Multi-objective Optimization for Materials Discovery via Adaptive Design.

Guiding experiments to find materials with targeted properties is a crucial aspect of materials discovery and design, and typically multiple properties, which often compete, are involved. In the case of two properties, new compounds are sought that will provide improvement to existing data points lying on the Pareto front (PF) in as few experiments or calculations as possible. Here we address this problem by using the concept and methods of optimal learning to determine their suitability and performance on three materials data sets; an experimental data set of over 100 shape memory alloys, a data set of 223 MAX phases obtained from density functional theory calculations, and a computational data set of 704 piezoelectric compounds.

Machine learning bandgaps of double perovskites.

The ability to make rapid and accurate predictions on bandgaps of double perovskites is of much practical interest for a range of applications. While quantum mechanical computations for high-fidelity bandgaps are enormously computation-time intensive and thus impractical in high throughput studies, informatics-based statistical learning approaches can be a promising alternative. Here we demonstrate a systematic feature-engineering approach and a robust learning framework for efficient and accurate predictions of electronic bandgaps of double perovskites.

Classification of octet AB-type binary compounds using dynamical charges: A materials informatics perspective.

The role of dynamical (or Born effective) charges in classification of octet AB-type binary compounds between four-fold (zincblende/wurtzite crystal structures) and six-fold (rocksalt crystal structure) coordinated systems is discussed. We show that the difference in the dynamical charges of the fourfold and sixfold coordinated structures, in combination with Harrison's polarity, serves as an excellent feature to classify the coordination of 82 sp-bonded binary octet compounds. We use a support vector machine classifier to estimate the average classification accuracy and the associated variance in our model where a decision boundary is learned in a supervised manner.

Classification of ABO3 perovskite solids: a machine learning study.

We explored the use of machine learning methods for classifying whether a particular ABO3 chemistry forms a perovskite or non-perovskite structured solid. Starting with three sets of feature pairs (the tolerance and octahedral factors, the A and B ionic radii relative to the radius of O, and the bond valence distances between the A and B ions from the O atoms), we used machine learning to create a hyper-dimensional partial dependency structure plot using all three feature pairs or any two of them. Doing so increased the accuracy of our predictions by 2-3 percentage points over using any one pair.

An infinite swapping approach to the rare-event sampling problem.

We describe a new approach to the rare-event Monte Carlo sampling problem. This technique utilizes a symmetrization strategy to create probability distributions that are more highly connected and, thus, more easily sampled than their original, potentially sparse counterparts. After discussing the formal outline of the approach and devising techniques for its practical implementation, we illustrate the utility of the technique with a series of numerical applications to Lennard-Jones clusters of varying complexity and rare-event character.

Comparative Monte Carlo efficiency by Monte Carlo analysis.

We propose a modified power method for computing the subdominant eigenvalue λ{2} of a matrix or continuous operator. While useful both deterministically and stochastically, we focus on defining simple Monte Carlo methods for its application. The methods presented use random walkers of mixed signs to represent the subdominant eigenfunction.

Band structure of SnTe studied by photoemission spectroscopy.

We present an angle-resolved photoemission spectroscopy study of the electronic structure of SnTe and compare the experimental results to ab initio band structure calculations as well as a simplified tight-binding model of the p bands. Our study reveals the conjectured complex Fermi surface structure near the L points showing topological changes in the bands from disconnected pockets, to open tubes, and then to cuboids as the binding energy increases, resolving lingering issues about the electronic structure. The chemical potential at the crystal surface is found to be 0.

Monte Carlo determination of multiple extremal eigenpairs.

We present a Monte Carlo algorithm that allows the simultaneous determination of a few extremal eigenpairs of a very large matrix without the need to compute the inner product of two vectors or store all the components of any one vector. The algorithm, a Monte Carlo implementation of a deterministic one we recently benchmarked, is an extension of the power method. In the implementation presented, we used a basic Monte Carlo splitting and termination method called the comb, incorporated the weight cancellation method of Arnow et al, and exploited a sampling method, the sewing method, that does a large state space sampling as a succession of small state space samplings.

Strong coupling approach to actinide metals.

We present a strongly correlated approach to the electronic structure of actinide metals by deriving a low-energy Hamiltonian H[over] under the assumption that kinetic energy is small compared to Coulomb and spin-orbit interactions. The H[over]Pu for Pu metal is similar to the models used for Ce and other lanthanides but qualitatively different from the H[over] presented for the rest of the actinides. With H[over]Pu, we computed the photoemission spectrum and specific heat for alpha and delta-Pu and found good agreement with experiment.

Direct observation of itinerant magnetism in the 5f-electron system UTe.

Our electron photoemission experiments demonstrate that the magnetization of the ferromagnetic state of UTe is proportional to the binding energy of the hybridized band centered around 50 meV below EF. This proportionality is direct evidence that the ferromagnetism of UTe is itinerant; i.e.

Intermediate coupling theory of electronic ferroelectricity.

We calculate the quantum phase diagram of an extended Falicov-Kimball model for one- and two-dimensional systems in the intermediate coupling regime. Even though some features of the phase diagram are obtained analytically, the main results are calculated with a constrained path Monte Carlo technique. We find that this regime is dominated by a Bose-Einstein condensation of excitons with a built-in electric polarization.

Segmented band mechanism for itinerant ferromagnetism.

We introduce a novel mechanism for itinerant ferromagnetism, which is based on a simple two-band model, and, by using numerical and analytical methods, we show that the periodic Anderson model contains this mechanism. We propose that the mechanism, which does not assume an intra-atomic Hund's coupling, is present in both the iron group and some f electron compounds.