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

A Method for Efficiently Predicting the Radial Distribution Function and Osmotic Coefficients of Aqueous Electrolyte Solutions

The prediction of the structural and thermodynamic properties of electrolyte solutions is critical for a huge range of practical situations where these solutions play a vital role. Theoretical models, such as the continuum solvent model, attempt to explain the behavior of solutions using a coarse-grained description of the interactions of species in the solution, whereas molecular simulations aim to directly compute the behavior of the solution, including the interactions between all ions and molecules in the system. Both methods have limitations: theoretical models are generally less accurate because they rely on assumptions, while molecular simulations require significant computational resources, particularly if higher accuracy is desired. To address these issues, we propose an affordable and effective method that combines the advantages of the modified Poisson-Boltzmann equation (MPBE) with classical molecular dynamics (MD) simulations to predict the radial distribution functions and thermodynamic properties of electrolyte solutions. We demonstrate a method of using the MPBE to compute the short-range potential of mean force (PMF) from the radial distribution functions (RDFs) and vice versa. Furthermore, we provide insights into the relationship between the RDFs and the short-range PMF based on the MPBE. Our analysis reveals that the effective short-range PMFs can be approximately calculated using low concentration simulations but the short-range PMFs are slightly concentration-dependent in simulations at higher concentrations. Additionally, we demonstrate that for concentrated solutions, osmotic coefficients can be calculated in agreement with experiment using a virial approach. This is based on the effective short-range PMFs and RDFs obtained from the MPBE method. Our proposed MPBE can therefore accelerate the calculation of the structural and thermodynamic properties of electrolyte solutions.

Ion association behaviors in the initial stage of calcium carbonate formation: An ab initio study

In this work, we performed static density functional theory calculations and ab initio metadynamics simulations to systematically investigate the association mechanisms and dynamic structures of four kinds of ion pairs that could be formed before the nucleation of CaCO3. For Ca2+-HCO3- and Ca2+-CO32- pairs, the arrangement of ligands around Ca2+ evolves between the six-coordinated octahedral structure and the seven-coordinated pentagonal bipyramidal structure. The formation of ion pairs follows an associative ligand substitution mechanism. Compared with HCO3-, CO32- exhibits a stronger affinity to Ca2+, leading to the formation of a more stable precursor phase in the prenucleation stage, which promotes the subsequent CaCO3 nucleation. In alkaline environments, excessive OH- ions decrease the coordination preference of Ca2+. In this case, the formation of Ca(OH)+-CO32- and Ca(OH)2-CO32- pairs favors the dissociative ligand substitution mechanism. The inhibiting effects of OH- ion on the CaCO3 association can be interpreted from two aspects, i.e., (1) OH- neutralizes positive charges on Ca2+, decreases the electrostatic interactions between Ca2+ and CO32-, and thus hinders the formation of the CaCO3 monomer, and (2) OH- decreases the capacity of Ca2+ for accommodating O, making it easier to separate Ca2+ and CO32- ions. Our findings on the ion association behaviors in the initial stage of CaCO3 formation not only help scientists evaluate the impact of ocean acidification on biomineralization but also provide theoretical support for the discovery and development of more effective approaches to manage undesirable scaling issues.

To Pair or not to Pair? Machine-Learned Explicitly-Correlated Electronic Structure for NaCl in Water

The extent of ion pairing in solution is an important phenomenon to rationalize transport and thermodynamic properties of electrolytes. A fundamental measure of this pairing is the potential of mean force (PMF) between solvated ions. The relative stabilities of the paired and solvent shared states in the PMF and the barrier between them are highly sensitive to the underlying potential energy surface. However, direct application of accurate electronic structure methods is challenging, since long simulations are required. We develop wave function based machine learning potentials with the random phase approximation (RPA) and second order Møller-Plesset (MP2) perturbation theory for the prototypical system of Na and Cl ions in water. We show both methods in agreement, predicting the paired and solvent shared states to have similar energies (within 0.2 kcal/mol). We also provide the same benchmarks for different DFT functionals as well as insight into the PMF based on simple analyses of the interactions in the system.

Prenucleation Cluster Pathway is Inconsistent with CaCO3 Kinetics

It has been debated whether CaCO3 nucleates classically with the attainment of a critical cluster size or nonclassically with the restructuring of a prenucleation cluster (PNC). Here, we determine from the nucleation kinetics of CaCO3 that the transition state is composed of about 10 formula units, irrespective of the supersaturation. Crucially, the size of the transition state is considerably smaller than the average PNC size estimated from experimental characterization. This size discrepancy suggests the PNCs are uninvolved in nucleation, and the kinetics indicate that if CaCO3 nucleates classically, the transition state must be an abnormally unstable (antimagic) cluster.

