Amir Haji‐Akbari

Proteins fold through ensembles of competing pathways, yet the kinetic contribution of each route remains difficult to quantify. Structure-prediction methods such as AlphaFold identify folded endpoints, but do not resolve folding kinetics, pathway heterogeneity, or how flux partitions among competing mechanisms. Here, we introduce a framework that directly decomposes folding flux into pathway-specific kinetic contributions by combining forward-flux sampling with trajectory-level unsupervised learning, avoiding millisecond-scale trajectories, biasing potentials, and a priori state discretization. Applied to 2,637 statistically representative folding events of the TC5b variant of Trp-cage, the framework recovers a folding time in near-quantitative agreement with experiments and identifies four pathways distinguished by the ordering of helix formation, hydrophobic collapse, and salt-bridge stabilization. The resulting decomposition shows that structural prevalence is a poor proxy for kinetic importance: the most populated pathways are not the fastest, whereas a rare helix– salt-bridge route is disproportionately efficient and a premature salt bridge produces a frustrated slow route. By assigning statistical weights to competing pathways, this framework links structural evolution to kinetic relevance in biomolecular rare events and reveals how folding landscapes select kinetically important routes from many plausible structural sequences.

Accurate calculation of free energies and their derivatives is central to assessing the thermodynamic stability of molecular and particulate systems across length scales. Yet such quantities can be difficult to compute reliably in strongly interacting systems, such as solutions of ionic species in polar solvents. One important example is the chemical potential of water in aqueous electrolytes, which can be estimated through staged particle insertion by gradually coupling an inserted molecule to its environment. Although the resulting insertion free energy should be independent of the alchemical pathway, the order and manner in which van der Waals and electrostatic interactions are activated can strongly affect convergence and, in some cases, yield inconsistent estimates. Here, we examine this issue by calculating water's chemical potential in aqueous KCl solutions using eight alchemical insertion pathways that differ in the extent and order of van der Waals and Coulombic coupling. We find that concurrently activating these interactions, particularly in fully coupled and partially end-coupled protocols, can produce chemically implausible insertion free energies. These anomalies arise from intermediate states in which the inserted water molecule develops strong electrostatic interactions with a chloride ion before sufficient short-range repulsion has been established. In contrast, pathways that activate short-range van der Waals interactions before electrostatics yield more consistent and chemically plausible estimates. These findings demonstrate that practical alchemical calculations in polar and ionic environments can be highly sensitive to pathway design, underscoring the importance of decoupling short-range and electrostatic interactions in staged insertion alchemical protocols.

Accurate calculation of free energies and their derivatives is central to assessing the thermodynamic stability of molecular and particulate systems across length scales. Yet such quantities can be difficult to compute reliably in strongly interacting systems, such as solutions of ionic species in polar solvents. One important example is the chemical potential of water in aqueous electrolytes, which can be estimated through staged particle insertion by gradually coupling an inserted molecule to its environment. Although the resulting insertion free energy should be independent of the alchemical pathway, the order and manner in which van der Waals and electrostatic interactions are activated can strongly affect convergence and, in some cases, yield inconsistent estimates. Here, we examine this issue by calculating water's chemical potential in aqueous KCl solutions using eight alchemical insertion pathways that differ in the extent and order of van der Waals and Coulombic coupling. We find that concurrently activating these interactions, particularly in fully coupled and partially end-coupled protocols, can produce chemically implausible insertion free energies. These anomalies arise from intermediate states in which the inserted water molecule develops strong electrostatic interactions with a chloride ion before sufficient short-range repulsion has been established. In contrast, pathways that activate short-range van der Waals interactions before electrostatics yield more consistent and chemically plausible estimates. These findings demonstrate that practical alchemical calculations in polar and ionic environments can be highly sensitive to pathway design, underscoring the importance of decoupling short-range and electrostatic interactions in staged insertion alchemical protocols.

