Informative Training Data for Efficient Property Prediction in Metal-Organic Frameworks by Active Learning.

In recent data-driven approaches to material discovery, scenarios where target quantities are expensive to compute and measure are often overlooked. In such cases, it becomes imperative to construct a training set that includes the most diverse, representative, and informative samples. Here, a novel regression tree-based active learning algorithm is employed for such a purpose. It is applied to predict the band gap and adsorption properties of metal-organic frameworks (MOFs), a novel class of materials that results from the virtually infinite combinations of their building units. Simpler and low dimensional descriptors, such as those based on stoichiometric and geometric properties, are used to compute the feature space for this model owing to their ability to better represent MOFs in the low data regime. The partitions given by a regression tree constructed on the labeled part of the data set are used to select new samples to be added to the training set, thereby limiting its size while maximizing the prediction quality. Tests on the QMOF, hMOF, and dMOF data sets reveal that our method constructs small training data sets to learn regression models that predict the target properties more efficiently than existing active learning approaches, and with lower variance. Specifically, our active learning approach is highly beneficial when labels are unevenly distributed in the descriptor space and when the label distribution is imbalanced, which is often the case for real world data. The regions defined by the tree help in revealing patterns in the data, thereby offering a unique tool to efficiently analyze complex structure-property relationships in materials and accelerate materials discovery.

Artificial Neural Network-Based Density Functional Approach for Adiabatic Energy Differences in Transition Metal Complexes.

During the past decades, approximate Kohn-Sham density functional theory schemes have garnered many successes in computational chemistry and physics, yet the performance in the prediction of spin state energetics is often unsatisfactory. By means of a machine learning approach, an enhanced exchange and correlation functional is developed to describe adiabatic energy differences in transition metal complexes. The functional is based on the computationally efficient revision of the regularized, strongly constrained, and appropriately normed functional and improved by an artificial neural network correction trained over a small data set of electronic densities, atomization energies, and/or spin state energetics. The training process, performed using a bioinspired nongradient-based approach adapted for this work from the particle swarm optimization, is analyzed and discussed extensively. The resulting machine learned meta-generalized gradient approximation functional is shown to outperform most known density functionals in the prediction of adiabatic energy differences for a diverse set of transition metal complexes with varying local coordinations and metal choices.

Machine learning interatomic potentials for aluminium: application to solidification phenomena.

In studying solidification process by simulations on the atomic scale, the modeling of crystal nucleation or amorphization requires the construction of interatomic interactions that are able to reproduce the properties of both the solid and the liquid states. Taking into account rare nucleation events or structural relaxation under deep undercooling conditions requires much larger length scales and longer time scales than those achievable byab initiomolecular dynamics (AIMD). This problem is addressed by means of classical molecular dynamics simulations using a well established high dimensional neural network potential trained on a set of configurations generated by AIMD relevant for solidification phenomena. Our dataset contains various crystalline structures and liquid states at different pressures, including their time fluctuations in a wide range of temperatures. Applied to elemental aluminium, the resulting potential is shown to be efficient to reproduce the basic structural, dynamics and thermodynamic quantities in the liquid and undercooled states. Early stages of crystallization are further investigated on a much larger scale with one million atoms, allowing us to unravel features of the homogeneous nucleation mechanisms in the fcc phase at ambient pressure as well as in the bcc phase at high pressure with unprecedented accuracy close to theab initioone. In both cases, a single step nucleation process is observed.

Unsupervised topological learning for identification of atomic structures.

We propose an unsupervised learning methodology with descriptors based on topological data analysis (TDA) concepts to describe the local structural properties of materials at the atomic scale. Based only on atomic positions and without a priori knowledge, our method allows for an autonomous identification of clusters of atomic structures through a Gaussian mixture model. We apply successfully this approach to the analysis of elemental Zr in the crystalline and liquid states as well as homogeneous nucleation events under deep undercooling conditions. This opens the way to deeper and autonomous study of complex phenomena in materials at the atomic scale.

Unsupervised topological learning approach of crystal nucleation.

Nucleation phenomena commonly observed in our every day life are of fundamental, technological and societal importance in many areas, but some of their most intimate mechanisms remain however to be unravelled. Crystal nucleation, the early stages where the liquid-to-solid transition occurs upon undercooling, initiates at the atomic level on nanometre length and sub-picoseconds time scales and involves complex multidimensional mechanisms with local symmetry breaking that can hardly be observed experimentally in the very details. To reveal their structural features in simulations without a priori, an unsupervised learning approach founded on topological descriptors loaned from persistent homology concepts is proposed. Applied here to monatomic metals, it shows that both translational and orientational ordering always come into play simultaneously as a result of the strong bonding when homogeneous nucleation starts in regions with low five-fold symmetry. It also reveals the specificity of the nucleation pathways depending on the element considered, with features beyond the hypothesis of Classical Nucleation Theory.