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.

The impact of stoichiometry on the initial steps of crystal formation: Stability and lifetime of charged triple-ion complexes

Minerals form in natural systems from solutions with varying ratios of their lattice ions, yet non-stoichiometric conditions have generally been overlooked in investigations of new formation (nucleation) of ionic crystals. Here, we investigated the influence of cation:anion ratio in the solution on the initial steps of nucleation by studying positively and negatively charged triple ion complexes and subsequent particle size evolution. Our model systems are carbonates and sulfates of calcium and barium, as it was recently shown that solution stoichiometry affects the timing and rate of their nucleation. Molecular dynamics (MD) simulations and dynamic light scattering (DLS) flow experiments show that nucleation correlates with the stability and lifetime of the initial complexes, which were significantly impacted by the cation:anion stoichiometry and ion type. Specifically,B a S O 4 2 2 - ${{\rm B}{\rm a}{\left({{\rm S}{\rm O}}_{4}\right)}_{2}^{2-}}$ was found to have higher association constants and its lifetime was twofold longer thanB a 2 S O 4 2 + ${{{\rm B}{\rm a}}_{2}{{\rm S}{\rm O}}_{4}^{2+}}$ . Similar trends were observed forB a C O 3 ${{{\rm B}{\rm a}{\rm C}{\rm O}}_{3}}$ andC a S O 4 ${{{\rm C}{\rm a}{\rm S}{\rm O}}_{4}}$ . Contrastingly, forC a C O 3 ${{{\rm C}{\rm a}{\rm C}{\rm O}}_{3}}$ ,C a C O 3 2 2 - ${{\rm C}{\rm a}{\left({{\rm C}{\rm O}}_{3}\right)}_{2}^{2-}}$ was found to have lower association constants and its lifetime was shorter thanC a 2 C O 3 2 + ${{{\rm C}{\rm a}}_{2}{{\rm C}{\rm O}}_{3}^{2+}}$ . These trends in stability and lifetime follow the same asymmetrical behaviour as observed experimentally for particle formation using techniques like DLS. This suggests a causal relationship between the stability and lifetime of the initial charged complexes and the nucleation under non-stoichiometric conditions.

Interaction of microorganisms with carbonates from the micro to the macro scales during sedimentation: Insights into the early stage of biodegradation

The assembly process of Organic Matter (OM) from single molecules to polymers and the formation process of Ca-CO3 ion-pairs are explored at the micro-scale, and then the relationship between OM and carbonate based on the results of microbially-induced carbonate precipitation (MICP) laboratory experiments is established at the macro-scale. Molecular dynamics (MD) is used to model the assembly of OM (a) in an aqueous solution, (b) on surfaces of calcite (10 1‾ 4) crystals and (c) on defective calcite (101‾ 4) crystal surfaces. From the MICP experiments, carbonate minerals containing abundant OM were precipitated and were characterized by Scanning Electron Microscopy (SEM), X-Ray Diffractometry (XRD) and Fourier Transform Infrared Spectroscopy (FTIR). The results of the MD show that OM is assembled into polymers in all three simulation systems. Although the Ca-CO3 ion-pairs and OM were briefly combined, the aggregation assembly of OM molecules and the precipitation of carbonate calcium are not related in the long run. The highly specific surface area of the defective calcite shows an increase in the adsorption of OM. The van der Waals forces, which are primarily responsible for controlling the assembly of OM molecules, increase with the degree of aggregation. According to the MICP experiments, OM is enriched on the mineral surfaces, and more OM is found at the steps of defective crystals with their larger surface areas. Through MD and MICP laboratory experiments, this work systematically describes the interaction of OM and carbonate minerals from the micro to the macro scales, and this provides insight into the interaction between OM and carbonates and biogeochemical processes related to the accumulation of OM in sediments.

