Crystal Structure Representations for Machine Learning Models of Formation Energies

We introduce and evaluate a set of feature vector representations of crystal structures for machine learning (ML) models of formation energies of solids. ML models of atomization energies of organic molecules have been successful using a Coulomb matrix representation of the molecule. We consider three ways to generalize such representations to periodic systems: (i) a matrix where each element is related to the Ewald sum of the electrostatic interaction between two different atoms in the unit cell repeated over the lattice; (ii) an extended Coulomb-like matrix that takes into account a number of neighboring unit cells; and (iii) an Ansatz that mimics the periodicity and the basic features of the elements in the Ewald sum matrix by using a sine function of the crystal coordinates of the atoms. The representations are compared for a Laplacian kernel with Manhattan norm, trained to reproduce formation energies using a data set of 3938 crystal structures obtained from the Materials Project. For training sets consisting of 3000 crystals, the generalization error in predicting formation energies of new structures corresponds to (i) 0.49, (ii) 0.64, and (iii) 0.37 eV/atom for the respective representations

Steric engineering of metal-halide perovskites with tunable optical band gaps

Owing to their high energy-conversion efficiency and inexpensive fabrication routes, solar cells based on metal-organic halide perovskites have rapidly gained prominence as a disruptive technology. An attractive feature of perovskite absorbers is the possibility of tailoring their properties by changing the elemental composition through the chemical precursors. In this context, rational in silico design represents a powerful tool for mapping the vast materials landscape and accelerating discovery. Here we show that the optical band gap of metal-halide perovskites, a key design parameter for solar cells, strongly correlates with a simple structural feature, the largest metal-halide-metal bond angle. Using this descriptor we suggest continuous tunability of the optical gap from the mid-infrared to the visible. Precise band gap engineering is achieved by controlling the bond angles through the steric size of the molecular cation. Based on these design principles we predict novel low-gap perovskites for optimum photovoltaic efficiency, and we demonstrate the concept of band gap modulation by synthesising and characterising novel mixed-cation perovskites.Comment: This manuscript was submitted for publication on March 6th, 2014. Many of the results presented in this manuscript were presented at the International Conference on Solution processed Semiconductor Solar Cells, held in Oxford, UK, on 10-12 September 2014. The manuscript is 37 pages long and contains 8 figure

Appearance of the Single Gyroid Network Phase in Nuclear Pasta Matter

Nuclear matter under the conditions of a supernova explosion unfolds into a rich variety of spatially structured phases, called nuclear pasta. We investigate the role of periodic network-like structures with negatively curved interfaces in nuclear pasta structures, by static and dynamic Hartree-Fock simulations in periodic lattices. As the most prominent result, we identify for the first time the {\it single gyroid} network structure of cubic chiral $I4_123$ symmetry, a well known configuration in nanostructured soft-matter systems, both as a dynamical state and as a cooled static solution. Single gyroid structures form spontaneously in the course of the dynamical simulations. Most of them are isomeric states. The very small energy differences to the ground state indicate its relevance for structures in nuclear pasta.Comment: 7 pages, 4 figure

Thermodynamic insight into stimuli-responsive behaviour of soft porous crystals

Knowledge of the thermodynamic potential in terms of the independent variables allows to characterize the macroscopic state of the system. However, in practice, it is difficult to access this potential experimentally due to irreversible transitions that occur between equilibrium states. A showcase example of sudden transitions between (meta) stable equilibrium states is observed for soft porous crystals possessing a network with long-range structural order, which can transform between various states upon external stimuli such as pressure, temperature and guest adsorption. Such phase transformations are typically characterized by large volume changes and may be followed experimentally by monitoring the volume change in terms of certain external triggers. Herein, we present a generalized thermodynamic approach to construct the underlying Helmholtz free energy as a function of the state variables that governs the observed behaviour based on microscopic simulations. This concept allows a unique identification of the conditions under which a material becomes flexible

Stability of magnesium binary and ternary compounds for batteries determined from first principles

Electrochemical stability is a critical performance parameter for the materials used as electrolytes and electrodes in batteries. Using first-principles electronic structure calculations, we have determined the electrochemical stability windows of magnesium binary and ternary spinel compounds. These materials are candidates for protective coating, solid electrolytes and cathodes in Mg-ion batteries, which represent a promising sustainable alternative to Li-ion batteries that still dominate the battery market. Furthermore, we have applied and assessed two different criteria for the chemical stability of compounds. For the spinel materials, we identify the critical role of the ionic radii of the transition metal for the stability of the compounds. In addition, we determine the ion mobility in these materials using a recently developed descriptor. We thus provide guidelines for the choice of promising solid materials for Mg-ion batteries with improved properties