Excess entropy scaling law: A potential energy landscape view.

The relationship between excess entropy and diffusion is revisited by means of large-scale computer simulation combined to supervised learning approach to determine the excess entropy for the Lennard-Jones potential. Results reveal a strong correlation with the properties of the potential energy landscape (PEL). In particular the exponential law holding in the liquid is seen to be linked with the landscape-influenced regime of the PEL whereas the fluidlike power-law corresponds to the free diffusion regime.

The intimate relationship between structural relaxation and the energy landscape of monatomic liquid metals.

The characteristic property of a liquid, discriminating it from a solid, is its fluidity, which can be expressed by a velocity field. The reaction of the velocity field on forces is enshrined in the transport parameter viscosity. In contrast, a solid reacts to forces elastically through a displacement field, the particles are trapped in their potential minimum. The flow in a liquid needs enough thermal energy to overcome the changing potential barriers, which is supported through a continuous rearrangement of surrounding particles. Cooling a liquid will decrease the fluidity of a particle and the mobility of the neighbouring particles, resulting in an increase of the viscosity until the system comes to an arrest. This process with a concomitant slowing down of collective particle rearrangements might already start deep inside the liquid state. The idea of the potential energy landscape provides an attractive picture for these dramatic changes. However, despite the appealing idea there is a scarcity of quantitative assessments, in particular, when it comes to experimental studies. Here we present results on a monatomic liquid metal through a combination of ab initio molecular dynamics, neutron spectroscopy and inelastic x-ray scattering. We investigated the collective dynamics of liquid aluminium to reveal the changes in dynamics when the high temperature liquid is cooled towards solidification. The results demonstrate the main signatures of the energy landscape picture, a reduction in the internal atomic structural energy, a transition to a stretched relaxation process and a deviation from the high-temperature Arrhenius behavior of the relaxation time. All changes occur in the same temperature range at about [Formula: see text], which can be regarded as the temperature when the liquid aluminium enters the landscape influenced phase and enters a more viscous liquid state towards solidification. The similarity in dynamics with other monatomic liquid metals suggests a universal dynamic crossover above the melting point.

Ab initiobased interionic interactions in calcium aluminotitanate oxide melts: structure and diffusion.

Calcium aluminotitanate (CaO-Al2O3-TiO2) ternary oxides are of fundamental interest in Materials as well as Earth and environmental science, and a key system for several industrial applications. As their properties at the atomic scale are scarcely known, interionic interactions for the melts are built from a bottom up strategy consisting in fitting first only Al2O3, CaO and TiO2single oxide compounds separately with a unified description of the oxygen charge and O-O interaction term. For this purpose, a mean-square difference minimization of the partial pair-correlation functions with respect to theab initioreference was performed. The potentials for the ternary oxide are finally built straightforwardly by adding purely Coulomb terms for dissimilar cation-cation interactions without further fit. This general and unified approach is transferable and successfully describes the structural and diffusion properties of the three single oxides as well as the ternary melts simultaneously. A possible underlying structural mechanism at the origin of the diffusion evolution with TiO2content is proposed based on the formation of Ti induced triply bonded oxygen.

Thermodynamics and structural properties of CaO: A molecular dynamics simulation study.

A detailed theoretical study of CaO in the solid and liquid states by means of combined classical and ab initio molecular dynamics simulations is presented. Evolution of the specific heat capacity at constant pressure as a function of temperature is studied, and the melting temperature and enthalpy of fusion are determined. It is shown that an empirical Born-Mayer-Huggins potential gives a good representation of pure CaO in the liquid and solid states as compared to available experimental data and density functional theory calculations. Consistency of the predicted results obtained for CaO with the data available in commercial thermodynamic databases and experimental values in the literature is discussed. The present methodology and theoretical results provide a new accurate basis for calculations of thermodynamic properties in a temperature range that is hardly accessible by experiments.

Pressure-induced effects in the spectra of collective excitations in pure liquid metals.

Collective dynamics of metallic melts at high pressures is one of the open issues of condensed matter physics. By means of ab initio molecular dynamics simulations, we examine features of dispersions of collective excitations through transverse current spectral functions, as a function of pressure. Typical metallic melts, such as Li and Na monovalent metals as well as Al, Pb and In polyvalent metals are considered. We firmly establish the emergence of a second branch of high-frequency transverse modes with pressure in these metals, that we associate with the pronounced high-frequency shoulder in the vibrational density of states. Similar correlation also exist with the low frequency modes. The origin of the pressure-induced evolution of transverse excitations in liquid metals is discussed.

Molecular dynamics simulations of amorphous Ni-P alloy formation by rapid quenching and atomic deposition.

