11 research outputs found
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
TiCrN 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