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.

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.

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.

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.

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'.

Obtaining Consistent Free Energies for Ion Binding at Surfaces from Solution: Pathways versus Alchemy for Determining Kink Site Stability.

Ion incorporation or removal from a solid at the interface with solution is a fundamental part of crystal growth. Despite this, there have been few quantitative determinations of the thermodynamics for such processes from atomistic molecular dynamics due to the associated technical challenges. In this study, we compute the free energies for ion removal from kink sites at the interface between NaCl and water as an illustrative example. To examine the influence of the free energy technique used, we compare methods that follow an explicit pathway for dissolution with those that focus on the thermodynamics of the initial and final states using metadynamics and free energy perturbation, respectively. While the initial results of the two approaches are found to be completely different, it is demonstrated that the thermodynamics can be reconciled with appropriate corrections for the standard states, thus illustrating the need for caution in interpreting raw free energy curves for ion binding as widely found in the literature. In addition, a new efficient approach is introduced to correct for the system size dependence of kink site energies both due to the periodic interaction of charges in an inhomogeneous dielectric system and due to the dipolar interactions between pairs of kinks along a row. Ultimately, it is shown that with suitable care, both classes of free energy techniques are capable of producing kink site stabilities that are consistent with the solubility of the underlying bulk solid. However, the precise values for individual kink sites exhibit a small systematic offset, which can be ascribed to the contribution of the interfacial potential to the pathway-based results. For the case of NaCl, the free energies of the kink sites relative to a 1 M aqueous solution for Na+ and Cl- are found to be surprisingly different and of opposite sign, despite the ions having very similar hydration free energies.

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.

Calculations of the Evolution of the Ca L23 Fine Structure in Amorphous Calcium Carbonate.

Amorphous calcium carbonate (ACC) has been found in many different organisms. Biogenic ACC is frequently a precursor in the formation of calcite and aragonite. The process of structural transformation is therefore of great interest in the study of crystallization pathways in biomineralization. Changes in the prepeak/main peak (L2'/L2) intensity ratio of the Ca L23-edge X-ray absorption spectroscopy (XAS) of Ca-rich particles in skeleton-building cells of sea urchin larva revealed that ACC precipitates through a continuum of states rather than through abrupt phase transitions involving two distinct phases as formerly believed. Using an atomic multiplet code, we show that only a tetragonal or "umbrella-like" distortion of the Ca coordination polyhedron can give rise to the observed continuum of states. We also show on the basis of the structures obtained from previous molecular dynamics simulations of hydrated nanoparticles that the Ca L23-edge is not sensitive to atomic arrangements in the early stages of the transformation process.

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.

A Universal Force Field for Materials, Periodic GFN-FF: Implementation and Examination.

In this study, the adaption of the recently published molecular GFN-FF for periodic boundary conditions (pGFN-FF) is described through the use of neighbor lists combined with appropriate charge sums to handle any dimensionality from 1D polymers to 2D surfaces and 3D solids. Numerical integration over the Brillouin zone for the calculation of π bond orders of periodic fragments is also included. Aside from adapting the GFN-FF method to handle periodicity, improvements to the method are proposed in regard to the calculation of topological charges through the inclusion of a screened Coulomb term that leads to more physical charges and avoids a number of pathological cases. Short-range damping of three-body dispersion is also included to avoid collapse of some structures. Analytic second derivatives are also formulated with respect to both Cartesian and strain variables, including prescreening of terms to accelerate the dispersion/coordination number contribution to the Hessian. The modified pGFN-FF scheme is then applied to a wide range of different materials in order to examine how well this universal model performs.

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.

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.

Ion Pairing and Multiple Ion Binding in Calcium Carbonate Solutions Based on a Polarizable AMOEBA Force Field and Ab Initio Molecular Dynamics.

The speciation of calcium carbonate in water is important to the geochemistry of the world's oceans and has ignited significant debate regarding the mechanism by which nucleation occurs. Here, it is vital to be able to quantify the thermodynamics of ion pairing versus higher order association processes in order to distinguish between possible pathways. Given that it is experimentally challenging to quantify such species, here we determine the thermodynamics for ion pairing and multiple binding of calcium carbonate species using bias-enhanced molecular dynamics. In order to examine the uncertainties underlying these results, we derived a new polarizable force field for both calcium carbonate and bicarbonate in water based on the AMOEBA model to compare against our earlier rigid ion model, both of which are further benchmarked against ab initio molecular dynamics for the ion pair. Both force fields consistently indicate that the association of calcium carbonate ion pairs to form larger species is stable, though with an equilibrium constant that is lower than for ion pairing itself.

Introducing the crystalline phase of dicalcium phosphate monohydrate.

