Dipole and quadrupole polarization in ionic systems: Ab initio studies

Thermodynamic anomalies, polyamorphism and all that

The appearance and evolution of thermodynamics anomalies, and related properties, are studied for two classes of system, modelling those dominated by covalent and ionic interactions, respectively. Such anomalies are most familiar in the density but are also present in other thermodynamics variables such as the compressibility and heat capacity. By systematically varying key model parameters the emergence and evolution of these anomalies can be tracked across the phase space. The interaction of the anomalies can often be rationalized by thermodynamics 'rules'. The emergence of these anomalies may also be correlated with the appearance of polyamorphism, the existence of multiple amorphous states which differ in density and entropy. This article is part of the theme issue 'Exploring the length scales, timescales and chemistry of challenging materials (Part 1)'.

Structure of molten NaCl and the decay of the pair-correlations

The structure of molten NaCl is investigated by combining neutron and x-ray diffraction with molecular dynamics simulations that employed interaction potentials with either rigid or polarizable ions. Special attention is paid to the asymptotic decay of the pair-correlation functions, which is related to the small-k behavior of the partial structure factors, where k denotes the magnitude of the scattering vector. The rigid-ion approach gives access to an effective restricted primitive model in which the anion and cation have equal but opposite charges and are otherwise identical. For this model, the decay of the pair-correlation functions is in qualitative agreement with simple theory. The polarizable ion approach gives a good account of the diffraction results and yields thermodynamic parameters (density, isothermal compressibility, Debye screening length, and heat capacity) in accord with experiment. The longest decay length for the partial pair-distribution functions is a factor of ≃2.5 times greater than the nearest-neighbor distance. The results are commensurate with the decay lengths found for the effective restricted primitive model, which are much shorter than those found in experiments on concentrated electrolytes or ionic liquids using surface force apparatus.

Computational methods to simulate molten salt thermophysical properties

Molten salts are important thermal conductors used in molten salt reactors and solar applications. To use molten salts safely, accurate knowledge of their thermophysical properties is necessary. However, it is experimentally challenging to measure these properties and a comprehensive evaluation of the full chemical space is unfeasible. Computational methods provide an alternative route to access these properties. Here, we summarize the developments in methods over the last 70 years and cluster them into three relevant eras. We review the main advances and limitations of each era and conclude with an optimistic perspective for the next decade, which will likely be dominated by emerging machine learning techniques. This article is aimed to help researchers in peripheral scientific domains understand the current challenges of molten salt simulation and identify opportunities to contribute.

Examination of the short-range structure of molten salts: ThF4, UF4, and related alkali actinide fluoride systems

The short-range structures of LiF-ThF₄, NaF-AnF₄, KF-AnF₄, and Cs-AnF₄ (An = Th, U), were probed using in situ high temperature Extended X-ray Absorption Fine Structure (EXAFS) spectroscopy. Signally, the EXAFS spectra of pure molten ThF₄ and UF₄ were measured for the first time. The data were interpreted with the aid of Molecular Dynamics (MD) and standard fitting of the EXAFS equation. As in related studies, a speciation distribution dominated by [AnF_x]^4-x (x = 7, 8, 9) coordination complexes was observed. The average coordination number was found to decrease with the increasing size of the alkali cation, and increase with AnF₄ content. An average coordination number close to 6, which had not been detected before in melts of alkali actinide fluorides, was seen when CsF was used as solvent.

Extension of the CL&Pol Polarizable Force Field to Electrolytes, Protic Ionic Liquids, and Deep Eutectic Solvents

The polarizable CL&Pol force field presented in our previous study, Transferable, Polarizable Force Field for Ionic Liquids (J. Chem. Theory Comput. 2019, 15, 5858, DOI: http://doi.org/10.1021/acs.jctc.9b0068910.1021/acs.jctc.9b00689), is extended to electrolytes, protic ionic liquids (PIL), deep eutectic solvents (DES), and glycols. These systems are problematic in polarizable simulations because they contain either small, highly charged ions or strong hydrogen bonds, which cause trajectory instabilities due to the pull exerted on the induced dipoles. We use a Tang-Toennies (TT) function to dampen, or smear, the interactions between charges and induced dipole at a short range involving small, highly charged atoms (such as hydrogen or lithium), thus preventing the "polarization catastrophe". The new force field gives stable trajectories and is validated through comparison with experimental data on density, viscosity, and ion diffusion coefficients of liquid systems of the above-mentioned classes. The results also shed light on the hydrogen-bonding pattern in ethylammonium nitrate, a PIL, for which the literature contains conflicting views. We describe the implementation of the TT damping function, of the temperature-grouped Nosé-Hoover thermostat for polarizable molecular dynamics (MD) and of the periodic perturbation method for viscosity evaluation from non-equilibrium trajectories in the LAMMPS MD code. The main result of this work is the wider applicability of the CL&Pol polarizable force field to new, important classes of fluids, achieving robust trajectories and a good description of equilibrium and transport properties in challenging systems. The fragment-based approach of CL&Pol will allow ready extension to a wide variety of PILs, DES, and electrolytes.

