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.

Remembering the Work of Phillip L. Geissler: A Coda to His Scientific Trajectory.

Phillip L. Geissler made important contributions to the statistical mechanics of biological polymers, heterogeneous materials, and chemical dynamics in aqueous environments. He devised analytical and computational methods that revealed the underlying organization of complex systems at the frontiers of biology, chemistry, and materials science. In this retrospective we celebrate his work at these frontiers.

Perspective: Atomistic simulations of water and aqueous systems with machine learning potentials.

As the most important solvent, water has been at the center of interest since the advent of computer simulations. While early molecular dynamics and Monte Carlo simulations had to make use of simple model potentials to describe the atomic interactions, accurate ab initio molecular dynamics simulations relying on the first-principles calculation of the energies and forces have opened the way to predictive simulations of aqueous systems. Still, these simulations are very demanding, which prevents the study of complex systems and their properties. Modern machine learning potentials (MLPs) have now reached a mature state, allowing us to overcome these limitations by combining the high accuracy of electronic structure calculations with the efficiency of empirical force fields. In this Perspective, we give a concise overview about the progress made in the simulation of water and aqueous systems employing MLPs, starting from early work on free molecules and clusters via bulk liquid water to electrolyte solutions and solid-liquid interfaces.

Comparing machine learning potentials for water: Kernel-based regression and Behler-Parrinello neural networks.

In this paper, we investigate the performance of different machine learning potentials (MLPs) in predicting key thermodynamic properties of water using RPBE + D3. Specifically, we scrutinize kernel-based regression and high-dimensional neural networks trained on a highly accurate dataset consisting of about 1500 structures, as well as a smaller dataset, about half the size, obtained using only on-the-fly learning. This study reveals that despite minor differences between the MLPs, their agreement on observables such as the diffusion constant and pair-correlation functions is excellent, especially for the large training dataset. Variations in the predicted density isobars, albeit somewhat larger, are also acceptable, particularly given the errors inherent to approximate density functional theory. Overall, this study emphasizes the relevance of the database over the fitting method. Finally, this study underscores the limitations of root mean square errors and the need for comprehensive testing, advocating the use of multiple MLPs for enhanced certainty, particularly when simulating complex thermodynamic properties that may not be fully captured by simpler tests.

Elastic forces drive nonequilibrium pattern formation in a model of nanocrystal ion exchange.

Chemical transformations, such as ion exchange, are commonly employed to modify nanocrystal compositions. Yet the mechanisms of these transformations, which often operate far from equilibrium and entail mixing diverse chemical species, remain poorly understood. Here we explore an idealized model for ion exchange in which a chemical potential drives compositional defects to accumulate at a crystal's surface. These impurities subsequently diffuse inward. We find that the nature of interactions between sites in a compositionally impure crystal strongly impacts exchange trajectories. In particular, elastic deformations which accompany lattice-mismatched species promote spatially modulated patterns in the composition. These same patterns can be produced at equilibrium in core/shell nanocrystals, whose structure mimics transient motifs observed in nonequilibrium trajectories. Moreover, the core of such nanocrystals undergoes a phase transition-from modulated to unstructured-as the thickness or stiffness of the shell is decreased. Our results help explain the varied patterns observed in heterostructured nanocrystals produced by ion exchange and suggest principles for the rational design of compositionally patterned nanomaterials.

Optimizing the architecture of Behler-Parrinello neural network potentials.

The architecture of neural network potentials is typically optimized at the beginning of the training process and remains unchanged throughout. Here, we investigate the accuracy of Behler-Parrinello neural network potentials for varying training set sizes. Using the QM9 and 3BPA datasets, we show that adjusting the network architecture according to the training set size improves the accuracy significantly. We demonstrate that both an insufficient and an excessive number of fitting parameters can have a detrimental impact on the accuracy of the neural network potential. Furthermore, we investigate the influences of descriptor complexity, neural network depth, and activation function on the model's performance. We find that for the neural network potentials studied here, two hidden layers yield the best accuracy and that unbounded activation functions outperform bounded ones.

Molecular Hessian matrices from a machine learning random forest regression algorithm.

In this article, we present a machine learning model to obtain fast and accurate estimates of the molecular Hessian matrix. In this model, based on a random forest, the second derivatives of the energy with respect to redundant internal coordinates are learned individually. The internal coordinates together with their specific representation guarantee rotational and translational invariance. The model is trained on a subset of the QM7 dataset but is shown to be applicable to larger molecules picked from the QM9 dataset. From the predicted Hessian, it is also possible to obtain reasonable estimates of the vibrational frequencies, normal modes, and zero point energies of the molecules.

High-density liquid (HDL) adsorption at the supercooled water/vapor interface and its possible relation to the second surface tension inflection point.

