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

A self-learning algorithm for biased molecular dynamics

A new self-learning algorithm for accelerated dynamics, reconnaissance metadynamics, is proposed that is able to work with a very large number of collective coordinates. Acceleration of the dynamics is achieved by constructing a bias potential in terms of a patchwork of one-dimensional, locally valid collective coordinates. These collective coordinates are obtained from trajectory analyses so that they adapt to any new features encountered during the simulation. We show how this methodology can be used to enhance sampling in real chemical systems citing examples both from the physics of clusters and from the biological sciences.Comment: 6 pages, 5 figures + 9 pages of supplementary informatio

Microscopic Mechanism and Kinetics of Ice Formation at Complex Interfaces: Zooming in on Kaolinite

Most ice in nature forms thanks to impurities which boost the exceedingly low nucleation rate of pure supercooled water. However, the microscopic details of ice nucleation on these substances remain largely unknown. Here, we have unraveled the molecular mechanism and the kinetics of ice formation on kaolinite, a clay mineral playing a key role in climate science. We find that the formation of ice at strong supercooling in the presence of this clay is twenty orders of magnitude faster than homogeneous freezing. The critical nucleus is substantially smaller than that found for homogeneous nucleation and, in contrast to the predictions of classical nucleation theory (CNT), it has a strong 2D character. Nonetheless, we show that CNT describes correctly the formation of ice at this complex interface. Kaolinite also promotes the exclusive nucleation of hexagonal ice, as opposed to homogeneous freezing where a mixture of cubic and hexagonal polytypes is observed

Building Maps in Collective Variable Space

Enhanced sampling techniques such as umbrella sampling and metadynamics are now routinely used to provide information on how the thermodynamic potential, or free energy, depends on a small number of collective variables. The free energy surfaces that one extracts by using these techniques provide a simplified or coarse-grained representation of the configurational ensemble. In this work we discuss how auxiliary variables can be mapped in collective variable (CV) space and how the dependence of the average value of a function of the atomic coordinates on the value of a small number of CVs can thus be visualised. We show that these maps allow one to analyse both the physics of the molecular system under investigation and the quality of the reduced representation of the system that is encoded in a set of CVs. We apply this approach to analyse the degeneracy of CVs and to compute entropy and enthalpy surfaces in CV space both for conformational transitions in alanine dipeptide and for phase transitions in carbon dioxide molecular crystals under pressure.Comment: 13 pages, 8 figure

Structure and energy relationships in ice and crystalline hydrates.

Computer simulations of the various phases of ice have been carried out using potential methods and density functional theory. Plane wave DFT and subsequent Wannier transformations of the Kohn-Sham orbitals were used to obtain highly localised orbitals, which were treated as molecular orbitals in the calculation of molecular multipoles. Using these multipoles it has been shown that the energy differences, calculated using DFT, between different proton topologies of ice VII and Ih are reproduced when the interaction electrostatic potential energy is calculated up to terms in (1/r6) and thus that the driving force for proton ordering is electro static. Armed with this knowledge, successful blind predictions, which have been experimentally verified, of the proton ordered forms of ice V and XII (ices XIII and XIV respectively) have been made using plane wave DFT. The recently developed TIP6P potential has been modified so as to reproduce the correct structure for ice XI, the proton ordered form of ice Ih, and to reproduce the DFT energy differences between different hydrogen bonding topologies. Total energy calculations, using this potential, show that the surface energy depends strongly on the hydrogen bond topology exposed at the surface. In particular surfaces on which under-coordinated protons are clustered have high energies. Monte Carlo calculations have shown that the hydrogen bond topology adopted by ice, both at the surface and in the bulk, depends on the temperature. A comparison of the structures that are possible to make out of silica and ice has been undertaken in the hope that new ice and silica phases can be identified. This comparison is possible because both silica and water form the backbones of 4-connected nets. DFT calculations have shown that the energy maps of the various four connected nets are very similar for both structures, with any differences arising because of the greater flexibility of the O-Si-O angle in silica. Furthermore, this analysis has highlighted a number of potential new ice phases and led to the proposal of a synthetic route to a new clathrate based on the zeolite framework SGT

