From first-principles to material properties

Capturing the interactions in the BaSnF4 ionic conductor: Comparison between a machine-learning potential and a polarizable force field

BaSnF4 is a prospective solid state electrolyte for fluoride ion batteries. However, the diffusion mechanism of the fluoride ions remains difficult to study, both in experiments and in simulations. In principle, ab initio molecular dynamics could allow to fill this gap, but this method remains very costly from the computational point of view. Using machine learning potentials is a promising method that can potentially address the accuracy issues of classical empirical potentials while maintaining high efficiency. In this work, we fitted a dipole polarizable ion model and trained machine learning potential for BaSnF4 and made comprehensive comparisons on the ease of training, accuracy and efficiency. We also compared the results with the case of a simpler ionic system (NaF). We show that contrarily to the latter, for BaSnF4 the machine learning potential offers much higher versatility. The current work lays foundations for the investigation of fluoride ion mobility in BaSnF4 and provides insight on the choice of methods for atomistic simulations.

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.

Study of the Partial Charge Transport Properties in the Molten Alumina via Molecular Dynamics

Knowing the charge-transport properties of molten oxides is essential for industrial applications, particularly when attempting to control the energy required to separate a metal from its ore concentrate. Nowadays, in the context of a drastic increase of computational resources, research in industrial process simulation and their optimization is gaining popularity. Such simulations require accurate data as input for properties in a wide range of compositions, temperatures, and mechanical stresses. Unfortunately, due to their high melting points, we observe a severe lack of (reproducible) experimental data for many of the molten oxides. An alternative consists in using molecular dynamic simulations employing nonempirical force fields to predict the charge-transport properties of molten oxides and thus alleviate the lack of experimental data. Here, we study molten alumina using two polarizable force fields, with different levels of sophistication, parameterized on electronic structure calculations only. After validating the models against the experimental sets of density and electrical conductivity, we are able to determine the various ionic contributions to the overall charge transport in a wide range of temperatures.

Molecular dynamics determination of liquid-vapor coexistence in molten alkali halides

We show by extensive molecular dynamics simulations that accurate predictions of liquid-vapor coexistence in molten alkali halides can be achieved in terms of a rigid ion potential description in which temperature-dependent ionic diameters are employed. The new ionic sizes result from the fitting of the experimental isothermal compressibilities, a condition whose physical implications and consequences are illustrated. The same diameters also allow us to formulate confident predictions for the compressibilities of salts in cases where the experimental data are lacking. The extension of the present approach to molten alkali-halide mixtures and to other classes of molten salts is discussed.

From atomic structure to excess entropy: a neutron diffraction and density functional theory study of CaO-Al₂O₃-SiO₂ melts

Calcium aluminosilicate CaO-Al2O3-SiO2 (CAS) melts with compositions (CaO-SiO2)(x)(Al2O3)(1-x) for x  <  0.5 and (Al2O3)(x)(SiO2)(1-x) for x ≥ 0.5 are studied using neutron diffraction with aerodynamic levitation and density functional theory molecular dynamics modelling. Simulated structure factors are found to be in good agreement with experimental structure factors. Local atomic structures from simulations reveal the role of calcium cations as a network modifier, and aluminium cations as a non-tetrahedral network former. Distributions of tetrahedral order show that an increasing concentration of the network former Al increases entropy, while an increasing concentration of the network modifier Ca decreases entropy. This trend is opposite to the conventional understanding that increasing amounts of network former should increase order in the network liquid, and so decrease entropy. The two-body correlation entropy S2 is found to not correlate with the excess entropy values obtained from thermochemical databases, while entropies including higher-order correlations such as tetrahedral order, O-M-O or M-O-M bond angles and Q(N) environments show a clear linear correlation between computed entropy and database excess entropy. The possible relationship between atomic structures and excess entropy is discussed.