Heterogeneous nucleation is a process wherein extrinsic impurities facilitate crystallization by lowering nucleation barriers and constitutes the dominant mechanism for crystallization in most systems. Classical nucleation theory ( cnt ) has been remarkably successful in predicting the kinetics of heterogeneous nucleation, even on chemically and topographically nonuniform surfaces, despite its reliance on several restrictive assumptions, such as the idealized spherical-cap geometry of the crystalline nuclei. Here, we employ molecular dynamics simulations and jumpy forward flux sampling to investigate the kinetics and mechanism of heterogeneous crystal nucleation in a model atomic liquid. We examine both a chemically uniform, weakly attractive liquiphilic surface and a checkerboard surface composed of alternating liquiphilic and liquiphobic patches. We find the nucleation rate to retain its canonical temperature dependence predicted by cnt in both systems. Moreover, the contact angles of crystalline nuclei exhibit negligible dependence on the nucleus size and temperature. On the checkerboard surface, nuclei maintain a fixed contact angle through pinning at patch boundaries and vertical growth into the bulk. These findings offer insights into the robustness of cnt in experimental scenarios, where nucleating surfaces often feature active hotspots surrounded by inert or liquiphobic domains.

Heterogeneous nucleation is a process wherein extrinsic impurities facilitate crystallization by lowering nucleation barriers and constitutes the dominant mechanism for crystallization in most systems. Classical nucleation theory (cnt) has been remarkably successful in predicting the kinetics of heterogeneous nucleation, even on chemically and topographically nonuniform surfaces, despite its reliance on several restrictive assumptions, such as the idealized spherical-cap geometry of the crystalline nuclei. Here, we employ molecular dynamics simulations and jumpy forward flux sampling to investigate the kinetics and mechanism of heterogeneous crystal nucleation in a model atomic liquid. We examine both a chemically uniform, weakly attractive liquiphilic surface and a checkerboard surface composed of alternating liquiphilic and liquiphobic patches. We find the nucleation rate to retain its canonical temperature dependence predicted by cnt in both systems. Moreover, the contact angles of crystalline nuclei exhibit negligible dependence on the nucleus size and temperature. On the checkerboard surface, nuclei maintain a fixed contact angle through pinning at patch boundaries and vertical growth into the bulk. These findings offer insights into the robustness of cnt in experimental scenarios, where nucleating surfaces often feature active hotspots surrounded by inert or liquiphobic domains.

Sustainable water treatment requires selective removal of deleterious ions, such as toxic metals and excess salts, while preserving beneficial minerals. Capacitive deionization (CDI), which is a membrane-free electrochemical desalination technology, offers a tunable alternative for targeted ion separation. Achieving high ion selectivity in CDI is, however, challenging as factors such as ion valence, hydrated radius, and hydration energy influence the preferential electrosorption of different ions into charged porous electrodes, making selectivity outcomes hard to predict and control. Theoretical and computational tools are crucial for understanding the selectivity mechanisms in CDI systems and informing the rational design of new materials and devices. However, these models operate at varying length scales, and integrating the insights gained from different scales into a unified multiscale framework still remains a grand challenge. Here, we overview recent advancements in computational modeling of CDI systems, showing how cross-scale insights can guide the design of next-generation CDI systems.

Ion transport through nanoscale channels and pores is pivotal to numerous natural processes and industrial applications. Experimental investigation of the kinetics and mechanisms of such processes is, however, hampered by the limited spatiotemporal resolution of existing experimental techniques. While molecular simulations have become indispensable for unraveling the underlying principles of nanoscale transport, they all suffer from some important technical limitations. In our previous works, we identified strong polarization-induced finite-size effects in molecular dynamics simulations of hindered ion transport, caused by spurious long-range interactions between the traversing ion and the periodic replicates of other ions. To rectify these artifacts, we introduced the ideal conductor/dielectric model (Icdm), which treats the system as a combination of conductors and dielectrics and constructs an analytical correction to the translocation free energy profile. Here, we investigate some limitations of this model. First, we propose a generalized approach based on Markov state models that is capable of estimating translocation time scales in the thermodynamic limit for free energy profiles with multiple comparable barriers. Second, we identify a new category of polarization-induced finite-size effects, which significantly alter the spatial distribution of nontraversing ions in smaller systems. These secondary effects cannot be corrected by the Icdm model and must be avoided by selecting sufficiently large system sizes. Additionally, we demonstrate through multiple case studies that finite-size artifacts can spuriously reverse expected trends in ion transport kinetics. Our findings underscore the necessity for careful selection of system sizes and the judicious application of the Icdm model to rectify residual finite-size artifacts.