Microbial-mineral interaction experiments and density functional theory calculations revealing accelerating effects for the dolomitization of calcite surfaces by organic components

Carbonates represent major sedimentary rocks in on the continental and oceanic crust of Earth and are often closely related to microbial activities. However, the origin of magnesium-containing carbonates, such as dolomites, has not yet been fully resolved and was debated for many years. In order to reveal the specific role of organic components and microbes on the precipitation of magnesium ions, different dolomitization experiments were carried out with various setups for the presence of eight amino acids and microbes. The Gibbs free energy for dehydration of Mg[6(H2O)]2+ and organic‑magnesium complexes (OMC) at the calcite (101¯4) step edges were calculated by density functional theory (DFT). Combined results of X-ray diffraction (XRD), scanning electron microscope-energy disperse spectroscopy (SEM-EDS), transmission electron microscope (TEM), X-ray photoelectron spectroscopy (XPS), Fourier transform infrared spectroscopy (FTIR) and high resolution transmission electron microscopy (HRTEM) indicated that magnesium ions were incorporated into the crystal lattice of calcite after calcite reacting with organic‑magnesium solutions (OMS). Dolomite was formed on the surface of calcite under the presence of microbes. The Gibbs free energy barrier of asp, glu, gly, thr, tyr, lys, ser, and ala bonding to Mg[6(H2O)]2+ were 17.8, 16.2, 14.8, 16.5, 19.2, 14.5, 19.0, 17.0 kcal/mol, those are lower than that of the direct dehydration of Mg[6(H2O)]2+ of 19.45 kcal/mol. The Gibbs free barrier of OMC bonding at the acute step ([481¯] and [4¯41]) of 29.7/34.25 kcal/mol are lower than that of Mg[6(H2O)]2+ of 32.45/36.7 kcal/mol and the Gibbs free barrier of OMC bonding at the obtuse step ([481¯] and [4¯41]) of 42.07/47.6 kcal/mol are lower than that of Mg[6(H2O)]2+ of 55.4/60.34 kcal/mol. The enhancing effects of organic components and microbes on the precipitation of magnesium ions were collectively determined through experimental and theoretical calculation, thus setting up a new direction for future studies of dolomitization with a focus on microbial- mineral interactions.

Efficient Assessment of 'Instantaneous pK' Values from Molecular Dynamics Simulations

We present a molecular simulation approach to studying the role of local and momentary molecular environment for potential acid-base reactions. For this, we combine thermodynamic considerations on the pK of ionic species with rapid sampling of energy changes related to (de)protonation. Using dispersed carbonate ions in water as a reference, our approach aims at the fast assessment of the momentary protonation energy, and thus the 'instantaneous pK', of calcium-carbonate ion aggregates. The latter include transient complexes that are elusive to long sampling runs. This motivated the elaboration of approximate, yet particularly fast assessable sampling strategies. Along this line, we were able to characterize instantaneous pK values at a statistical accuracy of 0.4 pK units within sampling runs of only 10 ps duration, whereas statistical errors reduce to 0.1 pK units in 75 ps sampling runs, respectively. This readily enabled the required time resolution for the characterization of [Cax (CO3 )y ]2(x-y) aggregates with x=1,2 and y=1,2,3, respectively. In turn, the analysis of the pH-dependent nature of calcite-water interfaces and dynamically ordered liquid-like oxyanion polymers (dollop) domains is outlined at 10 ps resolution.

Characterizing the Mechanisms of Ca and Mg Carbonate Ion-Pair Formation with Multi-Level Molecular Dynamics/Quantum Mechanics Simulations

The carbonate minerals of Ca and Mg are abundant throughout the lithosphere and have recently garnered significant research interest as possible long-term carbon sinks in the sequestration of atmospheric carbon dioxide. Nonetheless, an understanding of the atomic-level processes comprising their mineralization remains limited. Here, we characterize and contrast the mechanisms of contact ion-pair formation in aqueous Ca and Mg carbonate systems, which represents the most fundamental step leading to the formation of their mineral solids. Utilizing multilevel embedded correlated wavefunction-based ab initio molecular dynamics/quantum mechanics simulations, we characterize not only the dynamics of these processes but also factors arising from the electronic structure of the involved species, revealing further details of the fundamentally different mechanisms for the interconversion between the contact ion-pairs and solvent-shared ion-pairs of Ca versus Mg carbonate.

Dissolution enables dolomite crystal growth near ambient conditions

Crystals grow in supersaturated solutions. A mysterious counterexample is dolomite CaMg(CO3)2, a geologically abundant sedimentary mineral that does not readily grow at ambient conditions, not even under highly supersaturated solutions. Using atomistic simulations, we show that dolomite initially precipitates a cation-disordered surface, where high surface strains inhibit further crystal growth. However, mild undersaturation will preferentially dissolve these disordered regions, enabling increased order upon reprecipitation. Our simulations predict that frequent cycling of a solution between supersaturation and undersaturation can accelerate dolomite growth by up to seven orders of magnitude. We validated our theory with in situ liquid cell transmission electron microscopy, directly observing bulk dolomite growth after pulses of dissolution. This mechanism explains why modern dolomite is primarily found in natural environments with pH or salinity fluctuations. More generally, it reveals that the growth and ripening of defect-free crystals can be facilitated by deliberate periods of mild dissolution.