Sparse Cyclic Excitations Explain the Low Ionic Conductivity of Stoichiometric Li_{7}La_{3}Zr_{2}O_{12}

We have performed long time scale molecular dynamics simulations of the cubic and tetragonal phases of the solid lithium-ion electrolyte Li_{7}La_{3}Zr_{2}O_{12} (LLZO), using a first-principles parametrized interatomic potential. Collective lithium transport was analyzed by identifying dynamical excitations: persistent ion displacements over distances comparable to the separation between lithium sites, and stringlike clusters of ions that undergo cooperative motion. We find that dynamical excitations in c-LLZO (cubic) are frequent, with participating lithium numbers following an exponential distribution, mirroring the dynamics of fragile glasses. In contrast, excitations in t-LLZO (tetragonal) are both temporally and spatially sparse, consisting preferentially of highly concerted lithium motion around closed loops. This qualitative difference is explained as a consequence of lithium ordering in t-LLZO and provides a mechanistic basis for the much lower ionic conductivity of t-LLZO compared to c-LLZO.

Thermal transport properties of halide solid solutions: Experiments vs equilibrium molecular dynamics

The composition dependence of thermal transport properties of the (Na,K)Cl rocksalt solid solution is investigated through equilibrium molecular dynamics (EMD) simulations in the entire range of composition and the results are compared with experiments published in recent work [Gheribi et al., J. Chem. phys. 141, 104508 (2014)]. The thermal diffusivity of the (Na,K)Cl solid solution has been measured from 473 K to 823 K using the laser flash technique, and the thermal conductivity was deduced from critically assessed data of heat capacity and density. The thermal conductivity was also predicted at 900 K in the entire range of composition by a series of EMD simulations in both NPT and NVT statistical ensembles using the Green-Kubo theory. The aim of the present paper is to provide an objective analysis of the capability of EMD simulations in predicting the composition dependence of the thermal transport properties of halide solid solutions. According to the Klemens-Callaway [P. G. Klemens, Phys. Rev. 119, 507 (1960) and J. Callaway and H. C. von Bayer, Phys. Rev. 120, 1149 (1960)] theory, the thermal conductivity degradation of the solid solution is explained by mass and strain field fluctuations upon the phonon scattering cross section. A rigorous analysis of the consistency between the theoretical approach and the EMD simulations is discussed in detail.

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.

Direct computation of parameters for accurate polarizable force fields

We present an improved electronic linear response model to incorporate polarization and charge-transfer effects in polarizable force fields. This model is a generalization of the Atom-Condensed Kohn-Sham Density Functional Theory (DFT), approximated to second order (ACKS2): it can now be defined with any underlying variational theory (next to KS-DFT) and it can include atomic multipoles and off-center basis functions. Parameters in this model are computed efficiently as expectation values of an electronic wavefunction, obviating the need for their calibration, regularization, and manual tuning. In the limit of a complete density and potential basis set in the ACKS2 model, the linear response properties of the underlying theory for a given molecular geometry are reproduced exactly. A numerical validation with a test set of 110 molecules shows that very accurate models can already be obtained with fluctuating charges and dipoles. These features greatly facilitate the development of polarizable force fields.

Ceria co-doping: synergistic or average effect?

Ceria (CeO2) co-doping has been suggested as a means to achieve ionic conductivities that are significantly higher than those in singly doped systems. Rekindled interest in this topic over the last decade has given rise to claims of much improved performance. The present study makes use of computer simulations to investigate the bulk ionic conductivity of rare earth (RE) doped ceria, where RE = Sc, Gd, Sm, Nd and La. The results from the singly doped systems are compared to those from ceria co-doped with Nd/Sm and Sc/La. The pattern that emerges from the conductivity data is consistent with the dominance of local lattice strains from individual defects, rather than the synergistic co-doping effect reported recently, and as a result, no enhancement in the conductivity of co-doped samples is observed.

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.