Ion transport through nanoscale channels and pores is pivotal to numerous natural processes and industrial applications. Experimental investigation of the kinetics and mechanisms of such processes is, however, hampered by the limited spatiotemporal resolution of existing experimental techniques. While molecular simulations have become indispensable for unraveling the underlying principles of nanoscale transport, they also suffer from some important technical limitations. In our previous works, we identified strong polarization-induced finite-size effects in molecular dynamics simulations of hindered ion transport, caused by spurious long-range interactions between the traversing ion and the periodic replicates of other ions. To rectify these artifacts, we introduced the Ideal Conductor/Dielectric Model (\textsc{Icdm}), which treats the system as a combination of conductors and dielectrics, and constructs an analytical correction to the translocation free energy profile. Here, we investigate some limitations of this model. Firstly, we propose a generalized approach based on Markov State models that is capable of estimating translocation timescales in the thermodynamic limit for free energy profiles with multiple comparable barriers. Second, we identify a new category of polarization-induced finite-size effects, which significantly alter the spatial distribution of non-traversing ions in smaller systems. These secondary effects cannot be corrected by the ICDM model and must be avoided by selecting sufficiently large system sizes. Additionally, we demonstrate through multiple case studies that finite-size artifacts can reverse expected trends in ion transport kinetics. Our findings underscore the necessity for careful selection of system sizes and the judicious application of the \textsc{Icdm} model to rectify residual finite-size artifacts.

Ice nucleation plays a pivotal role in many natural and industrial processes, and molecular simulations have proven vital in uncovering its kinetics and mechanisms. A fundamental component of such simulations is the choice of an order parameter (OP) that quantifies the progress of nucleation, with the efficacy of an OP typically measured by its ability to predict the committor probabilities. Here, we leverage a machine learning framework introduced in our earlier work [Domingues et al., J. Phys. Chem. Lett. 15, 1279, (2024)] to systematically investigate how key implementation details influence the efficacy of standard Steinhardt OPs in capturing the progress of both homogeneous and heterogeneous ice nucleation. Our analysis identifies distance and q6 cutoffs as the primary determinants of OP performance, regardless of the mode of nucleation. We also examine the impact of two popular refinement strategies, namely chain exclusion and hydration shell inclusion, on OP efficacy. We find neither strategy to exhibit a universally consistent impact. Instead, their efficacy depends strongly on the chosen distance and q6 cutoffs. Chain exclusion enhances OP efficacy when the underlying OP lacks sufficient selectivity, whereas hydration shell inclusion is beneficial for overly selective OPs. Consequently, we demonstrate that selecting optimal combinations of such cutoffs can eliminate the need for these refinement strategies altogether. These findings provide a systematic understanding of how to design and optimize OPs for accurately describing complex nucleation phenomena, offering valuable guidance for improving the predictive power of molecular simulations.

A new class of membranes that can separate ions of similar size and charge is highly desired for resource recovery, water reuse and energy storage technologies. These separations require membrane nanochannels with simultaneous ångström-scale confinement and ion-selective binding sites. Conventional membrane material design uses continuous, volume-averaged properties that cannot account for discrete chemical interactions between ions and binding sites. In this Perspective, we present a design framework for ultraselective membranes by describing how to select and incorporate ion-specific binding sites into membrane nanochannels. We begin by discussing how the chemical features of ions, functional groups and solvents impact ion-binding energy. We then describe the role of binding energy in selective ion transport through nanochannels and discuss the critical importance of intersite spacing. Subsequently, we draw inspiration from machine learning methods used for drug discovery and suggest a similar approach to identify functional groups with optimal ion-binding affinity. We conclude by outlining synthetic methods to incorporate ion-specific binding sites into prevalent nanostructured materials such as covalent organic frameworks, metal–organic frameworks, two-dimensional materials and polymers. This Perspective proposes a way to design membranes to separate ions of similar size and charge with a view to their use in resource recovery, water reuse and energy storage technologies.