The progression of thermodynamic anomalies in MX2 networks with local tetrahedral geometries

Key thermodynamic anomalies in density and compressibility, as well as the related stability limits, are determined using an ionic model for BeF₂ which includes many-body polarization terms. BeF₂ is chosen as an example of an archetypal network-forming system whose structure can be rationalised in terms of connected local tetrahedral coordination polyhedra. The anion dipole polarizability (which effectively controls the bond angles linking neighbouring tetrahedra) is used as a single free parameter in order to help rationalise the changes in the anomaly locations in phase space, whilst all other potential parameters remain fixed. The anomalies and stability limits systematically shift to lower temperature and higher pressure as the anion polarizability is increased. At high dipole polarizabilities the temperature of maximum density anomaly locus becomes suppressed into the supercooled regime of the phase space. The movements of the anomaly loci are analysed in terms of the network structure and the correlation with the inter-tetrahedral bond angles is considered. The high sensitivity of the anomalies to the details of the potential models applied is discussed with reference to previous works on related systems. The relationship to analogous studies on Stillinger-Weber liquids is discussed.

Structure and dynamics in network-forming materials

The study of the structure and dynamics of network-forming materials is reviewed. Experimental techniques used to extract key structural information are briefly considered. Strategies for building simulation models, based on both targeting key (experimentally-accessible) materials and on systematically controlling key model parameters, are discussed. As an example of the first class of materials, a key target system, SiO₂, is used to highlight how the changing structure with applied pressure can be effectively modelled (in three dimensions) and used to link to both experimental results and simple structural models. As an example of the second class the topology of networks of tetrahedra in the MX₂ stoichiometry are controlled using a single model parameter linked to the M-X-M bond angles. The evolution of ordering on multiple length-scales is observed as are the links between the static structure and key dynamical properties. The isomorphous relationship between the structures of amorphous Si and SiO₂ is discussed as are the similarities and differences in the phase diagrams, the latter linked to potential polyamorphic and 'anomalous' (e.g. density maxima) behaviour. Links to both two-dimensional structures for C, Si and Ge and near-two-dimensional bilayers of SiO₂ are discussed. Emerging low-dimensional structures in low temperature molten carbonates are also uncovered.

CCSD(T) calculations of confined systems: in-crystal polarizabilities of F⁻, Cl⁻, O²⁻, and S²⁻

We explore dipole polarizabilities of the singly and doubly charged anions F(-), Cl(-), O(2-), and S(2-) in an external, harmonic oscillator (HO) confining potential ∑(i)½ω(2)r(i)(2). We find that in contrast to F(-) and Cl(-) those for O(2-) and S(2-) are unrealistically high due to the instability of the corresponding restricted Hartree-Fock (RHF) solutions. Yet, already a relatively weak HO confining potential stabilizes their RHF solutions and eliminates any possible broken-symmetry solutions. The coupled-cluster theory with single, double and noniterative triple excitations (CCSD(T)) then yields considerably reduced polarizabilities for O(2-) and S(2-) relative to their unconfined values. We showed that polarizabilities of O(2-) and S(2-) are more sensitive to the strength of a confinement potential than are those for F(-) and Cl(-). This enables us to relate the confining parameter ω with the known experimental polarizabilities for selected crystals (our "training set") and to find a specific confining parameter ω for which the CCSD(T) polarizability equals the experimental in-crystal polarizability of an anion in the training set. The latter may then be used as an alternative approach for determining the in-crystal polarizabilities of anions by exploiting the fact that the characteristic ω values depend linearly on the ionic radius of a cation participating in specific crystals containing these anions. Using this method we then calculate the isotropic dipole polarizabilities for F(-), Cl(-), O(2-), and S(2-) embedded in the LiF, LiCl, NaF, NaCl, KF, KCl, ZnO, ZnS, MgO, MgS, CaO, CaS, SrO, SrS, BaO, BaS, and other crystals containing halogen, oxygen, or sulphur anions. We compare our results with those obtained via alternative models of the in-crystal anionic polarizabilities.