Density-driven structural transformations in network forming glasses: a high-pressure neutron diffraction study of GeO2 glass up to 17.5 GPa

The structure of GeO(2) glass was investigated at pressures up to 17.5(5) GPa using in situ time-of-flight neutron diffraction with a Paris-Edinburgh press employing sintered diamond anvils. A new methodology and data correction procedure were developed, enabling a reliable measurement of structure factors that are largely free from diamond Bragg peaks. Calibration curves, which are important for neutron diffraction work on disordered materials, were constructed for pressure as a function of applied load for both single and double toroid anvil geometries. The diffraction data are compared to new molecular-dynamics simulations made using transferrable interaction potentials that include dipole-polarization effects. The results, when taken together with those from other experimental methods, are consistent with four densification mechanisms. The first, at pressures up to approximately equal 5 GPa, is associated with a reorganization of GeO(4) units. The second, extending over the range from approximately equal 5 to 10 GPa, corresponds to a regime where GeO(4) units are replaced predominantly by GeO(5) units. In the third, as the pressure increases beyond ~10 GPa, appreciable concentrations of GeO(6) units begin to form and there is a decrease in the rate of change of the intermediate-range order as measured by the pressure dependence of the position of the first sharp diffraction peak. In the fourth, at about 30 GPa, the transformation to a predominantly octahedral glass is achieved and further densification proceeds via compression of the Ge-O bonds. The observed changes in the measured diffraction patterns for GeO(2) occur at similar dimensionless number densities to those found for SiO(2), indicating similar densification mechanisms for both glasses. This implies a regime from about 15 to 24 GPa where SiO(4) units are replaced predominantly by SiO(5) units, and a regime beyond ~24 GPa where appreciable concentrations of SiO(6) units begin to form.

A transferable ab initio based force field for aqueous ions

We present a new polarizable force field for aqueous ions (Li(+), Na(+), K(+), Rb(+), Cs(+), Mg(2 +), Ca(2 +), Sr(2 +), and Cl(-)) derived from condensed phase ab initio calculations. We use maximally localized Wannier functions together with a generalized force and dipole-matching procedure to determine the whole set of parameters. Experimental data are then used only for validation purposes and a good agreement is obtained for structural, dynamic, and thermodynamic properties. The same procedure applied to crystalline phases allows to parametrize the interaction between cations and the chloride anion. Finally, we illustrate the good transferability of the force field to other thermodynamic conditions by investigating concentrated solutions.

A dipole polarizable potential for reduced and doped CeO(2) obtained from first principles

In this paper we present the parameterization of a new interionic potential for stoichiometric, reduced and doped CeO(2). We use a dipole polarizable potential (DIPPIM: the dipole polarizable ion model) and optimize its parameters by fitting them to a series of density functional theory calculations. The resulting potential was tested by calculating a series of fundamental properties for CeO(2) and by comparing them against experimental values. The values for all the calculated properties (thermal and chemical expansion coefficients, lattice parameters, oxygen migration energies, local crystalline structure and elastic constants) are within 10-15% of the experimental ones, an accuracy comparable to that of ab initio calculations. This result suggests the use of this new potential for reliably predicting atomic scale properties of CeO(2) in problems where ab initio calculations are not feasible due to their size limitations.

The structure of liquid calcium aluminates as investigated using neutron and high energy x-ray diffraction in combination with molecular dynamics simulation methods

The structure of laser heated aerodynamically levitated (CaO)(x)(Al₂O₃)(1-x) high temperature liquids, with x = 0.33, 0.5, 0.75, was measured by using neutron and high energy x-ray diffraction. The partial structure factors for the liquids at 2500 K were also determined using molecular dynamics computer simulations. The simulation results are in excellent agreement with the diffraction measurements. The results show a predominant tetrahedral Al coordination with approximately 20% of fivefold coordinated Al at x = 0.33 which reduces with increasing CaO concentration. The Ca atoms occupy a broad range of coordination environments but with a predominance of sixfold distorted octahedra. The simulations confirm the presence of 13, 7 and 0.6% OAl₃ triclusters connecting AlO₄ tetrahedra in the structure of CA2 (x = 0.33), CA (x = 0.5) and C3A (x = 0.75) liquids, respectively.

High-pressure behaviour of GeO2: a simulation study

In this work we study the high-pressure behaviour of liquid and glassy GeO(2) by means of molecular dynamics simulations. The interaction potential, which includes dipole polarization effects, was parametrized using first-principles calculations. Our simulations reproduce the most recent experimental structural data very well. The character of the pressure-induced structural transition in the glassy system has been a matter of controversy. We show that our simulations and the experimental data are consistent with a smooth transition from a tetrahedral to an octahedral network with a significant number of pentacoordinated germanium ions appearing over an extended pressure range. Finally, the study of high-pressure, liquid germania confirms that this material presents an anomalous behaviour of the diffusivity as observed in analogous systems such as silica and water. The importance of pentacoordinated germanium ions for such behaviour is stressed.

