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An important characteristic of RNA folding is the adoption of alternative configurations of similar stability, often referred to as misfolded configurations. These configurations are considered to compete with correctly folded configurations, although their rigorous thermodynamic and structural characterization remains elusive. Tetraloop motifs found in large ribozymes are ideal systems for an atomistically detailed computational quantification of folding free energy landscapes and the structural characterization of their constituent free energy basins, including nonnative states. In this work, we studied a group of closely related 10-mer tetraloops using a combined parallel tempering and metadynamics technique that allows a reliable sampling of the free energy landscapes, requiring only knowledge that the stem folds into a canonical A-RNA configuration. We isolated and analyzed unfolded, folded, and misfolded populations that correspond to different free energy basins. We identified a distinct misfolded state that has a stability very close to that of the correctly folded state. This misfolded state contains a predominant population that shares the same structural features across all tetraloops studied here and lacks the noncanonical A-G base pair in its loop portion. Further analysis performed with biased trajectories showed that although this competitive misfolded state is not an essential intermediate, it is visited in most of the transitions from unfolded to correctly folded states. Moreover, the tetraloops can transition from this misfolded state to the correctly folded state without requiring extensive unfolding.

A longstanding question in water research is the possibility that supercooled liquid water can undergo a liquid-liquid phase transition (LLT) into high- and low-density liquids. We used several complementary molecular simulation techniques to evaluate the possibility of an LLT in an ab initio neural network model of water trained on density functional theory calculations with the SCAN exchange correlation functional. We conclusively show the existence of a first-order LLT and an associated critical point in the SCAN description of water, representing the first definitive computational evidence for an LLT in water from first principles., 14 pages, 3 figures. Supplemental material contains 11 pages, 8 figures

The possible existence of a metastable liquid-liquid transition (LLT) and a corresponding liquid-liquid critical point (LLCP) in supercooled liquid water remains a topic of much debate. An LLT has been rigorously proved in three empirically parametrized molecular models of water, and evidence consistent with an LLT has been reported for several other such models. In contrast, experimental proof of this phenomenon has been elusive due to rapid ice nucleation under deeply supercooled conditions. In this work, we combined density functional theory (DFT), machine learning, and molecular simulations to shed additional light on the possible existence of an LLT in water. We trained a deep neural network (DNN) model to represent the ab initio potential energy surface of water from DFT calculations using the Strongly Constrained and Appropriately Normed (SCAN) functional. We then used advanced sampling simulations in the multithermal-multibaric ensemble to efficiently explore the thermophysical properties of the DNN model. The simulation results are consistent with the existence of an LLCP, although they do not constitute a rigorous proof thereof. We fit the simulation data to a two-state equation of state to provide an estimate of the LLCP's location. These combined results-obtained from a purely first-principles approach with no empirical parameters-are strongly suggestive of the existence of an LLT, bolstering the hypothesis that water can separate into two distinct liquid forms.

Molecular simulations have provided valuable insight into the microscopic mechanisms underlying homogeneous ice nucleation. While empirical models have been used extensively to study this phenomenon, simulations based on first-principles calculations have so far proven prohibitively expensive. Here, we circumvent this difficulty by using an efficient machine learning model trained on density-functional theory (DFT) energies and forces. We compute nucleation rates at atmospheric pressure, over a broad range of supercoolings, using the seeding technique and systems of up to hundreds of thousands of atoms simulated with ab initio accuracy. The key quantity provided by the seeding technique is the size of the critical cluster (i.e., a size such that the cluster has equal probabilities of growing or melting at the given supersaturation) which is used together with the equations of classical nucleation theory to compute nucleation rates. We find that nucleation rates for our model at moderate supercoolings are in good agreement with experimental measurements within the error of our calculation. We also study the impact of properties such as the thermodynamic driving force, interfacial free energy, and stacking disorder on the calculated rates., Comment: 20 pages, 5 figures

A widespread method of crystal preparation is to precipitate it from a supersaturated solution. In such a process, control of solution concentration is of paramount importance. The nucleation process, polymorph selection, and crystal habits depend crucially on this thermodynamic parameter. When performing molecular dynamics simulations with a fixed number of molecules in the canonical ensemble, crystal growth is accompanied by a decrease in the solution concentration. This modification of the thermodynamic condition leads to significant artifacts. Inspired by the recent development of the constant chemical potential molecular dynamics simulation method by Perego et al. [ J. Chem. Phys. 2015 , 142 , 144113 ] , we develop a spherical variant of it to study nucleation from solution. Our method allows determining the crystal nucleus size and nucleation rates at constant supersaturation. As an example, we study the homogeneous nucleation of sodium chloride from its supersaturated aqueous solution.