Enhancing the oxygen vacancy formation and migration in bulk chromium(iii) oxide by alkali metal doping: a change from isotropic to anisotropic oxygen diffusion

Oxygen vacancy formation and migration are vital properties for reducible oxides such as TiO2, CeO2 and Cr2O3 as the oxygen storage capacity (OSC) of these materials are important for a wide range of applications in photovoltaics, oxidative catalysis and solid oxide fuel cells. Substitutional doping these transition metal oxides enhances their OSC potential, in particular for oxygenation and surface reaction chemistry. This study uses density functional theory with on-site Coulomb interactions (PBE+U) for Cr 3d states (+U = 5 eV) and O 2p states (+U = 5.5 eV) to calculate the oxygen vacancy formation energy and oxygen diffusion pathways for alkali metal (Li, K, Na, Rb) doping of bulk chromium(III) oxide (α-Cr2O3). Substitutional doping of the lattice Cr3+ cations with alkali metals that have a +1 oxidation state, creates two hole states on the neighbouring lattice O atoms, and removal of a lattice oxygen charge compensates the dopants by filling the holes. The removal of the next oxygen describes the reducibility of doped Cr2O3. The oxygen vacancy formation energy is greatly promoted by the alkali dopants with a correlation between the ionic radius of the dopant cation and vacancy formation energy; larger dopants (K, Rb) improve the reducibility more than the smaller dopants (Li, Na). The activation barriers for oxygen migration along different directions in the alkali metal doped Cr2O3 bulk were also calculated to examine the effect of doping on the oxygen migration. The calculated activation energies for the undoped chromia are symmetric in three dimensions (isotropic) and the presence of the dopants break this isotropy. Alkali dopants promote oxygen migration in the oxygen intra-layers while suppressing oxygen migration across the Cr cation layers. The smaller dopants (Li, Na) facilitate easier migration in the oxygen intra-layers to a greater extent than the larger dopants (K, Rb). The Na–Cr2O3 bulk promotes both oxygen vacancy formation and migration which makes it a novel candidate for anode materials in medium temperature SOFCs and battery applications

On modifying properties of polymeric melts by nanoscopic particles

We study geometric and energetic factors that partake in modifying properties of polymeric melts via inserting well-dispersed nanoscopic particles (NP). Model systems are polybutadiene melts including 10-150 atom atomic clusters (0.1-1.5% v/v). We tune interactions between chains and particle by van der Waals terms. Using molecular dynamics we study equilibrium fluctuations and dynamical properties at the interface. Effect of bead size and interaction strength both on volume and volumetric fluctuations is manifested in mechanical properties, quantified here by bulk modulus, K. Tuning NP size and non-bonded interactions results in ~15% enhancement in K by addition of a maximum of 1.5% v/v NP.Comment: 25 pages, 7 figure

Machine learning on normalized protein sequences

<p>Abstract</p> <p>Background</p> <p>Machine learning techniques have been widely applied to biological sequences, e.g. to predict drug resistance in HIV-1 from sequences of drug target proteins and protein functional classes. As deletions and insertions are frequent in biological sequences, a major limitation of current methods is the inability to handle varying sequence lengths.</p> <p>Findings</p> <p>We propose to normalize sequences to uniform length. To this end, we tested one linear and four different non-linear interpolation methods for the normalization of sequence lengths of 19 classification datasets. Classification tasks included prediction of HIV-1 drug resistance from drug target sequences and sequence-based prediction of protein function. We applied random forests to the classification of sequences into "positive" and "negative" samples. Statistical tests showed that the linear interpolation outperforms the non-linear interpolation methods in most of the analyzed datasets, while in a few cases non-linear methods had a small but significant advantage. Compared to other published methods, our prediction scheme leads to an improvement in prediction accuracy by up to 14%.</p> <p>Conclusions</p> <p>We found that machine learning on sequences normalized by simple linear interpolation gave better or at least competitive results compared to state-of-the-art procedures, and thus, is a promising alternative to existing methods, especially for protein sequences of variable length.</p