We explore the potential of nanocrystals (a term used equivalently to nanoparticles) as building blocks for nanomaterials, and the current advances and open challenges for fundamental science developments and applications. Nanocrystal assemblies are inherently multiscale, and the generation of revolutionary material properties requires a precise understanding of the relationship between structure and function, the former being determined by classical effects and the latter often by quantum effects. With an emphasis on theory and computation, we discuss challenges that hamper current assembly strategies and to what extent nanocrystal assemblies represent thermodynamic equilibrium or kinetically trapped metastable states. We also examine dynamic effects and optimization of assembly protocols. Finally, we discuss promising material functions and examples of their realization with nanocrystal assemblies.

Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in characterizing such spatial heterogeneities and probing the impact of confinement on materials' properties. For static properties, this is a straightforward task and can be achieved via simple spatial binning. Such an approach, however, cannot be readily applied to transport coefficients due to lack of natural extensions of autocorrelations used for their calculation in the bulk. The prime example of this challenge is diffusivity, which, in the bulk, can be readily estimated from the particles' mobility statistics, which satisfy the Fokker-Planck equation. Under confinement, however, such statistics will follow the Smoluchowski equation, which lacks a closed-form analytical solution. This brief review explores the rich history of estimating profiles of the diffusivity tensor from MD simulations and discusses various approximate methods and algorithms developed for this purpose. Besides discussing heuristic extensions of bulk methods, we overview more rigorous algorithms, including kernel-based methods, Bayesian approaches, and operator discretization techniques. Additionally, we outline methods based on applying biasing potentials or imposing constraints on tracer particles. Finally, we discuss approaches that estimate diffusivity from mean first passage time or committor probability profiles, a conceptual framework originally developed in the context of collective variable spaces describing rare events in computational chemistry and biology. In summary, this paper offers a concise survey of diverse approaches for estimating diffusivity from MD trajectories, highlighting challenges and opportunities in this area.

Human γD-crystallin belongs to a crucial family of proteins known as crystallins located in the fiber cells of the human lens. Since crystallins do not undergo any turnover after birth, they need to possess remarkable thermodynamic stability. However, their sporadic misfolding and aggregation, triggered by environmental perturbations or genetic mutations, constitute the molecular basis of cataracts, which is the primary cause of blindness in the globe according to the World Health Organization. Here, we investigate the impact of high pressure on the conformational landscape of wild-type HγD-crystallin using replica exchange molecular dynamics simulations augmented with principal component analysis. We find pressure to have a modest impact on global measures of protein stability, such as root-mean-square displacement and radius of gyration. Upon projecting our trajectories along the first two principal components from principal component analysis, however, we observe the emergence of distinct free energy basins at high pressures. By screening local order parameters previously shown or hypothesized as markers of HγD-crystallin stability, we establish correlations between a tyrosine-tyrosine aromatic contact within the N-terminal domain and the protein's end-to-end distance with projections along the first and second principal components, respectively. Furthermore, we observe the simultaneous contraction of the hydrophobic core and its intrusion by water molecules. This exploration sheds light on the intricate responses of HγD-crystallin to elevated pressures, offering insights into potential mechanisms underlying its stability and susceptibility to environmental perturbations, crucial for understanding cataract formation.