Ice Ih, the common form of ice in the biosphere, contains proton disorder. Its proton-ordered counterpart, ice XI, is thermodynamically stable below 72 K. However, even below this temperature the formation of ice XI is kinetically hindered and experimentally it is obtained by doping ice with KOH. Doping creates ionic defects that promote the migration of protons and the associated change in proton configuration. In this article, we mimic the effect of doping in molecular dynamics simulations using a bias potential that enhances the formation of ionic defects. The recombination of the ions thus formed proceeds through fast migration of the hydroxide and results in the jump of protons along a hydrogen bond loop. This provides a physical and expedite way to change the proton configuration, and to accelerate diffusion in proton configuration space. A key ingredient of this approach is a machine learning potential trained with density functional theory data and capable of modeling molecular dissociation. We exemplify the usefulness of this idea by studying the order-disorder transition using an appropriate order parameter to distinguish the proton environments in ice Ih and XI. We calculate the changes in free energy, enthalpy, and entropy associated with the transition. Our estimated entropy agrees with experiment within the error bars of our calculation., 17 pages, 9 figures

Machine learning models are rapidly becoming widely used to simulate complex physicochemical phenomena with ab initio accuracy. Here, we use one such model as well as direct density functional theory (DFT) calculations to investigate the phase equilibrium of water, hexagonal ice (Ih), and cubic ice (Ic), with an eye towards studying ice nucleation. The machine learning model is based on deep neural networks and has been trained on DFT data obtained using the SCAN exchange and correlation functional. We use this model to drive enhanced sampling simulations aimed at calculating a number of complex properties that are out of reach of DFT-driven simulations and then employ an appropriate reweighting procedure to compute the corresponding properties for the SCAN functional. This approach allows us to calculate the melting temperature of both ice polymorphs, the driving force for nucleation, the heat of fusion, the densities at the melting temperature, the relative stability of ice Ih and Ic, and other properties. We find a correct qualitative prediction of all properties of interest. In some cases, quantitative agreement with experiment is better than for state-of-the-art semiempirical potentials for water. Our results also show that SCAN correctly predicts that ice Ih is more stable than ice Ic., Comment: 20 pages, 9 figures

We used molecular dynamics simulations to predict the steady state crystal shape of naphthalene grown from ethanol solution. The simulations were performed at constant supersaturation by utilizing a recently proposed algorithm [Perego et al., J. Chem. Phys., 2015, 142, 144113]. To bring the crystal growth within the timescale of a molecular dynamics simulation we applied well-tempered metadynamics with a spatially constrained collective variable, which focuses the sampling on the growing layer. We estimated that the resulting steady state crystal shape corresponds to a rhombic prism, which is in line with experiments. Further, we observed that at the investigated supersaturations, the {00} face grows in a two step two dimensional nucleation mechanism while the considerably faster growing faces {10} and {20} grow new layers with a one step two dimensional nucleation mechanism.

We study the phase equilibrium between liquid water and ice Ih modeled by the TIP4P/Ice interatomic potential using enhanced sampling molecular dynamics simulations. Our approach is based on the calculation of ice Ih-liquid free energy differences from simulations that visit reversibly both phases. The reversible interconversion is achieved by introducing a static bias potential as a function of an order parameter. The order parameter was tailored to crystallize the hexagonal diamond structure of oxygen in ice Ih. We analyze the effect of the system size on the ice Ih-liquid free energy differences and we obtain a melting temperature of 270 K in the thermodynamic limit. This result is in agreement with estimates from thermodynamic integration (272 K) and coexistence simulations (270 K). Since the order parameter does not include information about the coordinates of the protons, the spontaneously formed solid configurations contain proton disorder as expected for ice Ih., 9 pages, 6 figures

Significance Silica is one of the most abundant minerals in Earth’s crust and since the dawn of civilization its use has accompanied mankind’s technological evolution. Understanding crystallization is crucial in many industrial processes as well as in geology. Although experiments and simulations are difficult, we are able to perform an atomistic simulation of the β -cristobalite crystallization using an enhanced sampling method that uses as input only the intensity of the highest X-ray diffraction peak of β -cristobalite.