The effect of dispersion interactions on the properties of LiF in condensed phases

Classical molecular dynamics simulations are performed on LiF in the framework of the polarizable ion model. The overlap repulsion and polarization terms of the interaction potential are derived on a purely non-empirical, first-principles basis. For the dispersion, three cases are considered: a first one in which the dispersion parameters are set to zero and two others in which they are included, with different parametrizations. Various thermodynamic, structural and dynamic properties are calculated for the solid and liquid phases. The melting temperature is also obtained from direct coexistence simulations of the liquid and solid phases. Dispersion interactions appear to have an important effect on the densities of both phases and on the melting point, although the liquid properties are not affected when simulations are performed in the NVT ensemble at the experimental density.

The effects of topology on the structural, dynamic and mechanical properties of network-forming materials

The effects of network topology on the static structural, mechanical and dynamic properties of MX(2) network-forming liquids (with tetrahedral short-range order) are discussed. The network topology is controlled via a single model parameter (the anion polarizability) which effectively constrains the inter-tetrahedral linkages in a physically transparent manner. Critically, it is found to control the balance between the stability of corner- and edge-sharing tetrahedra. A potential rigidity transformation is investigated. The vibrational density of states is investigated, using an instantaneous normal model analysis, as a function of both anion polarizability and temperature. A low frequency peak is seen to appear and is shown to be correlated with the fraction of cations which are linked through solely edge-sharing structural motifs. A modified effective mean atom coordination number is proposed which allows the appearance of the low frequency feature to be understood in terms of a mean field rigidity percolation threshold.

Atomistic theory and simulation of the morphology and structure of ionic nanoparticles

Computational techniques are widely used to explore the structure and properties of nanomaterials. This review surveys the application of both quantum mechanical and force field based atomistic simulation methods to nanoparticles, with a particular focus on the methodologies available and the ways in which they can be utilised to study structure, phase stability and morphology. The main focus of this article is on partially ionic materials, from binary semiconductors through to mineral nanoparticles, with more detailed considered of three examples, namely titania, zinc sulphide and calcium carbonate.

Formation of, and ion-transport in, low-dimensional crystallites in carbon nanotubes

The formation of low-dimensional crystal structures, obtained by filling carbon nanotubes from the molten salts, is considered for three stoichiometries (the MX, MX2 and MX3). For the MX stoichiometry, general classes of inorganic nanotube (INT) are predicted to exist whose morphology depends both on the low-energy (bulk) crystal structure and the encasing carbon nanotube diameter. These INTs are generally found to have no direct bulk analogues. For both the MX2 and MX3 stoichiometries crystal structures are predicted which either have a direct bulk analogue, or whose structure can be considered as a distortion of a bulk fragment. In both of these stoichiometries unusual (high anion coordination) crystallites are predicted. For the MX stoichiometry the ion transport mechanism is investigated and discussed, whilst for the MX3 the vibrational densities of states are analysed with respect to both the pure liquid and idealized crystallites.

Ion mobilities and microscopic dynamics in liquid (Li,K)Cl

The dynamical properties of ionic melts formed from mixtures of LiCl and KCl have been studied across the full composition range in computer simulations of sufficient length to enable reliable values for such collective transport coefficients as the viscosity, conductivity, and internal mobilities to be determined reliably. Interest centers on the nontrivial concentration dependence exhibited by these transport coefficients, which agrees well with that observed experimentally, and in relating this to the strength of the association between an ion and its first coordination shell. The relationships between the various transport coefficients, such as those between the diffusion coefficient and the viscosity (Stokes-Einstein) and the conductivity (Nernst-Einstein) also exhibit composition dependences that reflect this association. The connection between the internal mobility and two measures of the coordination shell dynamics (the cage relaxation time and the self-exchange velocity) is explored; it is shown that the self-exchange velocity follows the composition and temperature dependence of the internal mobility very well. Finally, it is shown that allowing for anion polarization in the interaction model increases the mobility of all species without changing the structure of the melt discernibly, with the largest effect being found for the Li(+) ion.

Anharmonic Raman spectra in high-pressure ice from ab initio simulations

We calculate from ab initio molecular dynamics the Raman scattering of high-pressure ice. To this effect we apply a new method based on the Berry phase theory of polarization. Our results are in agreement with recent and difficult experiments and are compatible with a picture in which ice VII is a proton-disordered system and in ice X the hydrogen bond is symmetric.

Diffraction of trapped (CsI)(n)Cs+: the appearance of bulk structure

We report an investigation of (CsI)(n)Cs (+) cluster structures (n = 30-39) studied using the recently developed technique of trapped ion electron diffraction. Contributions to diffraction from both rock salt (NaCl) and cesium chloride lattice (CsCl) derived isomeric structures are observed at size n = 32. This size can form a closed shell rhombic dodecahedron corresponding to the CsI bulk structure. All other sizes, n not equal32, are dominated by the NaCl structure. Density functional calculations and molecular dynamic simulations identify the presence of a stable CsCl lattice derived structure isomer which is consistent with these results.