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'.

Untangling the Mechanisms of Lattice Distortions in Biogenic Crystals across Scales.

Biomineralized structures are complex functional hierarchical assemblies composed of biomineral building blocks joined together by an organic phase. The formation of individual mineral units is governed by the cellular tissue component that orchestrates the process of biomineral nucleation, growth, and morphogenesis. These processes are imprinted in the structural, compositional, and crystallographic properties of the emerging biominerals on all scales. Measurement of these properties can provide crucial information on the mechanisms that are employed by the organism to form these complex 3D architectures and to unravel principles of their functionality. Nevertheless, so far, this has only been possible at the macroscopic scale, by averaging the properties of the entire composite assembly, or at the mesoscale, by looking at extremely small parts of the entire picture. In this study, the newly developed synchrotron-based dark-field X-ray microscopy method is employed to study the link between 3D crystallographic properties of relatively large calcitic prisms in the shell of the mollusc Pinna nobilis and their local lattice properties with extremely high angular resolution down to 0.001°. Mechanistic links between variations in local lattice parameters and spacing, crystal orientation, chemical composition, and the deposition process of the entire mineral unit are unraveled.

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.

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.

The CRYSTAL code, 1976-2020 and beyond, a long story.

CRYSTAL is a periodic ab initio code that uses a Gaussian-type basis set to express crystalline orbitals (i.e., Bloch functions). The use of atom-centered basis functions allows treating 3D (crystals), 2D (slabs), 1D (polymers), and 0D (molecules) systems on the same grounds. In turn, all-electron calculations are inherently permitted along with pseudopotential strategies. A variety of density functionals are implemented, including global and range-separated hybrids of various natures and, as an extreme case, Hartree-Fock (HF). The cost for HF or hybrids is only about 3-5 times higher than when using the local density approximation or the generalized gradient approximation. Symmetry is fully exploited at all steps of the calculation. Many tools are available to modify the structure as given in input and simplify the construction of complicated objects, such as slabs, nanotubes, molecules, and clusters. Many tensorial properties can be evaluated by using a single input keyword: elastic, piezoelectric, photoelastic, dielectric, first and second hyperpolarizabilities, etc. The calculation of infrared and Raman spectra is available, and the intensities are computed analytically. Automated tools are available for the generation of the relevant configurations of solid solutions and/or disordered systems. Three versions of the code exist: serial, parallel, and massive-parallel. In the second one, the most relevant matrices are duplicated on each core, whereas in the third one, the Fock matrix is distributed for diagonalization. All the relevant vectors are dynamically allocated and deallocated after use, making the code very agile. CRYSTAL can be used efficiently on high performance computing machines up to thousands of cores.

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.

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.

Simulation of Calcium Phosphate Species in Aqueous Solution: Force Field Derivation.

A new force field has been derived for the aqueous calcium phosphate system that aims to reproduce the key thermodynamic properties of the system, including free energies of hydration of the ions and the solubility of the solid mineral phases. Interactions of three phosphate anions (PO43-, HPO42-, and H2PO4-) with water were calibrated through comparison with the results obtained from ab initio molecular dynamics using both GGA and hybrid density functional theory with dispersion corrections. In the solid state, the force field has been evaluated by benchmarking against experiment and other existing models and is shown to reproduce the structural and mechanical properties well, despite the primary focus being on thermodynamics. To validate the force field, the thermodynamics of ion pairing for calcium phosphate species in water has been computed and shown to be in excellent agreement with experimental data.

First-principle modelling of forsterite surface properties: Accuracy of methods and basis sets.