Cation composition effects on oxide conductivity in the Zr(2)Y(2)O(7)-Y(3)NbO(7) system

Polarizable interaction potentials, parametrized using ab initio electronic structure calculations, have been used in molecular dynamics simulations to study the effect of cation composition on the ionic conductivity in the Zr(2)Y(2)O(7)-Y(3)NbO(7) system and to link the dynamical properties to the degree of lattice disorder. Across the composition range, this system retains a disordered fluorite crystal structure and the vacancy concentration is constant. The observed trends of decreasing conductivity and increasing disorder with increasing Nb(5+) content were reproduced in simulations with the cations randomly assigned to positions on the cation sublattice. The trends were traced to the influences of the cation charges and relative sizes and their effect on vacancy ordering by carrying out additional calculations in which, for example, the charges of the cations were equalized. The simulations did not, however, reproduce all of the observed properties, particularly for Y(3)NbO(7). Its conductivity was significantly overestimated and prominent diffuse scattering features observed in small area electron diffraction studies were not always reproduced. Consideration of these deficiencies led to a preliminary attempt to characterize the consequence of partially ordering the cations on their lattice, which significantly affects the propensity for vacancy ordering. The extent and consequences of cation ordering seem to be much less pronounced on the Zr(2)Y(2)O(7) side of the composition range.

Local structure and ionic conductivity in the Zr(2)Y(2)O(7)-Y(3)NbO(7) system

The Zr(0.5-0.5x)Y(0.5+0.25x)Nb(0.25x)O(1.75) solid solution possesses an anion-deficient fluorite structure across the entire 0≤x≤1 range. The relationship between the disorder within the crystalline lattice and the preferred anion diffusion mechanism has been studied as a function of x, using impedance spectroscopy measurements of the ionic conductivity (σ), powder neutron diffraction studies, including analysis of the 'total' scattering to probe the nature of the short-range correlations between ions using reverse Monte Carlo (RMC) modelling, and molecular dynamics (MD) simulations using potentials derived with a strong ab initio basis. The highest total ionic conductivity (σ = 2.66 × 10(-2) Ω(-1) cm(-1) at 1473 K) is measured for the Zr(2)Y(2)O(7) (x = 0) end member, with a decrease in σ with increasing x, whilst the neutron diffraction studies show an increase in lattice disorder with x. This apparent contradiction can be understood by considering the local structural distortions around the various cation species, as determined from the RMC modelling and MD simulations. The addition of Nb(5+) and its stronger Coulomb interaction generates a more disordered local structure and enhances the mobility of some anions. However, the influence of these pentavalent cations is outweighed by the effect of the additional Y(3+) cations introduced as x increases, which effectively trap many anions and reduce the overall concentration of the mobile O(2-) species.

Many-body effects and simulations of potassium channels

The electronic polarizability of an ion or a molecule is a measure of the relative tendency of its electron cloud to be distorted from its normal shape by an electric field. On the molecular scale, in a condensed phase, any species sits in an electric field due to its neighbours, and the resulting polarization is an important contribution to the total interaction energy. Electrostatic interactions are crucial for determining the majority of chemical–physical properties of the system and electronic polarization is a fundamental component of these interactions. Thus, polarization effects should be taken into account if accurate descriptions are desired. In classical computer simulations, the forces required to drive the system are typically based on interatomic interaction potentials derived in part from electronic structure calculations or from experimental data. Owing to the difficulties in including polarization effects in classical force fields, most of them are based just on pairwise additive interaction potentials. At present, major efforts are underway to develop polarizable interaction potentials for biomolecular simulations. In this review, various ways of introducing explicit polarizability into biomolecular models and force fields are reviewed, and the progress that might be achieved in applying such methods to study potassium channels is described.