ADVERTISEMENT RETURN TO ISSUEEditorialNEXTIntroduction to Computational and Theoretical Studies Focused on Self-Assembly and Molecular OrganizationFernando A. Escobedo*Fernando A. EscobedoR. F. Smith School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, New York 14853, United StatesE-mail: [email protected]More by Fernando A. Escobedohttps://orcid.org/0000-0002-4722-9836, Amir Haji-Akbari*Amir Haji-AkbariDepartment of Chemical and Environmental Engineering, Yale University, New Haven, Connecticut 06511, United StatesE-mail: [email protected]More by Amir Haji-Akbarihttps://orcid.org/0000-0002-2228-6957, and Sumit Sharma*Sumit SharmaDepartment of Chemical and Biomolecular Engineering, Ohio University, Athens, Ohio 45701, United StatesE-mail: [email protected]More by Sumit Sharmahttps://orcid.org/0000-0003-3138-5487Cite this: J. Chem. Theory Comput. 2024, 20, 4, 1503–1504Publication Date (Web):February 27, 2024Publication History Received4 February 2024Published online27 February 2024Published inissue 27 February 2024https://doi.org/10.1021/acs.jctc.4c00147Copyright © Published 2024 by American Chemical Society. This publication is available under these Terms of Use. Request reuse permissions This publication is free to access through this site. Learn MoreArticle Views591Altmetric-Citations-LEARN ABOUT THESE METRICSArticle Views are the COUNTER-compliant sum of full text article downloads since November 2008 (both PDF and HTML) across all institutions and individuals. These metrics are regularly updated to reflect usage leading up to the last few days.Citations are the number of other articles citing this article, calculated by Crossref and updated daily. Find more information about Crossref citation counts.The Altmetric Attention Score is a quantitative measure of the attention that a research article has received online. Clicking on the donut icon will load a page at altmetric.com with additional details about the score and the social media presence for the given article. Find more information on the Altmetric Attention Score and how the score is calculated. Share Add toView InAdd Full Text with ReferenceAdd Description ExportRISCitationCitation and abstractCitation and referencesMore Options Share onFacebookTwitterWechatLinked InRedditEmail PDF (818 KB) Get e-AlertscloseSUBJECTS:Aggregation,Free energy,Nanoparticles,Polymers,Self organization Get e-Alerts

Confinement can substantially alter the physicochemical properties of materials by breaking translational isotropy and rendering all physical properties position-dependent. Molecular dynamics (MD) simulations have proven instrumental in characterizing such spatial heterogeneities and probing the impact of confinement on materials' properties. For static properties, this is a straightforward task and can be achieved via simple spatial binning. Such an approach, however, cannot be readily applied to transport coefficients due to lack of natural extensions of autocorrelations used for their calculation in the bulk. The prime example of this challenge is diffusivity, which, in the bulk, can be readily estimated from the particles' mobility statistics, which satisfy the Fokker-Planck equation. Under confinement, however, such statistics will follow the Smoluchowski equation, which lacks a closed-form analytical solution. This brief review explores the rich history of estimating profiles of the diffusivity tensor from MD simulations and discusses various approximate methods and algorithms developed for this purpose. Beside discussing heuristic extensions of bulk methods, we overview more rigorous algorithms, including kernel-based methods, Bayesian approaches, and operator discretization techniques. Additionally, we outline methods based on applying biasing potentials or imposing constraints on tracer particles. Finally, we discuss approaches that estimate diffusivity from mean first passage time or committor probability profiles, a conceptual framework originally developed in the context of collective variable spaces describing rare events in computational chemistry and biology. In summary, this paper offers a concise survey of diverse approaches for estimating diffusivity from MD trajectories, highlighting challenges and opportunities in this area.

Heterogeneous crystal nucleation is the dominant mechanism of crystallization in most systems, yet its underlying physics remains an enigma. While emergent interfacial crystalline order precedes heterogeneous nucleation, its importance in the nucleation mechanism is unclear. Here, we use path sampling simulations of two model systems to demonstrate that crystalline order in its traditional sense is not predictive of the outcome of the heterogeneous nucleation of close-packed crystals. Consequently, structure-based collective variables (CVs) that reliably describe homogeneous nucleation can be poor descriptors of heterogeneous nucleation. This divergence between structure and nucleation outcome is accompanied by an intriguing dynamical anomaly, wherein low-coordinated crystalline particles outpace their liquid-like counterparts. We use committor analysis, high-throughput screening, and machine learning to devise CV optimization strategies and present suitable structural heuristics within the metastable fluid for CV prescreening. Employing such optimized CVs is pivotal for properly characterizing the mechanism of heterogeneous nucleation in metallic and colloidal systems.

