Entropy based fingerprint for local crystalline order

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.Comment: 6 pages, 4 figure

Phase equilibrium of liquid water and hexagonal ice from enhanced sampling molecular dynamics simulations

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.Comment: 9 pages, 6 figure

Enhancing entropy and enthalpy fluctuations to drive crystallization in atomistic simulations

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.Comment: 4 pages, 2 figure

Enhancing the formation of ionic defects to study the ice Ih/XI transition with molecular dynamics simulations

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.Comment: 17 pages, 9 figure

Predicting polymorphism in molecular crystals using orientational entropy

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 figure

Naphthalene crystal shape prediction from molecular dynamics simulations

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., 142, 2015, 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 $\{00\bar{1}\}$ face grows in a two step two dimensional nucleation mechanism while the considerably faster growing faces $\{1\bar{1}0\}$ and $\{20\bar{1}\}$ grow new layers with a one step two dimensional nucleation mechanism

A local fingerprint for hydrophobicity and hydrophilicity: from methane to peptides

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 the 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. Lastly, we use the fingerprint as 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

Phase equilibrium of water with hexagonal and cubic ice using the SCAN functional

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 figure