Scaling Solute-Solvent Distances to Improve Solubility and Ion Paring Predictions in Rigid Ion Models

Force fields based on the rigid ion model (RIM) have been developed to accurately predict the various physical and chemical properties of salts and water. However, the combined use of these models often fails to accurately predict the solubility of salts in water. To address this issue, several approaches, such as charge scaling or reparameterization, have been proposed. Nevertheless, these methods require laborious reparameterization of nonbonded force field parameters. In this article, we propose a scaling solute-solvent distance (SSSD) method to improve force fields in predicting salt solubility without changing the solute-solute and solvent-solvent interactions in the original force fields. This method can also tune the ion pairing of salt in water. One main advantage of the SSSD method is that reparameterization of the crystal and water models is not needed. We use two RIMs for the NaCl-water system (JC-SPC/E and SD-SPC/E) and the CHARMM force field for the KCl-water system to demonstrate the improved accuracy in predicting solubility by the SSSD method. Furthermore, we use the RDG-SPC/Fw force field to show that the SSSD method can also be used to tune the ion pairing of CaCO3 in water. Limitations of this method are also discussed.

Agglomeration Drives the Reversed Fractionation of Aqueous Carbonate and Bicarbonate at the Air-Water Interface

In the course of our investigations of the adsorption of ions to the air-water interface, we previously reported the surprising result that doubly charged carbonate anions exhibit a stronger surface affinity than singly charged bicarbonate anions. In contrast to monovalent, weakly hydrated anions, which generally show enhanced concentrations in the interfacial region, multivalent (and strongly hydrated) anions are expected to show a much weaker surface propensity. In the present work, we use resonantly enhanced deep-UV second-harmonic generation spectroscopy to measure the Gibbs free energy of adsorption of both carbonate (CO32-) and bicarbonate (HCO3-) anions to the air-water interface. Contrasting the predictions of classical electrostatic theory and in support of our previous findings from X-ray photoelectron spectroscopy, we find that carbonate anions do indeed exhibit much stronger surface affinity than do the bicarbonate anions. Extensive computer simulations reveal that strong ion pairing of CO32- with the Na+ countercation in the interfacial region results in the formation of near-neutral agglomerate clusters, consistent with a theory of interfacial ion adsorption based on hydration free energy and capillary waves. Simulated X-ray photoelectron spectra predict a 1 eV shift in the carbonate spectra compared to that of bicarbonate, further confirming our experiments. These findings not only advance our fundamental understanding of ion adsorption chemistry but also impact important practical processes such as ocean acidification, sea-spray aerosol chemistry, and mammalian respiration physiology.

Probing pH-Dependent Dehydration Dynamics of Mg and Ca Cations in Aqueous Solutions with Multi-Level Quantum Mechanics/Molecular Dynamics Simulations

The dehydration of aqueous calcium and magnesium cations is the most fundamental process controlling their reactivity in chemical and biological phenomena, such as the formation of ionic solids or passing through ion channels. It holds particular relevance in light of recent advancements in the development of carbon capture techniques that rely on mineralization for long-term carbon storage. Specifically, dehydration of Ca2+ and Mg2+ is a key step in proposed carbon capture processes aiming to exploit the relatively high concentration of dissolved carbon dioxide in seawater via the formation of carbonate minerals from solvated Ca2+ and Mg2+ cations for sequestration and storage. Nevertheless, atomic-scale understanding of the dehydration of aqueous Ca2+ and Mg2+ cations remains limited. Here, we utilize rare event sampling via density functional theory molecular dynamics and embedded wavefunction theory calculations to elucidate the dehydration dynamics of aqueous Ca2+ and Mg2+. Emphasis is placed on the investigation of the effect pH has on the stability of the different coordination environments. Our results reveal significant differences in the dehydration dynamics of the two cations and provide insight into how they may be modulated by pH changes.

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'.

