions. Analyzing results using concepts from Local Molecular Field (LMF) theory and the recently proposed AI-based analysis tool "State predictive information bottleneck" (SPIB) we show that the system with short range interactions can accurately reproduce the transition rate for the dissociation process, the dynamics for moving between the underlying metastable states, and the transition state ensemble. Contributions from long range interactions can be largely neglected for these processes because long range forces from the direct interionic Coulomb interactions are almost completely canceled ($>90\%$) by those from solvent interactions over the length scale where the transition takes place. Thus for this important monovalent ion-pair system, short range forces alone are able to capture detailed consequences of the collective solvent motion, allowing the use of physically suggestive and computationally efficient short range models for the disassociation event. We believe that the framework here should be applicable to disentangling mechanisms for more complex processes such as multivalent ion disassociation, where previous work has suggested that long range contributions may be more important.

Understanding the driving forces behind the nucleation of different polymorphs is of great importance for material sciences and the pharmaceutical industry. This includes understanding the reaction coordinate that governs the nucleation process as well as correctly calculating the relative free energies of different polymorphs. Here we demonstrate, for the prototypical case of urea nucleation from melt, how one can learn such a 1-dimensional reaction coordinate as a function of pre-specified order parameters, and use it to perform efficient biased all-atom molecular dynamics simulations. The reaction coordinate is learnt as a function of generic thermodynamic and structural order parameters using the "Spectral Gap Optimization of Order Parameters (SGOOP)" approach [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. (2016)], and is biased using well-tempered metadynamics simulations. The reaction coordinate gives insight into the role played by different structural and thermodynamics order parameters, and the biased simulations obtain accurate relative free energies for different polymorphs. This includes accurate prediction of the approximate pressure at which urea undergoes a phase transition and one of the metastable polymorphs becomes the most stable conformation. We believe the ideas demonstrated in thus work will facilitate efficient sampling of nucleation in complex, generic systems.

Using simulations or experiments performed at some set of temperatures to learn about the physics or chemistry at some other arbitrary temperature is a problem of immense practical and theoretical relevance. Here we develop a framework based on statistical mechanics and generative Artificial Intelligence that allows solving this problem. Specifically, we work with denoising diffusion probabilistic models, and show how these models in combination with replica exchange molecular dynamics achieve superior sampling of the biomolecular energy landscape at temperatures that were never even simulated without assuming any particular slow degrees of freedom. The key idea is to treat the temperature as a fluctuating random variable and not a control parameter as is usually done. This allows us to directly sample from the joint probability distribution in configuration and temperature space. The results here are demonstrated for a chirally symmetric peptide and single-strand ribonucleic acid undergoing conformational transitions in all-atom water. We demonstrate how we can discover transition states and metastable states that were previously unseen at the temperature of interest, and even bypass the need to perform further simulations for wide range of temperatures. At the same time, any unphysical states are easily identifiable through very low Boltzmann weights. The procedure while shown here for a class of molecular simulations should be more generally applicable to mixing information across simulations and experiments with varying control parameters., Comment: Added new system (RNA nucleotide) and more detailed analysis including comparison with direct reweighting

Understanding kinetics including reaction pathways and associated transition rates is an important yet difficult problem in numerous chemical and biological systems especially in situations with multiple competing pathways. When these high-dimensional systems are projected on low-dimensional coordinates, which are often needed for enhanced sampling or for interpretation of simulations and experiments, one can end up losing the kinetic connectivity of the underlying high-dimensional landscape. Thus in the low-dimensional projection metastable states might appear closer or further than they actually are. To deal with this issue, in this work we develop a formalism that learns a multi-dimensional yet minimally complex reaction coordinate (RC) for generic high-dimensional systems. When projected along this RC, all possible kinetically relevant pathways can be demarcated and the true high-dimensional connectivity is maintained. One of the defining attributes of our method lies in that it can work on long unbiased simulations as well as biased simulations often needed for rare event systems. We demonstrate the utility of the method by studying a range of model systems including conformational transitions in a small peptide Ace-Ala$_3$-Nme, where we show how two-dimensional and three-dimensional reaction coordinate found by our previously published spectral gap optimization method "SGOOP" [P. Tiwary and B. J. Berne, Proc. Natl. Acad. Sci. 113, 2839 (2016)] can capture the kinetics for 23 and all 28 out of the 28 dominant state-to-state transitions respectively., Comment: 10 pages, 4 figures, 2 tables

