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

A SUPERHOME in Christchurch under winter conditions : real performance through post-occupancy evaluation : a thesis presented in partial fulfilment of the requirements for the degree of Master of Environmental Management at Massey University, Manawatū, New Zealand

The profile of energy-efficient, high performing, ‘sustainable’ buildings have greatly increased in recent years in response to the need for change in design, construction, and maintenance of the built environment. Residential buildings in particular have been in the spotlight when it comes to the application of ‘green’ building concept. Although it is generally understood that a ‘green’ home provides a healthier and more comfortable housing environment to its occupants aside from generating energy efficiency, little is known about the extent to which such a home actually performs while in use. In New Zealand, a nationwide industry led initiative, known as the ‘Superhome Movement’, was established to promote the designing and building of environmentally sound, healthier, more energy-efficient and overall high-performing homes known as SUPERHOMEs. This research investigated the post-occupancy performance and indoor environment quality of a SUPERHOME under winter conditions. This study incorporated the analysis of energy use, monitoring of IEQ, and the surveying of building occupants. Results suggest that (1) the study building has not achieved its design potential with regards to electricity use in the first winter that it is occupied; (2) a SUPERHOME achieves a high level of thermal performance and provides adequate IAQ in winter conditions; and, (3) occupants’ overall perceptions towards the postoccupancy and winter performance of a SUPERHOME are positive. These findings lead to a realization that the ‘green’ status of a build should not be limited to ratings by thirdparty certification

Machine Learning Energies of 2 M Elpasolite (ABC2_2D6_6) Crystals

Elpasolite is the predominant quaternary crystal structure (AlNaK$_2$F$_6$ prototype) reported in the Inorganic Crystal Structure Database. We have developed a machine learning model to calculate density functional theory quality formation energies of all $\sim$2 M pristine ABC$_2$D$_6$ elpasolite crystals which can be made up from main-group elements (up to bismuth). Our model's accuracy can be improved systematically, reaching 0.1 eV/atom for a training set consisting of 10 k crystals. Important bonding trends are revealed, fluoride is best suited to fit the coordination of the D site which lowers the formation energy whereas the opposite is found for carbon. The bonding contribution of elements A and B is very small on average. Low formation energies result from A and B being late elements from group (II), C being a late (I) element, and D being fluoride. Out of 2 M crystals, 90 unique structures are predicted to be on the convex hull---among which NFAl$_2$Ca$_6$, with peculiar stoichiometry and a negative atomic oxidation state for Al

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

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

On the challenge to improve the density response with unusual gradient approximations

Certain excitations, especially ones of long-range charge transfer character, are poorly described by time-dependent density functional theory (TDDFT) when typical (semi-)local functionals are used. A proper description of these excitations would require an exchange-correlation response differing substantially from the usual (semi-)local one. It has recently been shown that functionals of the generalized gradient approximation (GGA) type can yield unusual potentials, mimicking features of the exact exchange derivative discontinuity and showing divergences on orbital nodal surfaces. We here investigate whether these unusual potential properties translate into beneficial response properties. Using the Sternheimer formalism we closely investigate the response obtained with the 2013 exchange approximation by Armiento and K\"ummel (AK13) and the 1988 exchange approximation by Becke (B88), both of which show divergences on orbital nodal planes. Numerical calculations for Na2 as well as analytical and numerical calculations for the hydrogen atom show that the response of AK13 behaves qualitatively different from usual semi local functionals. However, the AK13 functional leads to fundamental instabilities in the asymptotic region that prevent its practical application in TDDFT. Our findings may help the development of future improved functionals, and corroborate that the frequency-dependent Sternheimer formalism is excellently suited for running and analyzing TDDFT calculations

UHECR narrow clustering correlating IceCube through-going muons

The recent UHECR events by AUGER and the Telescope Array (TA) suggested that wide clusterings as the North and South, named Hot Spot, are related to near AGNs such as the one in M82 and Cen A. In the same frame since 2008 we assumed that the UHECR are made by light and lightest nuclei to explain the otherwise embarrassing absence of the huge nearby Virgo cluster, absence due to the fragility and the opacity of lightest nuclei by photo-dissociation from Virgo distances. Moreover UHECR map exhibits a few narrow clustering, some near the galactic plane, as toward SS 433 and on the opposite side of the plane at celestial horizons: we tagged them in 2014 suggesting possible near source active also as a UHE neutrino. Indeed since last year, 2015, highest IceCube trough-going muons, UHE up-going neutrino events at hundreds TeV energy, did show (by two cases over three tagged in North sky) the expected overlapping of UHE neutrinos signals with narrow crowding UHECR. New data with higher energy threshold somehow re-confirmed our preliminary proposal; new possible sources appear by a additional correlated UHE-neutrino versus UHE-neutrino and-or with narrow UHECR clustering events. A possible role of relic neutrino mass scattering by ZeV neutrino arised.Comment: 6 pages, 5 figure

Structural and electronic properties of Li intercalated graphene on SiC(0001)

We investigate the structural and electronic properties of Li-intercalated monolayer graphene on SiC(0001) using combined angle-resolved photoemission spectroscopy and first-principles density functional theory. Li intercalates at room temperature both at the interface between the buffer layer and SiC and between the two carbon layers. The graphene is strongly $n$-doped due to charge transfer from the Li atoms and two $\pi$-bands are visible at the $\bar{K}$-point. After heating the sample to 300$^\circ$C, these $\pi$-bands become sharp and have a distinctly different dispersion to that of Bernal-stacked bilayer graphene. We suggest that the Li atoms intercalate between the two carbon layers with an ordered structure, similar to that of bulk LiC$_6$. An AA-stacking of these two layers becomes energetically favourable. The $\pi$-bands around the $\bar{K}$-point closely resemble the calculated band structure of a C$_6$LiC$_6$ system, where the intercalated Li atoms impose a super-potential on the graphene electronic structure that opens pseudo-gaps at the Dirac points of the two $\pi$-cones.Comment: 9 pages, 7 figure