Molecular simulations serve as indispensable tools for investigating the kinetics and elucidating the mechanism of hindered ion transport across nanoporous membranes. In particular, recent advancements in advanced sampling techniques have made it possible to access translocation timescales spanning several orders of magnitude. In our prior study [Shoemaker et al., J. Chem. Theory Comput. 18, 7142 (2022)], we identified significant finite size artifacts in simulations of pressure-driven hindered ion transport through nanoporous graphitic membranes. We introduced the ideal conductor model, which effectively corrects for such artifacts by assuming the feed to be an ideal conductor. In the present work, we introduce the ideal conductor dielectric model (Icdm), a generalization of our earlier model, which accounts for the dielectric properties of both the membrane and the filtrate. Using the Icdm model substantially enhances the agreement among corrected free energy profiles obtained from systems of varying sizes, with notable improvements observed in regions proximate to the pore exit. Moreover, the model has the capability to consider secondary ion passage events, including the transport of a co-ion subsequent to the traversal of a counter-ion, a feature that is absent in our original model. We also investigate the sensitivity of the new model to various implementation details. The Icdm model offers a universally applicable framework for addressing finite size artifacts in molecular simulations of ion transport. It stands as a significant advancement in our quest to use molecular simulations to comprehensively understand and manipulate ion transport processes through nanoporous membranes.

Human γ D-crystallin belongs to a crucial family of proteins known as crystallins located in fiber cells of the human lens. Since crystallins do not undergo any turnover after birth, they need to possess remarkable thermodynamic stability. However, their sporadic misfolding and aggregation, triggered by environmental perturbations or genetic mutations, constitute the molecular basis of cataracts, which is the primary cause of blindness in the globe according to the World Health Organization. Here, we investigate the impact of high pressure on the conformational landscape of the wild-type H γ D-crystallin using replica exchange molecular dynamics simulations augmented with principal component analysis. We find pressure to have a modest impact on global measures of protein stability, such as root mean square displacement and radius of gyration. Upon projecting our trajectories along the first two principal components from P ca , however, we observe the emergence of distinct free energy basins at high pressures. By screening local order parameters previously shown or hypothesized as markers of H γ D-crystallin stability, we establish correlations between a tyrosine-tyrosine aromatic contact within the N-terminal domain and the protein’s end-to-end distance with projections along the first and second principal components, respectively. Furthermore, we observe the simultaneous contraction of the hydrophobic core and its intrusion by water molecules. This exploration sheds light on the intricate responses of H γ D-crystallin to elevated pressures, offering insights into potential mechanisms underlying its stability and susceptibility to environmental perturbations, crucial for understanding cataract formation.

Nanoporous membranes have emerged as powerful tools for diverse applications, including gas separation and water desalination. Achieving high permeability for desired molecules alongside exceptional rejection of other species presents a significant design challenge. One potential strategy involves optimizing the chemistry and geometry of isolated nanopores to enhance permeability and selectivity while maximizing their density within a membrane. However, the impact of the pore proximity on membrane performance remains an open question. Through path sampling simulations of model graphitic membranes with multiple subnanometer pores, we reveal that nanoscale proximity between pores detrimentally affects water permeability and salt rejection. Specifically, counterion transport is decelerated, while co-ion transport is accelerated, due to direct interactions among water molecules, salt ions, and the dipoles within neighboring pores. Notably, the observed ionic transport time scales significantly deviate from established theories such as the access resistance model but are well explained using the simple phenomenological model that we develop in this work. We use this model to prescreen and optimize pore arrangements that elicit minimal correlations at a target pore density. These findings deepen our understanding of multipore systems, informing the rational design of nanoporous membranes for enhanced separation processes such as water desalination. They also shed light on the physiology of biological cells that employ ion channel proteins to modulate ion transport and reversal potentials.