The seven main crystal surfaces of forsterite (Mg2 SiO4 ) were modeled using various Gaussian-type basis sets, and several formulations for the exchange-correlation functional within the density functional theory (DFT). The recently developed pob-TZVP basis set provides the best results for all properties that are strongly dependent on the accuracy of the wavefunction. Convergence on the structure and on the basis set superposition error-corrected surface energy can be reached also with poorer basis sets. The effect of adopting different DFT functionals was assessed. All functionals give the same stability order for the various surfaces. Surfaces do not exhibit any major structural differences when optimized with different functionals, except for higher energy orientations where major rearrangements occur around the Mg sites at the surface or subsurface. When dispersions are not accounted for, all functionals provide similar surface energies. The inclusion of empirical dispersions raises the energy of all surfaces by a nearly systematic value proportional to the scaling factor s of the dispersion formulation. An estimation for the surface energy is provided through adopting C6 coefficients that are more suitable than the standard ones to describe O-O interactions in minerals. A 2 × 2 supercell of the most stable surface (010) was optimized. No surface reconstruction was observed. The resulting structure and surface energy show no difference with respect to those obtained when using the primitive cell. This result validates the (010) surface model here adopted, that will serve as a reference for future studies on adsorption and reactivity of water and carbon dioxide at this interface.

Assessing thermochemical properties of materials through ab initio quantum-mechanical methods: the case of α-Al2O3.

The thermochemical behavior of α-Al2O3 corundum in the whole temperature range 0-2317 K (melting point) and under pressures up to 12 GPa is predicted by applying ab initio methods based on the density functional theory (DFT), the use of a local basis set and periodic-boundary conditions. Thermodynamic properties are treated both within and beyond the harmonic approximation to the lattice potential. In particular, a recent implementation of the quasi-harmonic approximation, in the Crystal program, is here shown to provide a reliable description of the thermal expansion coefficient, entropy, constant-volume and constant-pressure specific heats, and temperature dependence of the bulk modulus, nearly up to the corundum melting temperature. This is a remarkable outcome suggesting α-Al2O3 to be an almost perfect quasi-harmonic crystal. The effect of using different computational parameters and DFT functionals belonging to different levels of approximations on the accuracy of the thermal properties is tested, providing a reference for further studies involving alumina polymorphs and, more generally, quasi-ionic minerals.

Oxygen spectroscopy and polarization-dependent imaging contrast (PIC)-mapping of calcium carbonate minerals and biominerals.

X-ray absorption near-edge structure (XANES) spectroscopy and spectromicroscopy have been extensively used to characterize biominerals. Using either Ca or C spectra, unique information has been obtained regarding amorphous biominerals and nanocrystal orientations. Building on these results, we demonstrate that recording XANES spectra of calcium carbonate at the oxygen K-edge enables polarization-dependent imaging contrast (PIC) mapping with unprecedented contrast, signal-to-noise ratio, and magnification. O and Ca spectra are presented for six calcium carbonate minerals: aragonite, calcite, vaterite, monohydrocalcite, and both hydrated and anhydrous amorphous calcium carbonate. The crystalline minerals reveal excellent agreement of the extent and direction of polarization dependences in simulated and experimental XANES spectra due to X-ray linear dichroism. This effect is particularly strong for aragonite, calcite, and vaterite. In natural biominerals, oxygen PIC-mapping generated high-magnification maps of unprecedented clarity from nacre and prismatic structures and their interface in Mytilus californianus shells. These maps revealed blocky aragonite crystals at the nacre-prismatic boundary and the narrowest calcite needle-prisms. In the tunic spicules of Herdmania momus, O PIC-mapping revealed the size and arrangement of some of the largest vaterite single crystals known. O spectroscopy therefore enables the simultaneous measurement of chemical and orientational information in CaCO3 biominerals and is thus a powerful means for analyzing these and other complex materials. As described here, PIC-mapping and spectroscopy at the O K-edge are methods for gathering valuable data that can be carried out using spectromicroscopy beamlines at most synchrotrons without the expense of additional equipment.

Development of accurate force fields for the simulation of biomineralization.