The ability to make sense of the massive amounts of high-dimensional data generated from molecular dynamics (MD) simulations is heavily dependent on the knowledge of a low dimensional manifold (parameterized by a reaction coordinate or RC) that typically distinguishes between relevant metastable states and which captures the relevant slow dynamics of interest. Methods based on machine learning and artificial intelligence have been proposed over the years to deal with learning such low-dimensional manifolds, but they are often criticized for a disconnect from more traditional and physically interpretable approaches. To deal with such concerns, in this work, we propose a deep learning based State Predictive Information Bottleneck (SPIB) approach to learn the RC from high dimensional molecular simulation trajectories. We demonstrate analytically and numerically how the RC learnt in this approach is deeply connected to the committor in chemical physics, and can be used to accurately identify transition states. A crucial hyperparameter in this approach is the time-delay, or how far into the future the algorithm should make predictions about. Through careful comparisons for benchmark systems, we demonstrate that this hyperparameter choice gives useful control over how coarse-grained we want the metastable state classification of the system to be. We thus believe that this work represents a step forward in systematic application of deep learning based ideas to molecular simulations in a way that bridges the gap between artificial intelligence and traditional chemical physics., Comment: 11 pages, 13 figures

Recurrent neural networks (RNNs) have led to breakthroughs in natural language processing and speech recognition, wherein hundreds of millions of people use such tools on a daily basis through smartphones, email servers and other avenues. In this work, we show such RNNs, specifically Long Short-Term Memory (LSTM) neural networks can also be applied to capturing the temporal evolution of typical trajectories arising in chemical and biological physics. Specifically, we use a character-level language model based on LSTM. This learns a probabilistic model from 1-dimensional stochastic trajectories generated from molecular dynamics simulations of a higher dimensional system. We show that the model can not only capture the Boltzmann statistics of the system but it also reproduce kinetics at a large spectrum of timescales. We demonstrate how the embedding layer, introduced originally for representing the contextual meaning of words or characters, exhibits here a nontrivial connectivity between different metastable states in the underlying physical system. We demonstrate the reliability of our model and interpretations through different benchmark systems and a single molecule force spectroscopy trajectory for multi-state riboswitch. We anticipate that our work represents a stepping stone in the understanding and use of RNNs for modeling and predicting dynamics of complex stochastic molecular systems.

In this work, we revisit our recent iterative machine learning (ML) -- molecular dynamics (MD) technique "Reweighted autoencoded variational Bayes for enhanced sampling (RAVE)" (Ribeiro, Bravo, Wang, Tiwary, J. Chem. Phys. 149 072301 (2018) and Wang, Ribeiro, Tiwary, Nature Commun. 10 3573 (2019)) and analyze as well as formalize some of its approximations. These including: (a) the choice of a predictive time-delay, or how far into the future should the ML try to predict the state of a given system output from MD, and (b) for short time-delays, how much of an error is made in approximating the biased propagator for the dynamics as the unbiased propagator. We demonstrate through a master equation framework as to why the exact choice of time-delay is irrelevant as long as a small non-zero value is adopted. We also derive a correction to reweight the biased propagator, and somewhat to our dissatisfaction but also to our reassurance, find that it barely makes a difference to the intuitive picture we had previously derived and used.

Here we propose the Reweighted Autoencoded Variational Bayes for Enhanced Sampling (RAVE) method, a new iterative scheme that uses the deep learning framework of variational autoencoders to enhance sampling in molecular simulations. RAVE involves iterations between molecular simulations and deep learning in order to produce an increasingly accurate probability distribution along a low-dimensional latent space that captures the key features of the molecular simulation trajectory. Using the Kullback-Leibler divergence between this latent space distribution and the distribution of various trial reaction coordinates sampled from the molecular simulation, RAVE determines an optimum, yet nonetheless physically interpretable, reaction coordinate and optimum probability distribution. Both then directly serve as the biasing protocol for a new biased simulation, which is once again fed into the deep learning module with appropriate weights accounting for the bias, the procedure continuing until estimates of desirable thermodynamic observables are converged. Unlike recent methods using deep learning for enhanced sampling purposes, RAVE stands out in that (a) it naturally produces a physically interpretable reaction coordinate, (b) is independent of existing enhanced sampling protocols to enhance the fluctuations along the latent space identified via deep learning, and (c) it provides the ability to easily filter out spurious solutions learned by the deep learning procedure. The usefulness and reliability of RAVE is demonstrated by applying it to model potentials of increasing complexity, including computation of the binding free energy profile for a hydrophobic ligand-substrate system in explicit water with dissociation time of more than three minutes, in computer time at least twenty times less than that needed for umbrella sampling or metadynamics.