A Tale of Two Foulants: The Coupling of Organic Fouling and Mineral Scaling in Membrane Desalination

Membrane desalination that enables the harvesting of purified water from unconventional sources such as seawater, brackish groundwater, and wastewater has become indispensable to ensure sustainable freshwater supply in the context of a changing climate. However, the efficiency of membrane desalination is greatly constrained by organic fouling and mineral scaling. Although extensive studies have focused on understanding membrane fouling or scaling separately, organic foulants commonly coexist with inorganic scalants in the feedwaters of membrane desalination. Compared to individual fouling or scaling, combined fouling and scaling often exhibits different behaviors and is governed by foulant-scalant interactions, resembling more complex but practical scenarios than using feedwaters containing only organic foulants or inorganic scalants. In this critical review, we first summarize the performance of membrane desalination under combined fouling and scaling, involving mineral scales formed via both crystallization and polymerization. We then provide the state-of-the-art knowledge and characterization techniques pertaining to the molecular interactions between organic foulants and inorganic scalants, which alter the kinetics and thermodynamics of mineral nucleation as well as the deposition of mineral scales onto membrane surfaces. We further review the current efforts of mitigating combined fouling and scaling via membrane materials development and pretreatment. Finally, we provide prospects for future research needs that guide the design of more effective control strategies for combined fouling and scaling to improve the efficiency and resilience of membrane desalination for the treatment of feedwaters with complex compositions.

Distance-dependent dielectric constant at the calcite/electrolyte interface: Implication for surface complexation modeling

HYPOTHESIS

The electrical double layer formed at the mineral/electrolyte interface is often modeled using mean-field approaches based on a continuum description of the solvent whose dielectric constant is assumed to decrease monotonically with decreasing distance to the surface. In contrast, molecular simulations show that the solvent polarizability oscillates near the surface similar to the water density profile - as shown previously, for example, by Bonthuis et al. (D.J. Bonthuis, S. Gekle, R.R. Netz, Dielectric Profile of Interfacial Water and its Effect on Double-Layer Capacitance, Phys Rev Lett 107(16) (2011) 166102). We showed that molecular and mesoscale pictures agree by spatially averaging the dielectric constant obtained from molecular dynamics simulations over the distances relevant to the mean-field representation. In addition, the values of capacitances used to describe the electrical double layer in Surface Complexation Models (SCMs) of the mineral/electrolyte interface can be estimated using molecularly informed spatially averaged dielectric constants and positions of hydration layers.

EXPERIMENTS

First, we used molecular dynamics simulations to model the calcite 101¯4/electrolyte interface. Next, by using atomistic trajectories, we calculated the distance-dependent static dielectric constant and water density in the direction normal to the. Finally, we applied spatial compartmentalization consistent with the model of parallel-plate capacitors connected in series to estimate SCM capacitances.

FINDINGS

Computationally expensive simulations are required to determine the dielectric constant profile of interfacial water near the mineral surface. On the other hand, water density profiles are readily assessable from much shorter simulation trajectories. Our simulations confirmed that dielectric and water density oscillations at the interface are correlated. Here, we parametrized linear regression models to estimate the dielectric constant directly from the local water density. This is a significant computational shortcut compared to slowly converging calculations relying on total dipole moment fluctuations. The amplitude of the interfacial dielectric constant oscillation can exceed the dielectric constant of the bulk water, suggesting an ice-like frozen state, but only if there are no electrolyte ions. The interfacial accumulation of electrolyte ions causes a decrease in the dielectric constant due to the reduction of water density and re-orientation of water dipoles in ion hydration shells. Finally, we show how to use the computed dielectric properties to estimate SCM's capacitances.

Physical insight into the entropy-driven ion association

The ion association is widely believed to be dominated by the favorable entropy change arising from the release of water molecules from ion hydration shells. However, no direct thermodynamic evidence exists to validate the reliability and suitability of this view. Herein, we employ complicated free energy calculations to rigorously split the free energy including its entropic and enthalpic components into the water-induced contributions and ion-ion interaction terms for several ion pairs from monatomic to polyatomic ions, spanning the size range from small kosmotropes to large chaotropes (Na⁺ , Cs⁺ , Ca²⁺ , F^- , I^- , CO₃ ^2- , and HPO₄ ^2- ). Our results successfully reveal that though ion associations are indeed determined by a delicate balance between the favorable entropy variation and the repulsive enthalpy change, the entropy gain dominated by the solvent occurs only for the monatomic ion pairing. The water-induced entropic contribution significantly goes against the ion pairing between polyatomic anion and cation, which is, alternatively, dominated by the favorable entropy from the ion-ion interaction term, due to the configurational arrangement of polyatomic anions involved in ion association. The structural and dynamic analysis demonstrates that the entropy penalty from the water phase is primarily ascribed to the enhanced stability of water molecules around the cation imposed by the incoming anion. Our study successfully provides a fundamental understanding of water-mediated ion associations and highlights disparate lengthscale dependencies of the dehydration thermodynamics on the specific types of ions.

