New model for aspartic acid species in aqueous calcium carbonate growth environments: challenges and perspectives.

The lack of experimental data on the dynamics of aspartic acid species in water for its range of protonation states and the details of their atomic-level interaction with aqueous calcium carbonate species is a driver for accurate force field development. A classical model that is consistent with the few pieces of experimental data available and with first principles calculations has been developed. The complex dynamics of the aspartate anions relevant to biomineralization and calcium carbonate crystal growth has been explored in water, providing a quantitative description of solvation structure and free energies, including conformational free energy profiles and pairing free energies. The model has been used to probe the structure and dynamics of aqueous calcium aspartate homo- and hetero-chiral clusters, confirming their unlikelihood due to weak and water-mediated interactions. This supports the hypothesis that the formation of such clusters, observed while growing vaterite in the presence of acidic chiral amino acids, is favoured by the presence of the crystal surface.

Solubility-consistent force field simulations for aqueous metal carbonate systems using graphical processing units.

Crystallization of alkaline earth metal carbonates from water is important for biomineralization and environmental geochemistry. Here, large-scale computer simulations are a useful approach to complement experimental studies by providing atomistic insights and even by quantitatively determining the thermodynamics of individual steps. However, this is dependent on the existence of force field models that are sufficiently accurate while being computationally efficient enough to sample complex systems. Here, we introduce a revised force field for aqueous alkaline earth metal carbonates that reproduces both the solubilities of the crystalline anhydrous minerals, as well as the hydration free energies of the ions. The model is also designed to run efficiently on graphical processing units thereby reducing the cost of such simulations. The performance of the revised force field is compared against previous results for important properties relevant to crystallization, including ion-pairing and mineral-water interfacial structure and dynamics. This article is part of a discussion meeting issue 'Supercomputing simulations of advanced materials'.

Computational workflows for perovskites: case study for lanthanide manganites.

Robust computational workflows are important for explorative computational studies, especially for cases where detailed knowledge of the system structure or other properties is not available. In this work, we propose a computational protocol for appropriate method selection for the study of lattice constants of perovskites using density functional theory, based strictly on open source software. The protocol does not require a starting crystal structure. We validate this protocol using a set of crystal structures of lanthanide manganites, surprisingly finding N12+U to be the best performing method for this class of materials out of the 15 density functional approximations studied. We also highlight that +U values derived from linear response theory are robust and their use leads to improved results. We investigate whether the performance of methods for predicting the bond length of related gas phase diatomics correlates with their performance for bulk structures, showing that care is required when interpreting benchmark results. Finally, using defective LaMnO3 as a case study, we investigate whether the four shortlisted methods (HCTH120, OLYP, N12+U, PBE+U) can computationally reproduce the experimentally determined fraction of MnIV+ at which the orthorhombic to rhombohedral phase transition occurs. The results are mixed, with HCTH120 providing good quantitative agreement with experiment, but failing to capture the spatial distribution of defects linked to the electronic structure of the system.

Predicting crystal growth via a unified kinetic three-dimensional partition model.

Understanding and predicting crystal growth is fundamental to the control of functionality in modern materials. Despite investigations for more than one hundred years, it is only recently that the molecular intricacies of these processes have been revealed by scanning probe microscopy. To organize and understand this large amount of new information, new rules for crystal growth need to be developed and tested. However, because of the complexity and variety of different crystal systems, attempts to understand crystal growth in detail have so far relied on developing models that are usually applicable to only one system. Such models cannot be used to achieve the wide scope of understanding that is required to create a unified model across crystal types and crystal structures. Here we describe a general approach to understanding and, in theory, predicting the growth of a wide range of crystal types, including the incorporation of defect structures, by simultaneous molecular-scale simulation of crystal habit and surface topology using a unified kinetic three-dimensional partition model. This entails dividing the structure into 'natural tiles' or Voronoi polyhedra that are metastable and, consequently, temporally persistent. As such, these units are then suitable for re-construction of the crystal via a Monte Carlo algorithm. We demonstrate our approach by predicting the crystal growth of a diverse set of crystal types, including zeolites, metal-organic frameworks, calcite, urea and l-cystine.

Crystal Nucleation and Growth of Inorganic Ionic Materials from Aqueous Solution: Selected Recent Developments, and Implications.

In this review article, selected, latest theoretical, and experimental developments in the field of nucleation and crystal growth of inorganic materials from aqueous solution are highlighted, with a focus on literature after 2015 and on non-classical pathways. A key point is to emphasize the so far underappreciated role of water and solvent entropy in crystallization at all stages from solution speciation through to the final crystal. While drawing on examples from current inorganic materials where non-classical behavior has been proposed, the potential of these approaches to be adapted to a wide-range of systems is also discussed, while considering the broader implications of the current re-assessment of pathways for crystallization. Various techniques that are suitable for the exploration of crystallization pathways in aqueous solution, from nucleation to crystal growth are summarized, and a flow chart for the assignment of specific theories based on experimental observations is proposed.