We investigate the properties of water along the liquid/vapor coexistence line in the supercooled regime down to the no-man's land. Extensive molecular dynamics simulations of the TIP4P/2005 liquid/vapor interface in the range 198-348 K allow us to locate the second surface tension inflection point with a high accuracy at 283 ± 5 K, close to the temperature of maximum density. This temperature also coincides with the appearance of a density anomaly at the interface known as the apophysis. We relate the emergence of the apophysis to the observation of high-density liquid (HDL) water adsorption in the proximity of the liquid/vapor interface.

Ab initio thermodynamics of liquid and solid water.

Thermodynamic properties of liquid water as well as hexagonal (Ih) and cubic (Ic) ice are predicted based on density functional theory at the hybrid-functional level, rigorously taking into account quantum nuclear motion, anharmonic fluctuations, and proton disorder. This is made possible by combining advanced free-energy methods and state-of-the-art machine-learning techniques. The ab initio description leads to structural properties in excellent agreement with experiments and reliable estimates of the melting points of light and heavy water. We observe that nuclear-quantum effects contribute a crucial [Formula: see text] to the stability of ice Ih, making it more stable than ice Ic. Our computational approach is general and transferable, providing a comprehensive framework for quantitative predictions of ab initio thermodynamic properties using machine-learning potentials as an intermediate step.

The microscopic mechanism of bulk melting of ice.

We study the initial stages of homogeneous melting of a hexagonal ice crystal at coexistence and at moderate superheating. Our trajectory-based computer simulation approach provides a comprehensive picture of the events that lead to melting, from the initial accumulation of 5+7 defects, via the formation of L-D and interstitial-vacancy pairs, to the formation of a liquid nucleus. Of the different types of defects that we observe to be involved in melting, a particular kind of 5+7 type defect (type 5) plays a prominent role as it often forms prior to the formation of the initial liquid nucleus and close to the site where the nucleus forms. Hence, like other solids, ice homogeneously melts via the prior accumulation of defects.

Identification of Protein Functional Regions.

Protein sequence stores the information relative to both functionality and stability, thus making it difficult to disentangle the two contributions. However, the identification of critical residues for function and stability has important implications for the mapping of the proteome interactions, as well as for many pharmaceutical applications, e. g. the identification of ligand binding regions for targeted pharmaceutical protein design. In this work, we propose a computational method to identify critical residues for protein functionality and stability and to further categorise them in strictly functional, structural and intermediate. We evaluate single site conservation and use Direct Coupling Analysis (DCA) to identify co-evolved residues both in natural and artificial evolution processes. We reproduce artificial evolution using protein design and base our approach on the hypothesis that artificial evolution in the absence of any functional constraint would exclusively lead to site conservation and co-evolution events of the structural type. Conversely, natural evolution intrinsically embeds both functional and structural information. By comparing the lists of conserved and co-evolved residues, outcomes of the analysis on natural and artificial evolution, we identify the functional residues without the need of any a priori knowledge of the biological role of the analysed protein.

Hierarchical self-assembly of patchy colloidal platelets.

Anisotropy at the level of the inter-particle interaction provides the particles with specific instructions for the self-assembly of target structures. The ability to synthesize non-spherical colloids, together with the possibility of controlling the particle bonding pattern via suitably placed interaction sites, is nowadays enlarging the playing field for materials design. We consider a model of anisotropic colloidal platelets with regular rhombic shape and two attractive sites placed along adjacent edges and we run Monte Carlo simulations in two-dimensions to investigate the two-stage assembly of these units into clusters with well-defined symmetries and, subsequently, into extended lattices. Our focus is on how the site positioning and site-site attraction strength can be tuned to obtain micellar aggregates that are robust enough to successively undergo to a second-stage assembly from sparse clusters into a stable hexagonal lattice.

The generic unfolding of a biomimetic polymer during force spectroscopy.

With the help of force spectroscopy, several analytical theories aim at estimating the rate coefficient of folding for various proteins. Nevertheless, a chief bottleneck lies in the fact that there is still no perfect consensus on how does a force generally perturb the crystal-coil transition. Consequently, the goal of our work is in clarifying the generic behavior of most proteins in force spectroscopy; in other words, what general signature does an arbitrary protein exhibit for its rate coefficient as a function of the applied force? By employing a biomimetic polymer in molecular simulations, we focus on evaluating its respective activation energy for unfolding, while pulling on various pairs of its monomers. Above all, we find that in the vicinity of the force-free scenario, this activation energy possesses a negative slope and a negative curvature as a function of the applied force. Our work is in line with the most recent theories for unfolding, which suggest that such a signature is expected for most proteins, and thus, we further reiterate that many of the classical formulae, that estimate the rate coefficient of the crystal-coil transition, are inadequate. Besides, we also present here an analytical expression which experimentalists can use for approximating the activation energy for unfolding; importantly, it is based on measurements for the mean and variance of the distance between the beads which are being pulled. In summary, our work presents an interesting view for protein folding in force spectroscopy.

Ab initio structure and thermodynamics of the RPBE-D3 water/vapor interface by neural-network molecular dynamics.

