Computing the Absolute Gibbs Free Energy in Atomistic Simulations: Applications to Defects in Solids

The Gibbs free energy is the fundamental thermodynamic potential underlying the relative stability of different states of matter under constant-pressure conditions. However, computing this quantity from atomic-scale simulations is far from trivial. As a consequence, all too often the potential energy of the system is used as a proxy, overlooking entropic and anharmonic effects. Here we discuss a combination of different thermodynamic integration routes to obtain the absolute Gibbs free energy of a solid system starting from a harmonic reference state. This approach enables the direct comparison between the free energy of different structures, circumventing the need to sample the transition paths between them. We showcase this thermodynamic integration scheme by computing the Gibbs free energy associated with a vacancy in BCC iron, and the intrinsic stacking fault free energy of nickel. These examples highlight the pitfalls of estimating the free energy of crystallographic defects only using the minimum potential energy, which overestimates the vacancy free energy by 60% and the stacking-fault energy by almost 300% at temperatures close to the melting point

Theoretical prediction of the homogeneous ice nucleation rate: disentangling thermodynamics and kinetics

Estimating the homogeneous ice nucleation rate from undercooled liquid water is at the same time crucial for understanding many important physical phenomena and technological applications, and challenging for both experiments and theory. From a theoretical point of view, difficulties arise due to the long time scales required, as well as the numerous nucleation pathways involved to form ice nuclei with different stacking disorders. We computed the homogeneous ice nucleation rate at a physically relevant undercooling for a single-site water model, taking into account the diffuse nature of ice-water interfaces, stacking disorders in ice nuclei, and the addition rate of particles to the critical nucleus.We disentangled and investigated the relative importance of all the terms, including interfacial free energy, entropic contributions and the kinetic prefactor, that contribute to the overall nucleation rate.There has been a long-standing discrepancy for the predicted homogeneous ice nucleation rates, and our estimate is faster by 9 orders of magnitude compared with previous literature values. Breaking down the problem into segments and considering each term carefully can help us understand where the discrepancy may come from and how to systematically improve the existing computational methods

Direct path integral estimators for isotope fractionation ratios

Fractionation of isotopes among distinct molecules or phases is a quantum effect which is often exploited to obtain insights on reaction mechanisms, biochemical, geochemical and atmospheric phenomena. Accurate evaluation of isotope ratios in atomistic simulations is challenging, because one needs to perform a thermodynamic integration with respect to the isotope mass, along with time-consuming path integral calculations. By re-formulating the problem as a particle exchange in the ring polymer partition function, we derive new estimators giving direct access to the differential partitioning of isotopes, which can simplify the calculations by avoiding thermodynamic integration. We demonstrate the efficiency of these estimators by applying them to investigate the isotope fractionation ratios in the gas-phase Zundel cation, and in a few simple hydrocarbons.Comment: 13 pages, 7 figure

Computing the Tolman length for solid-liquid interfaces

The curvature dependence of interfacial free energy, which is crucial in quantitatively predicting nucleation kinetics and the stability of bubbles and droplets, can be described in terms of the Tolman length {\delta}. For solid-liquid interfaces, however,{\delta} has never been computed directly due to various theoretical and practical challenges. Here we present a general method that enables the direct evaluation of the Tolman length from atomistic simulations of a solid-liquid planar interface in out-of-equilibrium conditions. This method works by first measuring the surface tension from the amplitude of thermal capillary fluctuations of a localized version of Gibbs dividing surface, and bythen computing the free energy difference between the surface of tension and the equimolar dividing surface. For benchmark purposes, we computed {\delta}for a model potential, and compared the results to less rigorous indirect approaches

The Gibbs free energy of homogeneous nucleation: from atomistic nuclei to the planar limit

In this paper we discuss how the information contained in atomistic simulations of homogeneous nucleation should be used when fitting the parameters in macroscopic nucleation models. We show how the number of solid and liquid atoms in such simulations can be determined unambiguously by using a Gibbs dividing surface and how the free energy as a function of the number of solid atoms in the nucleus can thus be extracted. We then show that the parameters of a model based on classical nucleation theory can be fit using the information contained in these free-energy profiles but that the parameters in such models are highly correlated. This correlation is unfortunate as it ensures that small errors in the computed free energy surface can give rise to large errors in the extrapolated properties of the fitted model. To resolve this problem we thus propose a method for fitting macroscopic nucleation models that uses simulations of planar interfaces and simulations of three-dimensional nuclei in tandem. We show that when the parameters of the macroscopic model are fitted in this way the numerical errors for the final fitted model are smaller and that the extrapolated predictions for large nuclei are thus more reliable

Hydrogen Diffusion and Trapping in {\alpha}-Iron: The Role of Quantum and Anharmonic Fluctuations

We investigate the thermodynamics and kinetics of a hydrogen interstitial in magnetic {\alpha}-iron, taking account of the quantum fluctuations of the proton as well as the anharmonicities of lattice vibrations and hydrogen hopping. We show that the diffusivity of hydrogen in the lattice of BCC iron deviates strongly from an Arrhenius behavior at and below room temperature. We compare a quantum transition state theory to explicit ring polymer molecular dynamics in the calculation of diffusivity and we find that the role of phonons is to inhibit, not to enhance, diffusivity at intermediate temperatures in constrast to the usual polaron picture of hopping. We then address the trapping of hydrogen by a vacancy as a prototype lattice defect. By a sequence of steps in a thought experiment, each involving a thermodynamic integration, we are able to separate out the binding free energy of a proton to a defect into harmonic and anharmonic, and classical and quantum contributions. We find that about 30% of a typical binding free energy of hydrogen to a lattice defect in iron is accounted for by finite temperature effects and about half of these arise from quantum proton fluctuations. This has huge implications for the comparison between thermal desorption and permeation experiments and standard electronic structure theory. The implications are even greater for the interpretation of muon spin resonance experiments

A streamlined molecular-dynamics workflow for computing solubilities of molecular and ionic crystals

Computing the solubility of crystals in a solvent using atomistic simulations is notoriously challenging due to the complexities and convergence issues associated with free-energy methods, as well as the slow equilibration in direct-coexistence simulations. This paper introduces a molecular-dynamics workflow that simplifies and robustly computes the solubility of molecular or ionic crystals. This method is considerably more straightforward than the state-of-the-art, as we have streamlined and optimised each step of the process. Specifically, we calculate the chemical potential of the crystal using the gas-phase molecule as a reference state, and employ the S0 method to determine the concentration dependence of the chemical potential of the solute. We use this workflow to predict the solubilities of sodium chloride in water, urea polymorphs in water, and paracetamol polymorphs in both water and ethanol. Our findings indicate that the predicted solubility is sensitive to the chosen potential energy surface. Furthermore, we note that the harmonic approximation often fails for both molecular crystals and gas molecules at or above room temperature, and that the assumption of an ideal solution becomes less valid for highly soluble substances

Bridging the gap between atomistic and macroscopic models of homogeneous nucleation

Macroscopic theories of nucleation such as classical nucleation theory envision that clusters of the bulk stable phase form inside the bulk metastable phase. Molecular dynamics simulations are often used to elucidate nucleation mechanisms, by capturing the microscopic configurations of all the atoms. In this paper, we introduce a thermodynamic model that links macroscopic theories and atomicscale simulations and thus provide a simple and elegant framework for testing the limits of classical nucleation theory. Published by AIP Publishing