A combined experimental and simulation study is carried out to compare the properties of amorphous Ni100-x P x alloys obtained by electroless deposition and rapid melt-quenching. The onset of crystallization of experimental electroless deposited amorphous films is measured by differential scanning calorimetry experiments. Classical molecular dynamics simulations using Embedded Atom Model-based interactions are performed to obtain glassy Ni-P by melt-quenching the liquid with various quenching rates, as well as via low-energy chemical deposition to mimic experimental electroless deposition. It is shown that the deposited amorphous and glassy states display similar short-range order. The amorphous deposit corresponds to a glassy state obtained with a cooling rate of 109 K s-1, indicating that deposition yields generally more relaxed amorphous structures. The appearance of phosphorus-enriched surface on the simulated deposited thin film, comparable to experimental observations, is discussed.

Structural and dynamic properties of aluminosilicate melts: a molecular dynamics study.

In the present work, the structural and dynamic properties of aluminosilicates (Al2O3) x -(SiO2)1-x (AS) as a function of the Al2O3 concentration x are studied by means of molecular dynamics simulations. Firstly, the parametrization of the Born-Mayer-Huggins type potential developed recently for the more general CaO-Al2O3-SiO2 ternary system is assessed. Comparison of local structural properties, such as the x-ray structure factor, partial pair-correlation functions, distributions of coordination numbers and bond angles, as well as the dynamics through the viscosity and self-diffusion coefficients to experimental data and other molecular dynamics simulations found in the literature, shows that this potential is transferable to AS melts for all compositions and is more reliable than other empirical potentials used so far. The evolution of viscosity with temperature in stable liquid and undercooled regions is studied in the whole composition range and results show a progressive increase of the fragility with increasing Al2O3 content correlated to that of local structural entities like the triply bonded oxygen (TBO), AlO5 and AlO6.

Pressure evolution of transverse collective excitations in liquid Al along the melting line.

Evolution of structure and dynamics of liquid Al with pressure along the melting line up to 300 GPa has been studied by means of ab initio molecular dynamics simulations. An analysis of structural properties shows that liquid Al undergoes uniform compression with pressure associated with a competition of the existing icosahedral local order with bcc ordering above 200 GPa. Dispersion of collective excitations indicates the presence of two branches of transverse nonpropagative modes in the second pseudo-Brillouin zone. Under pressure, the second high-frequency branch manifests as the second peak position in transverse current correlation functions, while, for ambient pressure, it corresponds to a smeared-out high-frequency shoulder. We report a correspondence of the peak locations in vibrational density of states with these two transverse collective excitations as well as their linear evolution with density.

Liquid Aluminum: atomic diffusion and viscosity from ab initio molecular dynamics.

We present a study of dynamic properties of liquid aluminum using density-functional theory within the local-density (LDA) and generalized gradient (GGA) approximations. We determine the temperature dependence of the self-diffusion coefficient as well the viscosity using direct methods. Comparisons with experimental data favor the LDA approximation to compute dynamic properties of liquid aluminum. We show that the GGA approximation induce more important backscattering effects due to an enhancement of the icosahedral short range order (ISRO) that impact directly dynamic properties like the self-diffusion coefficient. All these results are then used to test the Stokes-Einstein relation and the universal scaling law relating the diffusion coefficient and the excess entropy of a liquid.

Molecular-dynamics study of liquid nickel above and below the melting point.

We have investigated the structural and dynamic properties of liquid nickel by means of large-scale molecular-dynamics simulations, using an effective-pair potential derived from the second-order pseudopotential perturbation theory. The model of interactions is assessed on the single-atom as well as collective dynamic properties. The short-range order in the stable and undercooled liquids is also examined. We show that the present model potential gives a description of the local structure in both states in close agreement with first-principles molecular-dynamics simulations.

Ab initio molecular dynamics simulations of local structure of supercooled Ni.

We report results of first-principles molecular dynamics simulations for stable and undercooled nickel liquids. The calculated structure factors as a function of temperature are discussed with respect to recent experimental measurements. In addition, structural analysis using bonding orientational order and three-dimensional pair analysis techniques have been performed in detail and the effect of undercooling on the microstructure has been analyzed. More particularly, we show the importance of fivefold symmetry local structures.

Local order of liquid and supercooled zirconium by ab initio molecular dynamics.

It has been suggested that icosahedral short-range order (SRO) occurs in deeply undercooled melts of pure metallic elements. We report results of first-principles molecular dynamics simulations for stable and undercooled zirconium liquids. Our results emphasize the occurrence of a local order more complex than the icosahedral one. For stable liquid, the local order is interpreted on the basis of a competition between a polytetrahedral SRO and a bcc-type SRO. We also demonstrate that a bcc-type SRO increases with the degree of undercooling.