We consider a range of model potentials with metastable states undergoing molecular dynamics coupled to a thermal bath in the high friction regime, and consider how the optimal reaction coordinate depends on the diffusion anisotropy. For this we use our recently proposed method 'Spectral gap optimization of order parameters (SGOOP)' (Tiwary and Berne, Proc. Natl. Acad. Sci. 113 2839 2016). We show how available information about dynamical observables in addition to static information can be incorporated into SGOOP, which can then be used to accurately determine the 'best' reaction coordinate for arbitrary anisotropies. We compare our results with transmission coefficient calculations and published benchmarks where applicable or available respectively.

Metadynamics is a popular enhanced sampling scheme wherein by periodic application of a repulsive bias, one can surmount high free energy barriers and explore complex landscapes. Recently metadynamics was shown to be mathematically well founded, in the sense that the biasing procedure is guaranteed to converge to the true free energy surface in the long time limit irrespective of the precise choice of biasing parameters. A differential equation governing the post-transient convergence behavior of metadynamics was also derived. In this short communication, we revisit this differential equation, expressing it in a convenient and elegant Riccati-like form. A perturbative solution scheme is then developed for solving this differential equation, which is valid for any generic biasing kernel. The solution clearly demonstrates the robustness of metadynamics to choice of biasing parameters and gives further confidence in the widely used method., Comment: submitted to J. Chem. Phys

In modern day simulations of many-body systems much of the computational complexity is shifted to the identification of slowly changing molecular order parameters called collective variables (CV) or reaction coordinates. A vast array of enhanced sampling methods are based on the identification and biasing of these low-dimensional order parameters, whose fluctuations are important in driving rare events of interest. Here describe a new algorithm for finding optimal low-dimensional collective variables for use in enhanced sampling biasing methods like umbrella sampling, metadynamics and related methods, when limited prior static and dynamic information is known about the system, and a much larger set of candidate CVs is specified. The algorithm involves estimating the best combination of these candidate CVs, as quantified by a maximum path entropy estimate of the spectral gap for dynamics viewed as a function of that CV. Through multiple practical examples, we show how this post-processing procedure can lead to optimization of CV and several orders of magnitude improvement in the convergence of the free energy calculated through metadynamics, essentially giving the ability to extract useful information even from unsuccessful metadynamics runs., Comment: 7 pages, 4 figures; corrected missing figure number and added a reference

Condensation of a liquid droplet from a supersaturated vapour phase is initiated by a prototypical nucleation event. As such it is challenging to compute its rate from atomistic molecular dynamics simulations. In fact at realistic supersaturation conditions condensation occurs on time scales that far exceed what can be reached with conventional molecular dynamics methods. Another known problem in this context is the distortion of the free energy profile associated to nucleation due to the small, finite size of typical simulation boxes. In this work the problem of time scale is addressed with a recently developed enhanced sampling method while contextually correcting for finite size effects. We demonstrate our approach by studying the condensation of argon, and showing that characteristic nucleation times of the order of magnitude of hours can be reliably calculated, approaching realistic supersaturation conditions, thus bridging the gap between what standard molecular dynamics simulations can do and real physical systems., Comment: 9 pages, 7 figures, additional figures and data provided as supplementary information. Submitted to the Journal of Chemical Physiscs

We propose a new method to obtain kinetic properties of infrequent events from molecular dynamics simulation. The procedure employs a recently introduced variational approach [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] to construct a bias potential as a function of several collective variables that is designed to flood only the associated free energy surface up to a predefined level. The resulting bias potential effectively accelerates transitions between metastable free energy minima while ensuring bias-free transition states, thus allowing accurate kinetic rates to be obtained. We test the method on a few illustrative systems for which we obtain an order of magnitude improvement in efficiency relative to previous approaches, and several orders of magnitude relative to unbiased molecular dynamics. We expect an even larger improvement in more complex systems. This and the ability of the variational approach to deal efficiently with a large number of collective variables will greatly enhance the scope of these calculations. This work is a vindication of the potential that the variational principle has if applied in innovative ways, Comment: 6 pages, 3 figures, Supplemental Information