Structure and Surface Complexation at the Calcite(104)-Water Interface.

Calcite is the most stable polymorph of calcium carbonate (CaCO3) under ambient conditions and is ubiquitous in natural systems. It plays a major role in controlling pH in environmental settings. Electrostatic phenomena at the calcite-water interface and the surface reactivity of calcite in general have important environmental implications. They may strongly impact nutrient and contaminant mobility in soils and other subsurface environments, they control oil recovery from limestone reservoirs, and they may impact the safety of nuclear waste disposal sites. Besides the environmental relevance, the topic is significant for industrial applications and cultural heritage preservation. In this study, the structure of the calcite(104)-water interface is investigated on the basis of a new extensive set of crystal truncation rod data. The results agree with recently reported structures and resolve previous ambiguities with respect to the coordination sphere of surface Ca ions. These structural features are introduced into an electrostatic three-plane surface complexation model, describing ion adsorption and charging at the calcite-water interface. Inner surface potential data for calcite, as measured with a calcite single-crystal electrode, are used as constraints for the model in addition to zeta potential data. Ion adsorption parameters are compared with molecular dynamics simulations. All model parameters, including protonation constants, ion-binding parameters, and Helmholtz capacitances, are within physically and chemically plausible ranges. A PhreeqC version of the model is presented, which we hope will foster application of the model in environmental studies.

Simulating the binding of key organic functional groups to aqueous calcium carbonate species.

The interaction of organic molecules with mineral systems is relevant to a wide variety of scientific problems both in the environment and minerals processing. In this study, the coordination of small organics that contain the two most relevant functional groups for biomineralisation of calcium carbonate, namely carboxylate and ammonium, with the corresponding mineral ions are examined in aqueous solution. Specifically, two force fields have been examined based on rigid-ion or polarisable models, with the latter being within the AMOEBA formalism. Here the parameters for the rigid-ion model are determined to target the accurate reproduction of the hydration structure and solvation thermodynamics, while both force fields are designed to be compatible with the corresponding recently published models for aqueous calcium carbonate. The application of these force fields to ion pairing in aqueous solution is studied in order to quantitatively determine the extent of association.

Uncovering the Role of Bicarbonate in Calcium Carbonate Formation at Near-Neutral pH.

Mechanistic pathways relevant to mineralization are not well-understood fundamentally, let alone in the context of their biological and geological environments. Through quantitative analysis of ion association at near-neutral pH, we identify the involvement of HCO3- ions in CaCO3 nucleation. Incorporation of HCO3- ions into the structure of amorphous intermediates is corroborated by solid-state nuclear magnetic resonance spectroscopy, complemented by quantum mechanical calculations and molecular dynamics simulations. We identify the roles of HCO3- ions as being through (i) competition for ion association during the formation of ion pairs and ion clusters prior to nucleation and (ii) incorporation as a significant structural component of amorphous mineral particles. The roles of HCO3- ions as active soluble species and structural constituents in CaCO3 formation are of fundamental importance and provide a basis for a better understanding of physiological and geological mineralization.

Molecular dynamics simulations of liquid-liquid interfaces in an electric field: The water-1,2-dichloroethane interface.

The polarized interface between two immiscible liquids plays a central role in many technological processes. In particular, for electroanalytical and ion extraction applications, an external electric field is typically used to selectively induce the transfer of ionic species across the interfaces. Given that it is experimentally challenging to obtain an atomistic insight into the ion transfer process and the structure of liquid-liquid interfaces, atomistic simulations have often been used to fill this knowledge gap. However, due to the long-range nature of the electrostatic interactions and the use of 3D periodic boundary conditions, the use of external electric fields in molecular dynamics simulations requires special care. Here, we show how the simulation setup affects the dielectric response of the materials and demonstrate how by a careful design of the system it is possible to obtain the correct electric field on both sides of a liquid-liquid interface when using standard 3D Ewald summation methods. In order to prove the robustness of our approach, we ran extensive molecular dynamics simulations with a rigid-ion and polarizable force field of the water/1,2-dichloroethane interface in the presence of weak external electric fields.

Resolving Point Defects in the Hydration Structure of Calcite (10.4) with Three-Dimensional Atomic Force Microscopy.