Nanoporous membranes have emerged as powerful tools for diverse applications, including gas separation and water desalination. Achieving high permeability for desired molecules alongside exceptional rejection of other species presents a significant design challenge. One potential strategy involves optimizing the chemistry and geometry of isolated nanopores to enhance permeability and selectivity, while maximizing their density within a membrane. However, the impact of pore proximity on membrane performance remains an open question. Through path sampling simulations of model graphitic membranes with multiple sub-nanometer pores, we reveal that nanoscale proximity between pores detrimentally affects water permeability and salt rejection. Specifically, counter-ion transport is decelerated, while co-ion transport is accelerated, due to direct interactions between water molecules, salt ions, and the dipoles within neighboring pores. Notably, the observed ionic transport timescales significantly deviate from established theories such as the access resistance model, but are well explained using the simple phenomenological model that we develop in this work. We use this model to pre-screen and optimize pore arrangements that elicit minimal correlations at a target pore density. These findings deepen our understanding of multi-pore systems, informing the rational design of nanoporous membranes for enhanced separation processes such as water desalination. They also shed light onto the physiology of biological cells that employ ion channel proteins to modulate ion transport and reversal potentials.

Heterogeneous crystal nucleation is the dominant mechanism of crystallization in most systems, yet its underlying physics remains an enigma. While emergent interfacial crystalline order precedes heterogeneous nucleation, its importance in the nucleation mechanism is unclear. Here, we use molecular dynamics simulations and path sampling techniques to demonstrate that crystalline order in its traditional sense is not predictive of the outcome of heterogeneous nucleation of close-packed crystals. Consequently, structure-based collective variables (CVs) that reliably describe homogeneous nucleation can be poor descriptors of heterogeneous nucleation. This divergence between structure and nucleation outcome is accompanied by an intriguing dynamical anomaly wherein low- coordinated crystalline particles outpace their liquid-like counterparts. Both these anomalies are morphologically associated with low-coordinated crystalline particles participating in bridges connecting crystalline domains. We also demonstrate that reliance on ineffective CVs yields a flawed comprehension of the nucleation mechanism by overestimating the face-centered cubic (FCC) content of crystalline nuclei in the systems and surfaces considered here. We use committor analysis, high-throughput screening, and machine learning to devise CV optimization strategies, and present suitable structural heuristics within the metastable fluid for CV pre-screening. Employing such optimized CVs is pivotal in properly characterizing the mechanism of heterogeneous nucleation in a wide variety of systems, including inorganic, metallic and colloidal systems.

Molecular simulations serve as indispensable tools for investigating the kinetics and elucidating the mechanism of hindered ion transport across nanoporous membranes. In particular, recent advancements in advanced sampling techniques have made it possible to access translocation timescales spanning several orders of magnitude. In our prior study (\href{https://doi.org/10.1021/acs.jctc.2c00375}{Shoemaker,~\emph{et al.},~\emph{J. Chem. Theory Comput.}, 18: 7142, {\bf 2022}}), we identified significant finite size artifacts in simulations of pressure-driven hindered ion transport through nanoporous graphitic membranes. We introduced the ideal conductor model, which effectively corrects for such artifacts by assuming the feed to be an ideal conductor. In the present work, we introduce the ideal conductor dielectric model (ICDM), a generalization of our earlier model, which accounts for the dielectric properties of both the membrane and the filtrate. Using the ICDM model substantially enhances the agreement among corrected free energy profiles obtained from systems of varying sizes, with notable improvements observed in regions proximate to the pore exit. Moreover, the model has the capability to consider secondary ion passage events, including the transport of a co-ion subsequent to the traversal of a counter-ion, a feature absent in our original model. We also investigate the sensitivity of the new model to various implementation details. The ICDM model offers a universally applicable framework for addressing finite size artifacts in molecular simulations of ion transport. It stands as a significant advancement in our quest to use molecular simulations to comprehensively understand and manipulate ion transport processes through nanoporous membranes.