A Fully Quantum-Mechanical Treatment for Kaolinite

Neural network potentials for kaolinite minerals have been fitted to data extracted from density functional theory calculation that were performed using the revPBE + D3 and revPBE + vdW functionals. These potentials have then been used to calculate static and dynamic properties of the mineral. We show that revPBE + vdW is better at reproducing the static properties. However, revPBE + D3 does a better job of reproducing the experimental IR spectrum. We also consider what happens to these properties when a fully-quantum treatment of the nuclei is employed. We find that nuclear quantum effects (NQEs) do not make a substantial difference to the static properties. However, when NQEs are included the dynamic properties of the material change substantially.Comment: 12 pages (10 supplementary), 6 figures (10 supplementary

Modeling the ferroelectric phase transition in barium titanate with DFT accuracy and converged sampling

The accurate description of the structural and thermodynamic properties of ferroelectrics has been one of the most remarkable achievements of Density Functional Theory (DFT). However, running large simulation cells with DFT is computationally demanding, while simulations of small cells are often plagued with non-physical effects that are a consequence of the system's finite size. Therefore, one is often forced to use empirical models that describe the physics of the material in terms of effective interaction terms, that are fitted using the results from DFT, to perform simulations that do not suffer from finite size effects. In this study we use a machine-learning (ML) potential trained on DFT, in combination with accelerated sampling techniques, to converge the thermodynamic properties of Barium Titanate (BTO) with first-principles accuracy and a full atomistic description. Our results indicate that the predicted Curie temperature depends strongly on the choice of DFT functional and system size, due to the presence of emergent long-range directional correlations in the local dipole fluctuations. Our findings demonstrate how the combination of ML models and traditional bottom-up modeling allow one to investigate emergent phenomena with the accuracy of first-principles calculations and the large size and time scales afforded by empirical models.Comment: 15 pages, 10 figure

Ice formation on kaolinite: Insights from molecular dynamics simulations

The formation of ice affects many aspects of our everyday life as well as important technologies such as cryotherapy and cryopreservation. Foreign substances almost always aid water freezing through heterogeneous ice nucleation, but the molecular details of this process remain largely unknown. In fact, insight into the microscopic mechanism of ice formation on different substrates is difficult to obtain even if state-of-the-art experimental techniques are used. At the same time, atomistic simulations of heterogeneous ice nucleation frequently face extraordinary challenges due to the complexity of the water-substrate interaction and the long time scales that characterize nucleation events. Here, we have investigated several aspects of molecular dynamics simulations of heterogeneous ice nucleation considering as a prototypical ice nucleating material the clay mineral kaolinite, which is of relevance in atmospheric science. We show via seeded molecular dynamics simulations that ice nucleation on the hydroxylated (001) face of kaolinite proceeds exclusively via the formation of the hexagonal ice polytype. The critical nucleus size is two times smaller than that obtained for homogeneous nucleation at the same supercooling. Previous findings suggested that the flexibility of the kaolinite surface can alter the time scale for ice nucleation within molecular dynamics simulations. However, we here demonstrate that equally flexible (or non flexible) kaolinite surfaces can lead to very different outcomes in terms of ice formation, according to whether or not the surface relaxation of the clay is taken into account. We show that very small structural changes upon relaxation dramatically alter the ability of kaolinite to provide a template for the formation of a hexagonal overlayer of water molecules at the water-kaolinite interface, and that this relaxation therefore determines the nucleation ability of this mineral

Computational evaluation of the diffusion mechanisms for C8 aromatics in porous organic cages

The development of adsorption and membrane-based separation technologies toward more energy and cost-efficient processes is a significant engineering problem facing the world today. An example of a process in need of improvement is the separation of C8 aromatics to recover para-xylene, which is the precursor to the widely used monomer terephthalic acid. Molecular simulations were used to investigate whether the separation of C8 aromatics can be carried out by the porous organic cages CC3 and CC13, both of which have been previously used in the fabrication of amorphous thin-film membranes. Metadynamics simulations showed significant differences in the energetic barriers to the diffusion of different C8 aromatics through the porous cages, especially for CC3. These differences imply that meta-xylene and ortho-xylene will take significantly longer to enter or leave the cages. Therefore, it may be possible to use membranes composed of these materials to separate ortho- and meta-xylene from para-xylene by size exclusion. Differences in the C8 aromatics’ diffusion barriers were caused by their different diffusion mechanisms, while the lower selectivity of CC13 was largely down to its more significant pore breathing. These observations will aid the future design of adsorbents and membrane systems with improved separation performance