It seems natural to assume that defects at mineral surfaces critically influence interfacial processes such as the dissolution and growth of minerals in water. The experimental verification of this claim, however, is challenging and requires real-space methods with utmost spatial resolution, such as atomic force microscopy (AFM). While defects at mineral-water interfaces have been resolved in 2D AFM images before, the perturbation of the surrounding hydration structure has not yet been analyzed experimentally. In this Letter, we demonstrate that point defects on the most stable and naturally abundant calcite (10.4) surface can be resolved using high-resolution 3D AFM-even within the fifth hydration layer. Our analysis of the hydration structure surrounding the point defect shows a perturbation of the hydration with a lateral extent of approximately one unit cell. These experimental results are corroborated by molecular dynamics simulations.

Uncovering the Atomistic Mechanism for Calcite Step Growth.

Determining a complete atomic-level picture of how minerals grow from aqueous solution remains a challenge as macroscopic rates can be a convolution of many reactions. For the case of calcite (CaCO3 ) in water, computer simulations have been used to map the complex thermodynamic landscape leading to growth of the two distinct steps, acute and obtuse, on the basal surface. The carbonate ion is found to preferentially adsorb at the upper edge of acute steps while Ca2+ only adsorbs after CO32- . In contrast to the conventional picture, ion pairs prefer to bind at the upper edge of the step with only one ion, at most, coordinated to the step and lower terrace. Migration of the first carbonate ion to a growth site is found to be rate-limiting for kink nucleation, with this process having a lower activation energy on the obtuse step.

Can Point Defects in Surfaces in Solution be Atomically Resolved by Atomic Force Microscopy?

While the atomic force microscope (AFM) is able to image mineral surfaces in solution with atomic resolution, so far, it has been a matter of debate whether imaging point defects is also possible under these conditions. The difficulties stem from the limited knowledge of what types of defects may be stable in the presence of an AFM tip, as well as from the complicated imaging mechanism involving interactions between hydration layers over the surface and around the tip apex. Here, we present atomistic molecular dynamics and free energy calculations of the AFM imaging of vacancies and ionic substitutions in the calcite (101[over ¯]4) surface in water, using a new silica AFM tip model. Our results indicate that both calcium and carbonate vacancies, as well as a magnesium substitution, could be resolved in an AFM experiment, albeit with different imaging mechanisms.

Entropy Drives Calcium Carbonate Ion Association.

The understanding of the molecular mechanisms underlying the early stages of crystallisation is still incomplete. In the case of calcium carbonate, experimental and computational evidence suggests that phase separation relies on so-called pre-nucleation clusters (PNCs). A thorough thermodynamic analysis of the enthalpic and entropic contributions to the overall free energy of PNC formation derived from three independent methods demonstrates that solute clustering is driven by entropy. This can be quantitatively rationalised by the release of water molecules from ion hydration layers, explaining why ion association is not limited to simple ion pairing. The key role of water release in this process suggests that PNC formation should be a common phenomenon in aqueous solutions.

A general forcefield for accurate phonon properties of metal-organic frameworks.

We report the development of a forcefield capable of reproducing accurate lattice dynamics of metal-organic frameworks. Phonon spectra, thermodynamic and mechanical properties, such as free energies, heat capacities and bulk moduli, are calculated using the quasi-harmonic approximation to account for anharmonic behaviour due to thermal expansion. Comparison to density functional theory calculations of properties such as Grüneisen parameters, bulk moduli and thermal expansion supports the accuracy of the derived forcefield model. Material properties are also reported in a full analysis of the lattice dynamics of an initial subset of structures including: MOF-5, IRMOF-10, UiO-66, UiO-67, NOTT-300, MIL-125, MOF-74 and MOF-650.

Pre-nucleation clusters as solute precursors in crystallisation.

Crystallisation is at the heart of various scientific disciplines, but still the understanding of the molecular mechanisms underlying phase separation and the formation of the first solid particles in aqueous solution is rather limited. In this review, classical nucleation theory, as well as established concepts of spinodal decomposition and liquid-liquid demixing, is introduced together with a description of the recently proposed pre-nucleation cluster pathway. The features of pre-nucleation clusters are presented and discussed in relation to recent modifications of the classical and established models for phase separation, together with a review of experimental work and computer simulations on the characteristics of pre-nucleation clusters of calcium phosphate, calcium carbonate, iron(oxy)(hydr)oxide, silica, and also amino acids as an example of small organic molecules. The role of pre-nucleation clusters as solute precursors in the emergence of a new phase is summarized, and the link between the chemical speciation of homogeneous solutions and the process of phase separation via pre-nucleation clusters is highlighted.

Redefined ion association constants have consequences for calcium phosphate nucleation and biomineralization.