Confinement breaks translational and rotational symmetry in materials and makes all physical properties functions of position. Such spatial variations are key to modulating material properties at the nanoscale, and characterizing them accurately is therefore an intense area of research in the molecular simulations community. This is relatively easy to accomplish for basic mechanical observables. Determining spatial profiles of transport properties, such as diffusivity, is, however, much more challenging, as it requires calculating position-dependent autocorrelations of mechanical observables. In our previous paper (Domingues, T.S.; Coifman, R.; Haji-Akbari, A. J. Phys. Chem. B 2023, 127, 5273 10.1021/acs.jpcb.3c00670), we analytically derive and numerically validate a set of filtered covariance estimators (FCEs) for quantifying spatial variations of the diffusivity tensor from stochastic trajectories. In this work, we adapt these estimators to extract diffusivity profiles from MD trajectories and validate them by applying them to a Lennard-Jones fluid within a slit pore. We find our MD-adapted estimator to exhibit the same qualitative features as its stochastic counterpart, as it accurately estimates the lateral diffusivity across the pore while systematically underestimating the normal diffusivity close to hard boundaries. We introduce a conceptually simple and numerically efficient correction scheme based on simulated annealing and diffusion maps to resolve the latter artifact and obtain normal diffusivity profiles that are consistent with the self-part of the van Hove correlation functions. Our findings demonstrate the potential of this MD-adapted estimator in accurately characterizing spatial variations of diffusivity in confined materials.

Materials under confinement can possess properties that deviate considerably from their bulk counterparts. Indeed, confinement makes all physical properties position-dependent and possibly anisotropic, and characterizing such spatial variations and directionality has been an intense area of focus in experimental and computational studies of confined matter. While this task is fairly straightforward for simple mechanical observables, it is far more daunting for transport properties such as diffusivity that can only be estimated from autocorrelations of mechanical observables. For instance, there are well established methods for estimating diffusivity from experimentally observed or computationally generated trajectories in bulk systems. No rigorous generalizations of such methods, however, exist for confined systems. In this work, we present two filtered covariance estimators for computing anisotropic and position-dependent diffusivity tensors and validate them by applying them to stochastic trajectories generated according to known diffusivity profiles. These estimators can accurately capture spatial variations that span over several orders of magnitude and that assume different functional forms. Our kernel-based approach is also very robust to implementation details such as the localization function and time discretization and performs significantly better than estimators that are solely based on local covariance. Moreover, the kernel function does not have to be localized and can instead belong to a dictionary of orthogonal functions. Therefore, the proposed estimator can be readily used to obtain functional estimates of diffusivity rather than a tabulated collection of pointwise estimates. Nonetheless, the susceptibility of the proposed estimators to time discretization is higher at the immediate vicinity of hard boundaries. We demonstrate this heightened susceptibility to be common among all covariance-based estimators.

Materials under confinement can possess properties that deviate considerably from their bulk counterparts. Indeed, confinement makes all physical properties position-dependent and possibly anisotropic, and characterizing such spatial variations and directionality is an intense area of focus in experimental and computational studies of confined matter. While this task is fairly straightforward for simple mechanical observables, it is far more daunting for transport properties such as diffusivity that can only be estimated from autocorrelations of mechanical observables. For instance, there are well established methods for estimating diffusivity from experimentally observed or computationally generated trajectories in the bulk. No rigorous generalizations of such methods, however, exist for confined systems. In this work, we present two filtered covariance estimators for computing anisotropic and position-dependent diffusivity tensors and validate them by applying them to stochastic trajectories generated according to known diffusivity profiles. These estimators can accurately capture spatial variations spanning over several orders of magnitude and assuming different functional forms. Our approach is also very robust to implementation details such as the localization function and time discretization and performs significantly better than estimators that are solely based on local covariance. Moreover, the kernel function does not have to be localized and can instead belong to a dictionary of orthogonal functions. Therefore, the proposed estimator can be readily used to obtain functional estimates of diffusivity rather than a tabulated collection of pointwise estimates. Nonetheless, the susceptibility of the proposed estimators to time discretization is higher close to hard boundaries. We demonstrate this heightened susceptibility to be common among all covariance-based estimators.