Calcium orthophosphates (CaPs) are important in geology, biomineralization, animal metabolism and biomedicine, and constitute a structurally and chemically diverse class of minerals. In the case of dicalcium phosphates, ever since brushite (CaHPO4·2H2O, dicalcium phosphate dihydrate, DCPD) and monetite (CaHPO4, dicalcium phosphate, DCP) were first described in 19th century, the form with intermediary chemical formula CaHPO4·H2O (dicalcium phosphate monohydrate, DCPM) has remained elusive. Here, we report the synthesis and crystal structure determination of DCPM. This form of CaP is found to crystallize from amorphous calcium hydrogen phosphate (ACHP) in water-poor environments. The crystal structure of DCPM is determined to show a layered structure with a monoclinic symmetry. DCPM is metastable in water, but can be stabilized by organics, and has a higher alkalinity than DCP and DCPD. This study serves as an inspiration for the future exploration of DCPM's potential role in biomineralization, or biomedical applications.

CrystalGrower: a generic computer program for Monte Carlo modelling of crystal growth.

A Monte Carlo crystal growth simulation tool, CrystalGrower, is described which is able to simultaneously model both the crystal habit and nanoscopic surface topography of any crystal structure under conditions of variable supersaturation or at equilibrium. This tool has been developed in order to permit the rapid simulation of crystal surface maps generated by scanning probe microscopies in combination with overall crystal habit. As the simulation is based upon a coarse graining at the nanoscopic level features such as crystal rounding at low supersaturation or undersaturation conditions are also faithfully reproduced. CrystalGrower permits the incorporation of screw dislocations with arbitrary Burgers vectors and also the investigation of internal point defects in crystals. The effect of growth modifiers can be addressed by selective poisoning of specific growth sites. The tool is designed for those interested in understanding and controlling the outcome of crystal growth through a deeper comprehension of the key controlling experimental parameters.

Homochirality in biomineral suprastructures induced by assembly of single-enantiomer amino acids from a nonracemic mixture.

Since Pasteur first successfully separated right-handed and left-handed tartrate crystals in 1848, the understanding of how homochirality is achieved from enantiomeric mixtures has long been incomplete. Here, we report on a chirality dominance effect where organized, three-dimensional homochiral suprastructures of the biomineral calcium carbonate (vaterite) can be induced from a mixed nonracemic amino acid system. Right-handed (counterclockwise) homochiral vaterite helicoids are induced when the amino acid L-Asp is in the majority, whereas left-handed (clockwise) homochiral morphology is induced when D-Asp is in the majority. Unexpectedly, the Asp that incorporates into the homochiral vaterite helicoids maintains the same enantiomer ratio as that of the initial growth solution, thus showing chirality transfer without chirality amplification. Changes in the degree of chirality of the vaterite helicoids are postulated to result from the extent of majority enantiomer assembly on the mineral surface. These mechanistic insights potentially have major implications for high-level advanced materials synthesis.

Anomalous heat transport in binary hard-sphere gases.

Equilibrium and nonequilibrium molecular dynamics (MD) are used to investigate the thermal conductivity of binary hard-sphere fluids. It is found that the thermal conductivity of a mixture can not only lie outside the series and parallel bounds set by their pure component values, but can lie beyond even the pure component fluid values. The MD simulations verify that revised Enskog theory can accurately predict nonequilibrium thermal conductivities at low densities and this theory is applied to explore the model parameter space. Only certain mass and size ratios are found to exhibit conductivity enhancements above the parallel bounds and dehancement below the series bounds. The anomalous dehancement is experimentally accessible in helium-hydrogen gas mixtures and a review of the literature confirms the existence of mixture thermal conductivity below the series bound and even below the pure fluid values, in accordance with the predictions of revised Enskog theory. The results reported here may reignite the debate in the nanofluid literature on the possible existence of anomalous thermal conductivities outside the series and parallel bounds as this Rapid Communication demonstrates they are a fundamental feature of even simple fluids.

Simulation of Calcium Phosphate Prenucleation Clusters in Aqueous Solution: Association beyond Ion Pairing.

Classical molecular dynamics simulations and free energy methods have been used to obtain a better understanding of the molecular processes occurring prior to the first nucleation event for calcium phosphate biominerals. The association constants for the formation of negatively charged complexes containing calcium and phosphate ions in aqueous solution have been computed, and these results suggest that the previously proposed calcium phosphate building unit, [Ca(HPO4)3]4-, should only be present in small amounts under normal experimental conditions. However, the presence of an activation barrier for the removal of an HPO4 2- ion from this complex indicates that this species could be kinetically trapped. Aggregation pathways involving CaHPO4, [Ca(HPO4)2]2-, and [Ca(HPO4)3]4- complexes have been explored with the finding that dimerization is favorable up to a Ca/HPO4 ratio of 1:2.