Calcium orthophosphates (CaPs), as hydroxyapatite (HAP) in bones and teeth are the most important biomineral for humankind. While clusters in CaP nucleation have long been known, their speciation and mechanistic pathways to HAP remain debated. Evidently, mineral nucleation begins with two ions interacting in solution, fundamentally underlying solute clustering. Here, we explore CaP ion association using potentiometric methods and computer simulations. Our results agree with literature association constants for Ca2+ and H2PO4-, and Ca2+ and HPO42-, but not for Ca2+ and PO43- ions, which previously has been strongly overestimated by two orders of magnitude. Our data suggests that the discrepancy is due to a subtle, premature phase separation that can occur at low ion activity products, especially at higher pH. We provide an important revision of long used literature constants, where association of Ca2+ and PO43- actually becomes negligible below pH 9.0, in contrast to previous values. Instead, [CaHPO4]0 dominates the aqueous CaP speciation between pH ~6-10. Consequently, calcium hydrogen phosphate association is critical in cluster-based precipitation in the near-neutral pH regime, e.g., in biomineralization. The revised thermodynamics reveal significant and thus far unexplored multi-anion association in computer simulations, constituting a kinetic trap that further complicates aqueous calcium phosphate speciation.

A transferable quantum mechanical energy model for intermolecular interactions using a single empirical parameter.

The calculation of intermolecular interactions in molecular crystals using model energies provides a unified route to understanding the complex interplay of driving forces in crystallization, elastic properties and more. Presented here is a new single-parameter interaction energy model (CE-1p), extending the previous CrystalExplorer energy model and calibrated using density functional theory (DFT) calculations at the ωB97M-V/def2-QZVP level over 1157 intermolecular interactions from 147 crystal structures. The new model incorporates an improved treatment of dispersion interactions and polarizabilities using the exchange-hole dipole model (XDM), along with the use of effective core potentials (ECPs), facilitating application to molecules containing elements across the periodic table (from H to Rn). This new model is validated against high-level reference data with outstanding performance, comparable to state-of-the-art DFT methods for molecular crystal lattice energies over the X23 set (mean absolute deviation 3.6 kJ mol-1) and for intermolecular interactions in the S66x8 benchmark set (root mean-square deviation 3.3 kJ mol-1). The performance of this model is further examined compared to the GFN2-xTB tight-binding model, providing recommendations for the evaluation of intermolecular interactions in molecular crystal systems.

CrystalClear: an open, modular protocol for predicting molecular crystal growth from solution.

We present a new protocol for the prediction of free energies that determine the growth of sites in molecular crystals for subsequent use in Monte Carlo simulations using tools such as CrystalGrower [Hill et al., Chemical Science, 2021, 12, 1126-1146]. Key features of the proposed approach are that it requires minimal input, namely the crystal structure and solvent only, and provides automated, rapid generation of the interaction energies. The constituent components of this protocol, namely interactions between molecules (growth units) in the crystal, solvation contributions and treatment of long-range interactions are described in detail. The power of this method is shown via prediction of crystal shapes for ibuprofen grown from ethanol, ethyl acetate, toluene and acetonitrile, adipic acid grown from water, and five polymorphs (ON, OP, Y, YT04 and R) of ROY (5-methyl-2-[(2-nitrophenyl)amino]-3-thiophenecarbonitrile), with promising results. The predicted energies may be used directly or subsequently refined against experimental data, facilitating insight into the interactions governing crystal growth, while also providing a prediction of the solubility of the material. The protocol has been implemented in standalone, open-source software made available alongside this publication.

Accurate rates of the complex mechanisms for growth and dissolution of minerals using a combination of rare-event theories.

Mineral growth and dissolution are often treated as occurring via a single reversible process that governs the rate of reaction. We show that multiple distinct intermediate states can occur during both growth and dissolution. Specifically, we used metadynamics, a method for efficiently exploring the free-energy landscape of a system, coupled to umbrella sampling and reactive flux calculations to examine the mechanism and rates of attachment and detachment of a barium ion onto a stepped barite (BaSO(4)) surface. The activation energies calculated for the rate-limiting reactions, which are different for attachment and detachment, precisely match those measured experimentally during both growth and dissolution. These results can potentially explain anomalous non-steady-state mineral reaction rates observed experimentally and will enable the design of more efficient growth inhibitors and facilitate an understanding of the effect of impurities.

Calcium carbonate polyamorphism and its role in biomineralization: how many amorphous calcium carbonates are there?

Although the polymorphism of calcium carbonate is well known, and its polymorphs--calcite, aragonite, and vaterite--have been highly studied in the context of biomineralization, polyamorphism is a much more recently discovered phenomenon, and the existence of more than one amorphous phase of calcium carbonate in biominerals has only very recently been understood. Here we summarize what is known about polyamorphism in calcium carbonate as well as what is understood about the role of amorphous calcium carbonate in biominerals. We show that consideration of the amorphous forms of calcium carbonate within the physical notion of polyamorphism leads to new insights when it comes to the mechanisms by which polymorphic structures can evolve in the first place. This not only has implications for our understanding of biomineralization, but also of the means by which crystallization may be controlled in medical, pharmaceutical, and industrial contexts.