Aided by a neural network representation of the density functional theory potential energy landscape of water in the Revised Perdew-Burke-Ernzerhof approximation corrected for dispersion, we calculate several structural and thermodynamic properties of its liquid/vapor interface. The neural network speed allows us to bridge the size and time scale gaps required to sample the properties of water along its liquid/vapor coexistence line with unprecedented precision.

Numerical evidence for thermally induced monopoles.

Electric charges are conserved. The same would be expected to hold for magnetic charges, yet magnetic monopoles have never been observed. It is therefore surprising that the laws of nonequilibrium thermodynamics, combined with Maxwell's equations, suggest that colloidal particles heated or cooled in certain polar or paramagnetic solvents may behave as if they carry an electric/magnetic charge. Here, we present numerical simulations that show that the field distribution around a pair of such heated/cooled colloidal particles agrees quantitatively with the theoretical predictions for a pair of oppositely charged electric or magnetic monopoles. However, in other respects, the nonequilibrium colloidal particles do not behave as monopoles: They cannot be moved by a homogeneous applied field. The numerical evidence for the monopole-like fields around heated/cooled colloidal particles is crucial because the experimental and numerical determination of forces between such colloidal particles would be complicated by the presence of other effects, such as thermophoresis.

Design of Patchy Rhombi: From Close-Packed Tilings to Open Lattices.

In the realm of functional materials, the production of two-dimensional structures with tunable porosity is of paramount relevance for many practical applications: surfaces with regular arrays of pores can be used for selective adsorption or immobilization of guest units that are complementary in shape and/or size to the pores, thus achieving, for instance, selective filtering or well-defined responses to external stimuli. The principles that govern the formation of such structures are valid at both the molecular and the colloidal scale. Here we provide simple design directions to combine the anisotropic shape of the building units-either molecules or colloids-and selective directional bonding. Using extensive computer simulations, we show that regular rhombic platelets decorated with attractive and repulsive interaction sites form specific tilings, going smoothly from close-packed arrangements to open lattices. The rationale behind the rich tiling scenario observed can be described in terms of steric incompatibilities, unsatisfied bonding geometries, and interplays between local and long-range order.

Consequences of Lattice Mismatch for Phase Equilibrium in Heterostructured Solids.

Lattice mismatch can substantially impact the spatial organization of heterogeneous materials. We examine a simple model for lattice-mismatched solids over a broad range of temperature and composition, revealing both uniform and spatially modulated phases. Scenarios for coexistence among them are unconventional due to the extensive mechanical cost of segregation. Together with an adapted Maxwell construction for elastic phase separation, mean field theory predicts a phase diagram that captures key low-temperature features of Monte Carlo simulations.

An efficient method to reconstruct free energy profiles for diffusive processes in transition interface sampling and forward flux sampling simulations.

We propose a Reweighted Partial Path (RPP) method to compute free energy profiles for diffusive processes in single Transition Interface Sampling (TIS) or Forward Flux Sampling (FFS) simulations. The method employs a partial path reweighting strategy, based on the memory loss assumption for diffusive systems, to derive the equilibrium distribution of states along a chosen order parameter from TIS or FFS trajectories. No additional calculations such as reverse TIS or umbrella sampling are required. The application of the RPP method is demonstrated by calculating the nucleation free energy of early-stage Cu precipitates in a dilute Fe-Cu alloy.

Phase stability of the ice XVII-based CO2 chiral hydrate from molecular dynamics simulations.

We computed the phase diagram of CO2 hydrates at high pressure (HP), from 0.3 to 20 kbar, by means of molecular dynamics simulations. The two CO2 hydrates known to occur in this pressure range are the cubic structure I (sI) clathrate and the HP hydrate, whose water framework is the recently discovered ice XVII. We investigated the stability of both hydrates upon heating (melting) as well as the phase changes upon compression. The CO2-filled ice XVII is found to be more stable than the sI clathrate and than the mixture of ice VI and dry ice at pressure values ranging from 6 to 18 kbar and in a wide temperature range, although a phenomenological correction suggests that the stability should more realistically range from 6.5 to 13.5 kbar. Our simulation results support the current hypothesis that the HP hydrate is stable at temperatures above the melting curve of ice VI.

How van der Waals interactions determine the unique properties of water.

Whereas the interactions between water molecules are dominated by strongly directional hydrogen bonds (HBs), it was recently proposed that relatively weak, isotropic van der Waals (vdW) forces are essential for understanding the properties of liquid water and ice. This insight was derived from ab initio computer simulations, which provide an unbiased description of water at the atomic level and yield information on the underlying molecular forces. However, the high computational cost of such simulations prevents the systematic investigation of the influence of vdW forces on the thermodynamic anomalies of water. Here, we develop efficient ab initio-quality neural network potentials and use them to demonstrate that vdW interactions are crucial for the formation of water's density maximum and its negative volume of melting. Both phenomena can be explained by the flexibility of the HB network, which is the result of a delicate balance of weak vdW forces, causing, e.g., a pronounced expansion of the second solvation shell upon cooling that induces the density maximum.