Canonical molecular dynamics simulations of crystal growth from solution suffer from severe finite-size effects. As the crystal grows, the solute molecules are drawn from the solution to the crystal, leading to a continuous drop in the solution concentration. This is in contrast to experiments in which the crystal grows at an approximately constant supersaturation of a bulk solution. Recently, Perego et al. [ J. Chem. Phys. 2015, 142, 144113] showed that in a periodic setup in which the crystal is represented as a slab, the concentration in the vicinity of the two surfaces can be kept constant while the molecules are drawn from a part of the solution that acts as a molecular reservoir. This method is quite effective in studying crystallization under controlled supersaturation conditions. However, once the reservoir is depleted, the constant supersaturation conditions cannot be maintained. We propose a variant of this method to tackle this depletion problem by simultaneously dissolving one side of the crystal while letting the other side grow. A continuous supply of particles to the solution due to the crystal dissolution maintains a steady solution concentration and avoids reservoir depletion. In this way, a constant supersaturation condition can be maintained for as long as necessary. We have applied this method to study the growth and dissolution of urea crystal from water solution under constant supersaturation and undersaturation conditions, respectively. The computed growth and dissolution rates are in good agreement with those obtained in previous studies.

From the Ising model and the Lennard-Jones fluid, to water and the iron-carbon system, phase diagrams are an indispensable tool to understand phase equilibria. In spite of the effort of the simulation community the calculation of a large portion of a phase diagram using computer simulation is still today a significant challenge. Here we propose a method to calculate phase diagrams involving liquid and solid phases by the reversible transformation of the liquid and the solid. To this end we introduce an order parameter that breaks the rotational symmetry and we leverage our recently introduced method to sample the multithermal-multibaric ensemble. In this way in a single molecular dynamics simulation we are able to compute the liquid-solid coexistence line for entire regions of the temperature and pressure phase diagram. We apply our approach to the bcc-liquid phase diagram of sodium and the fcc-bcc-liquid phase diagram of aluminum., 9 pages, 4 figures

An important characteristic that determines the behavior of a solute in water is whether it is hydrophobic or hydrophilic. The traditional classification is based on chemical experience and heuristics. However, this does not reveal how the local environment modulates this important property. We present a local fingerprint for hydrophobicity and hydrophilicity inspired by the two body contribution to the entropy. This fingerprint is an inexpensive, quantitative, and physically meaningful way of studying hydrophilicity and hydrophobicity that only requires as input the water-solute radial distribution functions. We apply our fingerprint to octanol, benzene, and 20 proteinogenic amino acids. Our measure of hydrophilicity is coherent with chemical experience, and moreover, it also shows how the character of an atom can change as its environment is changed. Finally, we use the fingerprint as a collective variable in a funnel metadynamics simulation of a host-guest system. The fingerprint serves as a desolvation collective variable that enhances transitions between the bound and unbound states. España Ministerio de Educacion Cultura y Deporte Grant (No. FPU14/02100)

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The hydrogen behavior in nanocrystalline W (ncW) samples with grain size of 5 and 10 nm is studied using Molecular Dynamics (MD) with a bond order potential (BOP) for the W-H system. The dependence of the hydrogen diffusion coefficient on grain size (5 and 10 nm) and hydrogen concentration (0.1 at.% < [H] < 10.0 at.%) is calculated. These data show that in all cases the hydrogen diffusion coefficient is lower for ncW than for coarse-grained samples. Trapping energies of grain boundaries are estimated and a broad distribution roughly centered at the vacancy trapping energy is found. Hydrogen diffusion results are interpreted within the trapping model by Kirchheim for nanocrystalline materials. The H-H interaction is evaluated and the possible formation of H2 is disregarded for the conditions in these simulations. Hydrogen segregation and trapping in grain boundaries for ncW is discussed, including extrapolations for micron-sized polycrystals. Fil: Piaggi, Pablo M.. Universidad Nacional de San Martín. Instituto Sabato; Argentina Fil: Bringa, Eduardo Marcial. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de Cuyo. Facultad de Ciencias Exactas y Naturales; Argentina Fil: Pasianot, Roberto Cesar. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad Nacional de San Martín. Instituto Sabato; Argentina. Comisión Nacional de Energía Atómica; Argentina Fil: Gordillo, Nuria. Universidad Politécnica de Madrid; España Fil: Panizo Laiz, M.. Universidad Politécnica de Madrid; España Fil: Del Río, J.. Universidad Complutense de Madrid; España Fil: Gómez De Castro, C.. Universidad Complutense de Madrid; España Fil: Gonzalez Arrabal, R.. Universidad Politécnica de Madrid; España

We introduce a computational method to discover polymorphs in molecular crystals at finite temperature. The method is based on reproducing the crystallization process starting from the liquid and letting the system discover the relevant polymorphs. This idea, however, conflicts with the fact that crystallization has a time scale much longer than that of molecular simulations. In order to bring the process within affordable simulation time, we enhance the fluctuations of a collective variable by constructing a bias potential with well tempered metadynamics. We use as collective variable an entropy surrogate based on an extended pair correlation function that includes the correlation between the orientation of pairs of molecules. We also propose a similarity metric between configurations based on the extended pair correlation function and a generalized Kullback-Leibler divergence. In this way, we automatically classify the configurations as belonging to a given polymorph using our metric and a hierarchical clustering algorithm. We find all relevant polymorphs for both substances and we predict new polymorphs. One of them is stabilized at finite temperature by entropic effects., Comment: 7 pages, 4 figures