Metadynamics is a commonly used and successful enhanced sampling method. By the introduction of a history dependent bias which depends on a restricted number of collective variables(CVs) it can explore complex free energy surfaces characterized by several metastable states separated by large free energy barriers. Here we extend its scope by introducing a simple yet powerful method for calculating the rates of transition between different metastable states. The method does not rely on a previous knowledge of the transition states or reaction co-ordinates, as long as CVs are known that can distinguish between the various stable minima in free energy space. We demonstrate that our method recovers the correct escape rates out of these stable states and also preserves the correct sequence of state-to-state transitions, with minimal extra computational effort needed over ordinary metadynamics. We apply the formalism to three different problems and in each case find excellent agreement with the results of long unbiased molecular dynamics runs., Comment: 4 pages, 2 figures, 1 supplemental file

We present a new method, called SISYPHUS (Stochastic Iterations to Strengthen Yield of Path Hopping over Upper States), for extending accessible time-scales in atomistic simulations. The method proceeds by separating phase space into basins, and transition regions between the basins based on a general collective variable (CV) criterion. The transition regions are treated via traditional molecular dynamics (MD) while Monte Carlo (MC) methods are used to (i) estimate the expected time spent in each basin and (ii) thermalize the system between two MD episodes. In particular, an efficient adiabatic switching based scheme is used to estimate the time spent inside the basins. The method offers various advantages over existing approaches in terms of (i) providing an accurate real time scale, (ii) avoiding reliance on harmonic transition state theory and (iii) avoiding the need to enumerate all possible transition events. Applications of SISYPHUS to low temperature vacancy diffusion in BCC Ta and adatom island ripening in FCC Al are presented. A new CV appropriate for such condensed phases, especially for transitions involving collective motions of several atoms, is also introduced., Comment: 5 pages, 4 figures, see ancillary material as well (includes 6 movies and a PDF document)

We use our recently proposed accelerated dynamics algorithm (Tiwary & van de Walle, 2011) to calculate temperature and stress dependence of activation free energy for surface nucleation of dislocations in pristine Gold nanopillars under realistic loads. While maintaining fully atomistic resolution, we achieve the fraction of a second time-scale regime. We find that the activation free energy depends significantly on the driving force (stress or strain) and temperature, leading to very high activation entropies. We also perform compression tests on Gold nanopillars for strain rates varying between 7 orders of magnitudes, reaching as low as 10^3/s. Our calculations show the quantitative effects on the yield point of unrealistic strain-rate Molecular Dynamics calculations: we find that while the failure mechanism for <001> compression of Gold nanopillars remains the same across the entire strain-rate range, the elastic limit (defined as stress for nucleation of the first dislocation) depends significantly on the strain-rate. We also propose a new methodology that overcomes some of the limits in our original accelerated dynamics scheme (and accelerated dynamics methods in general). We lay out our methods in sufficient details so as to be used for understanding and predicting deformation mechanism under realistic driving forces for various problems., Comment: 29 pages, 8 figures. Submitted. Corrected acknowledgments

We propose a hybrid deterministic and stochastic approach to achieve extended time scales in atomistic simulations that combines the strengths of molecular dynamics (MD) and Monte Carlo (MC) simulations in an easy-to-implement way. The method exploits the rare event nature of the dynamics similar to most current accelerated MD approaches but goes beyond them by providing, without any further computational overhead, (a) rapid thermalization between infrequent events, thereby minimizing spurious correlations, and (b) control over accuracy of time-scale correction, while still providing similar or higher boosts in computational efficiency. We present two applications of the method: (a) Vacancy-mediated diffusion in Fe yields correct diffusivities over a wide range of temperatures and (b) source-controlled plasticity and deformation behavior in Au nanopillars at realistic strain rates (10^4/s and lower), with excellent agreement with previous theoretical predictions and in situ high-resolution transmission electron microscopy observations. The method gives several orders-of-magnitude improvements in computational efficiency relative to standard MD and good scalability with the size of the system., Comment: 4 pages, 2 figures. Corrected logarithm base in figures 2 and 4