Energetics of the AK13 Semi-Local Kohn-Sham Exchange Energy Functional

The recent non-empirical semi-local exchange functional of Armiento and K\"ummel, the AK13 [PRL 111, 036402 (2013)] incorporates a number of features reproduced by higher-order theory. The AK13 potential behaves analogously with the discontinuous jump associated with the derivative discontinuity at integer particle numbers. Recent works have established that AK13 gives a qualitatively improved orbital description compared to other semi-local methods, and reproduces a band structure closer to higher-order theory. However, its energies and energetics are inaccurate. The present work further investigates the deficiency in energetics. In addition to AK13 results, we find that applying the local-density approximation (LDA) non-self-consistently on the converged AK13 density gives very reasonable energetics with equilibrium lattice constants and bulk moduli well described across 14 systems. We also confirm that the attractive orbital features of AK13 are retained even after full structural relaxation. Hence, the deficient energetics cannot be a result of the AK13 orbitals having adversely affected the quality of the electron density compared to that of usual semi-local functionals; an improved orbital description and good energetics are not in opposition. We also prove that the non-self-consistent scheme is equivalent to using a single external-potential dependent functional in an otherwise consistent KS-DFT scheme. Furthermore, our results also demonstrate that, while an internally consistent KS functional is presently missing, non-self-consistent LDA on AK13 orbitals works as a practical non-empirical computational scheme to predict geometries, bulk moduli, while retaining the band structure features of AK13 at the computational cost of semi-local DFT.Comment: 7 pages, 4 figure

Quantum oscillations in the kinetic energy density: Gradient corrections from the Airy gas

We derive a closed form expression for the quantum corrections to the kinetic energy density (KED) in the Thomas-Fermi (TF) limit of a linear potential model system in three dimensions (the Airy gas). The universality of the expression is tested numerically in a number of three dimensional model systems: (i) jellium surfaces, (ii) hydrogen-like potentials, (iii) systems confined by an harmonic potential in one and (iv) all three dimensions, and (v) a system with a cosine potential (the Mathieu gas). Our results confirm that the usual gradient expansion of extended Thomas-Fermi theory (ETF) does not describe the quantum oscillations for systems that incorporate surface regions where the electron density drops off to zero. We find that the correction derived from the Airy gas is universally applicable to relevant spatial regions of systems of type (i), (ii), and (iv), but somewhat surprisingly not (iii). We discuss possible implications of our findings to the development of functionals for the kinetic energy density.Comment: 15 pages, 9 figure

Exchange Interactions in Paramagnetic Amorphous and Disordered Crystalline CrN-based Systems

We present a first principles supercell methodology for the calculation of exchange interactions of magnetic materials with arbitrary degrees of structural and chemical disorder in their high temperature paramagnetic state. It is based on a projection of the total magnetic energy of the system onto local pair clusters, allowing the interactions to vary independently as a response to their local environments. We demonstrate our method by deriving the distance dependent exchange interactions in vibrating crystalline CrN, a Ti$_{0.5}$Cr$_{0.5}$N solid solution as well as in amorphous CrN. Our method reveals strong local environment effects in all three systems. In the amorphous case we use the full set of exchange interactions in a search for the non-collinear magnetic ground state.Comment: 5 pages, 3 figure

Database-driven High-Throughput Calculations and Machine Learning Models for Materials Design

This paper reviews past and ongoing efforts in using high-throughput ab-inito calculations in combination with machine learning models for materials design. The primary focus is on bulk materials, i.e., materials with fixed, ordered, crystal structures, although the methods naturally extend into more complicated configurations. Efficient and robust computational methods, computational power, and reliable methods for automated database-driven high-throughput computation are combined to produce high-quality data sets. This data can be used to train machine learning models for predicting the stability of bulk materials and their properties. The underlying computational methods and the tools for automated calculations are discussed in some detail. Various machine learning models and, in particular, descriptors for general use in materials design are also covered.Comment: 19 pages, 2 figure