In the ongoing intense quest to increase the photoconversion efficiencies of lead halide perovskites, it has become evident that optimizing the morphology of the material is essential to achieve high peformance. Despite the fact that nucleation plays a key role in controlling the crystal morphology, very little is known about the nucleation and crystal growth processes. Here, we perform metadynamics simulations of nucleation of methylammonium lead triiodide (MAPI) in order to unravel the atomistic details of perovskite crystallization from a $\gamma$-butyrolactone solution. The metadynamics trajectories show that the nucleation process takes place in several stages. Initially, dense amorphous clusters mainly consisting of lead and iodide appear from the homogeneous solution. These clusters evolve into lead iodide (PbI$_{2}$) like structures. Subsequently, methylammonium (MA$^{+}$) ions diffuse into this PbI$_{2}$-like aggregates triggering the transformation into a perovskite crystal through a solid-solid transformation. Demonstrating the crucial role of the monovalent cations in crystallization, our simulations provide key insights into the evolution of the perovskite microstructure which is essential to make high-quality perovskite based solar cells and optoelectronics.

We study by computer simulation the nucleation of a supersaturated Lennard-Jones vapor into the liquid phase. The large free energy barriers to transition make the time scale of this process impossible to study by ordinary molecular dynamics simulations.Therefore we use a recently developed enhanced sampling method [Valsson and Parrinello, Phys. Rev. Lett. 113, 090601 (2014)] based on the variational determination of a bias potential. We differ from previous applications of this method in that the bias is constructed on the basis of the physical model provided by the classical theory of nucleation. We examine the technical problems associated with this approach. Our results are very satisfactory and will pave the way for calculating the nucleation rates in many systems., Comment: 3 figures

We introduce a new fingerprint that allows distinguishing between liquid-like and solid-like atomic environments. This fingerprint is based on an approximate expression for the entropy projected on individual atoms. When combined with a local enthalpy, this fingerprint acquires an even finer resolution and it is capable of discriminating between different crystal structures., 6 pages, 4 figures

Computational crystal-phase prediction means have become an important tool in materials science for the acceleration of material discovery. Material phases stabilized by substantial entropic effects, however, cannot be accounted for with today’s widely used methods. We propose a new search method for such phases in the framework of metadynamics using surrogates for entropy and enthalpy as collective variables. Applying the method to AgI at low pressure, the method is found to be effective in discovering the material’s entropically stabilized superionic phase as well as its enthalpically stabilized β phase. Through calculating the material’s free-energy surfaces at different temperatures, we additionally estimate the system’s melting temperature as well as the transition temperature between the β and superionic phases. The calculation of the free energy is accelerated by the use of a path collective variable defined in the space of our surrogates for entropy and enthalpy.

Crystallization is a process of great practical relevance in which rare but crucial fluctuations lead to the formation of a solid phase starting from the liquid. Like in all first order first transitions there is an interplay between enthalpy and entropy. Based on this idea, to drive crystallization in molecular simulations, we introduce two collective variables, one enthalpic and the other entropic. Defined in this way, these collective variables do not prejudge the structure the system is going to crystallize into. We show the usefulness of this approach by studying the case of sodium and aluminum that crystallize in the bcc and fcc crystalline structure, respectively. Using these two generic collective variables, we perform variationally enhanced sampling and well tempered metadynamics simulations, and find that the systems transform spontaneously and reversibly between the liquid and the solid phases., 4 pages, 2 figures

Elemental gallium possesses several intriguing properties, such as a low melting point, a density anomaly and an electronic structure in which covalent and metallic features coexist. In order to simulate this complex system, we construct an ab initio quality interaction potential by training a neural network on a set of density functional theory calculations performed on configurations generated in multithermal–multibaric simulations. Here we show that the relative equilibrium between liquid gallium, α-Ga, β-Ga, and Ga-II is well described. The resulting phase diagram is in agreement with the experimental findings. The local structure of liquid gallium and its nucleation into α-Ga and β-Ga are studied. We find that the formation of metastable β-Ga is kinetically favored over the thermodinamically stable α-Ga. Finally, we provide insight into the experimental observations of extreme undercooling of liquid Ga., Exploring nucleation processes of gallium by molecular simulation is extremely challenging due to its structural complexity. Here the authors demonstrate a neural network potential trained on a multithermal–multibaric DFT data for the study of the phase diagram of gallium in a wide temperature and pressure range.