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.

Development and application of ReaxFF methodology for understanding the chemical dynamics of metal carbonates in aqueous solutions

A new ReaxFF reactive force field has been developed for metal carbonate systems including Na⁺, Ca²⁺, and Mg²⁺ cations and the CO₃^2- anion. This force field is fully transferable with previous ReaxFF water and water/electrolyte descriptions. The Me-O-C (Me = metal) three-body valence angle parameters and Me-C non-reactive parameters of the force field have been optimized against quantum mechanical calculations including equations of state, heats of formation, heats of reaction, angle distortions and vibrational frequencies. The new metal carbonate force field has been validated using molecular dynamics simulations to study the solvation and reactivity of metal and carbonate ions in water at 300 K and 700 K. The coordination radius and self-diffusion coefficient show good consistency with existing experimental and simulation results. The angular distribution analysis explains the structural preference of carbonate ions to form carbonates and bicarbonates, where Na⁺ predominantly forms carbonates due to weaker angular strain, while Ca²⁺ and Mg²⁺ prefer to form bicarbonate monodentate in nature. Residence time distribution analyses on different systems reveal the role of ions in accelerating and decelerating the dynamics of water and carbonate ions under different thermodynamic conditions. The formation and dissolution of bicarbonates and carbonates in solution were explored on the basis of the protonation capability in different systems. The nucleation phenomenon of metal carbonates at ambient and supercritical conditions is explained from the perspective of cluster formation over time: Ca²⁺ ions can form prenucleation clusters at ambient temperature but show saturation with increasing temperature, whereas Na⁺ and Mg²⁺ ions show a rapid increase in cluster size and amount upon increasing time and temperature.

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.

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.

The atomic structure and dynamics at the CaCO3 vaterite-water interface: A classical molecular dynamics study

Classical molecular and lattice dynamics were applied to explore the structure and dynamics of water on different surfaces of vaterite, the least abundant calcium carbonate polymorph. Surfaces were generated starting from the three possible structural models for vaterite (monoclinic, hexagonal/trigonal, and triclinic) and pre-screened using their surface energies in an implicit solvent. Surfaces with energies lower than 0.55 J/m² were then run in explicit water. The majority of these surfaces dissolve in less than 100 ns, highlighting the low stability of this phase in abiotic environments. Three stable surfaces were identified; they exhibited only minor structural changes when in contact with explicit water and did not show any tendency to dissolve during 1 µs molecular dynamics simulations. The computed water density profiles show that all these surfaces have two distinct hydration layers. The water residence time at the various calcium sites was computed to be within 0.7 and 20.5 ns, which suggests that specific Ca ions will be more readily available to bind with organic molecules present in solution. This analysis is a step forward in understanding the structure of this complex mineral and its role in biomineralization, as it provides a solid theoretical background to explore its surface chemistry. In particular, this study provides realistic surface models and predicts the effect of water exchange at the surface active sites on the adsorption of other molecules.

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.

Amino Acid and Oligopeptide Effects on Calcium Carbonate Solutions

Biological organisms display sophisticated control of nucleation and crystallization of minerals. In order to mimic living systems, deciphering the mechanisms by which organic molecules control the formation of mineral phases from solution is a key step. We have used computer simulations to investigate the effects of the amino acids arginine, aspartic acid, and glycine on species that form in solutions of calcium carbonate (CaCO₃) at lower and higher levels of supersaturation. This provides net positive, negative, and neutral additives. In addition, we have prepared simulations containing hexapeptides of the amino acids to consider the effect of additive size on the solution species. We find that additives have limited impact on the formation of extended, liquid-like CaCO₃ networks in supersaturated solutions. Additives control the amount of (bi)carbonate in solution, but more importantly, they are able to stabilize these networks on the time scales of the simulations. This is achieved by coordinating the networks and assembled additive clusters in solutions. The association leads to subtle changes in the coordination of CaCO₃ and reduced mobility of the cations. We find that the number of solute association sites and the size and topology of the additives are more important than their net charge. Our results help to understand why polymer additives are so effective at stabilizing dense liquid CaCO₃ phases.