The existence of an accurate force field (FF) model that reproduces the free-energy landscape is a key prerequisite for the simulation of biomineralization. Here, the stages in the development of such a model are discussed including the quality of the water model, the thermodynamics of polymorphism, and the free energies of solvation for the relevant species. The reliability of FFs can then be benchmarked against quantities such as the free energy of ion pairing in solution, the solubility product, and the structure of the mineral-water interface.

Stable prenucleation mineral clusters are liquid-like ionic polymers.

Calcium carbonate is an abundant substance that can be created in several mineral forms by the reaction of dissolved carbon dioxide in water with calcium ions. Through biomineralization, organisms can harness and control this process to form various functional materials that can act as anything from shells through to lenses. The early stages of calcium carbonate formation have recently attracted attention as stable prenucleation clusters have been observed, contrary to classical models. Here we show, using computer simulations combined with the analysis of experimental data, that these mineral clusters are made of an ionic polymer, composed of alternating calcium and carbonate ions, with a dynamic topology consisting of chains, branches and rings. The existence of a disordered, flexible and strongly hydrated precursor provides a basis for explaining the formation of other liquid-like amorphous states of calcium carbonate, in addition to the non-classical behaviour during growth of amorphous calcium carbonate.

On the use of symmetry in the ab initio quantum mechanical simulation of nanotubes and related materials.

Nanotubes can be characterized by a very high point symmetry, comparable or even larger than the one of the most symmetric crystalline systems (cubic, 48 point symmetry operators). For example, N = 2n rototranslation symmetry operators connect the atoms of the (n,0) nanotubes. This symmetry is fully exploited in the CRYSTAL code. As a result, ab initio quantum mechanical large basis set calculations of carbon nanotubes containing more than 150 atoms in the unit cell become very cheap, because the irreducible part of the unit cell reduces to two atoms only. The nanotube symmetry is exploited at three levels in the present implementation. First, for the automatic generation of the nanotube structure (and then of the input file for the SCF calculation) starting from a two-dimensional structure (in the specific case, graphene). Second, the nanotube symmetry is used for the calculation of the mono- and bi-electronic integrals that enter into the Fock (Kohn-Sham) matrix definition. Only the irreducible wedge of the Fock matrix is computed, with a saving factor close to N. Finally, the symmetry is exploited for the diagonalization, where each irreducible representation is separately treated. When M atomic orbitals per carbon atom are used, the diagonalization computing time is close to Nt, where t is the time required for the diagonalization of each 2M x 2M matrix. The efficiency and accuracy of the computational scheme is documented.

Single-layered chrysotile nanotubes: A quantum mechanical ab initio simulation.

Chrysotile single-layered nanotubes, obtained by wrapping the Mg(3)Si(2)O(5)(OH)(4) lizardite monolayer along the (n,-n) hexagonal lattice vector, are simulated at the ab initio level by using an all electron 6-31G( *) basis set and the B3LYP functional for n varying from 14 to 24 (the nanotube radius R referred to the oxygen connecting the Mg and Si layers increases from 20 to 35 A). Because of the full exploitation of the helical symmetry, recently implemented in the CRYSTAL code, the computational cost for the full self-consistent field (SCF) and gradient calculation increases only by a factor of 2 and 1.2, respectively, when passing from the lizardite monolayer [18 atoms and 236 AOs (atomic orbitals) in the unit cell] to the (24, -24) tube (864 atoms and 11,328 AOs). The total energy of the tubes is always larger than that of the lizardite monolayer; the difference DeltaE decreases very rapidly with n; for the largest tube here considered (n=24) DeltaE is as small as 2.7 kJ/mol per formula unit (f.u.); extrapolating to larger n values, at about R=50 A, DeltaE becomes smaller than 1 kJ mol f.u. Very large energy gains are observed for small n values during optimization after rolling, mainly due to the rotation of the SiO(4) tetrahedra that are in the inner part of the cylinder ("normal rolling"); such a rigid rotation accounts for about 85% of the overall relaxation energy. "Inverse rolling" tubes (SiO(4) on the external wall of the tube) are shown to be less stable than the corresponding "normal" tubes.