110 research outputs found
Screening for high-performance piezoelectrics using high-throughput density functional theory
No full textWe present a large-scale density functional theory (DFT) investigation of the ABO3 chemical space in the perovskite crystal structure, with the aim of identifying those that are relevant for forming piezoelectric materials. Screening criteria on the DFT results are used to select 49 compositions, which can be seen as the fundamental building blocks from which to create alloys with potentially good piezoelectric performance. This screening finds all the alloy end points used in three well-known high-performance piezoelectrics. The energy differences between different structural distortions, deformation, coupling between the displacement of the A and B sites, spontaneous polarization, Born effective charges, and stability is analyzed in each composition. We discuss the features that cause the high piezoelectric performance of the well-known piezoelectric lead zirconate titanate (PZT), and investigate to what extent these features occur in other compositions. We demonstrate how our results can be useful in the design of isovalent alloys with high piezoelectric performance
Subsystem functionals and the missing ingredient of confinement physics in density functionals
No full textThe subsystem functional scheme is a promising approach recently proposed for constructing exchange-correlation density functionals. In this scheme, the physics in each part of real materials is described by mapping to a characteristic model system. The “confinement physics,” an essential physical ingredient that has been left out in present functionals, is studied by employing the harmonic-oscillator (HO) gas model. By performing the potential→density and the density→exchange energy per particle mappings based on two model systems characterizing the physics in the interior (uniform electron-gas model) and surface regions (Airy gas model) of materials for the HO gases, we show that the confinement physics emerges when only the lowest subband of the HO gas is occupied by electrons. We examine the approximations of the exchange energy by several state-of-the-art functionals for the HO gas, and none of them produces adequate accuracy in the confinement dominated cases. A generic functional that incorporates the description of the confinement physics is needed.Laboratory Directed Research and Development Progra
Implementing and testing the AM05 spin density functional
No full textWe show that the spin density generalization of the AM05 density functional [R. Armiento and A. E. Mattsson, Phys. Rev. B 72, 085108 (2005)] predicts the correct ground spin state for iron, a system known to be heavily dependent on proper spin treatment. Using the fundamental assumptions in the subsystem functional scheme, we resolve an ambiguity in how to treat the separate spin densities in AM05 but also show that the other less preferred treatments give no significantly different numerical outcome of the iron body-centered-cubic and face-centered-cubic test cases. Details and formulas are given to aid in the implementation of functionals in general, and the spin-resolved AM05 exchange-correlation potentials in particular, into different types of computer codes
Using the electron localization function to correct for confinement physics in semi-local density functional theory
No full textWe have previously proposed that further improved functionals for density functional theory can be constructed based on the Armiento-Mattsson subsystem functional scheme if, in addition to the uniform electron gas and surface models used in the Armiento-Mattsson 2005 functional, a model for the strongly confined electron gas is also added. However, of central importance for this scheme is an index that identifies regions in space where the correction provided by the confined electron gas should be applied. The electron localization function (ELF) is a well-known indicator of strongly localized electrons. We use a model of a confined electron gas based on the harmonic oscillator to show that regions with high ELF directly coincide with regions where common exchange energy functionals have large errors. This suggests that the harmonic oscillator model together with an index based on the ELF provides the crucial ingredients for future improved semi-local functionals. For a practical illustration of how the proposed scheme is intended to work for a physical system we discuss monoclinic cupric oxide, CuO. A thorough discussion of this system leads us to promote the cell geometry of CuO as a useful benchmark for future semi-local functionals. Very high ELF values are found in a shell around the O ions, and take its maximum value along the Cu–O directions. An estimate of the exchange functional error from the effect of electron confinement in these regions suggests a magnitude and sign that could account for the error in cell geometry
Challenges for semilocal density functionals with asymptotically nonvanishing potentials
No full textThe Becke-Johnson model potential [A. D. Becke and E. R. Johnson, J. Chem. Phys. 124, 221101 ( 2006)] and the potential of the AK13 functional [R. Armiento and S. Kummel, Phys. Rev. Lett. 111, 036402 ( 2013)] have been shown to mimic features of the exact Kohn-Sham exchange potential, such as step structures that are associated with shell closings and particle-number changes. A key element in the construction of these functionals is that the potential has a limiting value far outside a finite system that is a system-dependent constant rather than zero. We discuss a set of anomalous features in these functionals that are closely connected to the nonvanishing asymptotic potential. The findings constitute a formidable challenge for the future development of semilocal functionals based on the concept of a nonvanishing asymptotic constant.Funding Agencies|German-Israeli Foundation for Scientific Research and Development; University of Bayreuth Graduate School; Swedish Research Council (V.R.) [2016-04810]; Swedish e-Science Research Centre (SeRC)</p
Energetics of the AK13 semilocal Kohn-Sham exchange energy functional
No full textThe recent nonempirical semilocal exchange functional of Armiento and Kummel [Phys. Rev. Lett. 111, 036402 (2013)], AK13, 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 semilocal 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 13 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 semilocal functionals; an improved orbital description and good energetics are not in opposition. This is also confirmed by direct calculation of the principal component of the electric field gradient. In addition, we prove that the non-self-consistent scheme is equivalent to using a single external-potential-dependent functional in an otherwise consistent, nonvariational Kohn-Sham density-functional theory (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 nonempirical computational scheme to predict geometries, bulk moduli, while retaining the band structure features of AK13 at the computational cost of semi-local DFT.Funding Agencies|Swedish Research Council (VR) [621-2011-4249]; Linnaeus Environment at Linkoping on Nanoscale Functional Materials (LiLi-NFM) - VR; Swedish e-Science Research Centre (SeRC)</p
On the challenge to improve the density response with unusual gradient approximations
No full textCertain 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 Kümmel (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. They also corroborate that the frequency-dependent Sternheimer formalism is excellently suited for running and analyzing TDDFT calculations
Hybrid density functional calculations of redox potentials and formation energies of transition metal compounds
No full textWe compare the accuracy of conventional semilocal density functional theory (DFT), the DFT+U method, and the Heyd-Scuseria-Ernzerhof (HSE06) hybrid functional for structural parameters, redox reaction energies, and formation energies of transition metal compounds. Conventional DFT functionals significantly underestimate redox potentials for these compounds. Zhou et al. [Phys. Rev. B 70, 235121 (2004)] addressed this issue with DFT+U and a linear-response scheme for calculating U values. We show that the Li intercalation potentials of prominent Li-ion intercalation battery materials, such as the layered LixMO2 (M=Co and Ni), LixTiS2; olivine LixMPO4 (M=Mn, Fe, Co, and Ni); and spinel-like LixMn2O4, LixTi2O4, are also well reproduced by HSE06, due to the self-interaction error correction from the partial inclusion of Hartree-Fock exchange. For formation energies, HSE06 performs well for transition metal compounds, which typically are not well reproduced by conventional DFT functionals but does not significantly improve the results of nontransition metal oxides. Hence, we find that hybrid functionals provide a good alternative to DFT+U for transition metal applications when the large extra computational effort is compensated by the benefits of (i) avoiding species-specific adjustable parameters and (ii) a more universal treatment of the self-interaction error that is not exclusive to specific atomic orbital projections on selected ions.United States. Dept. of Energy (Contract No. DE-FG02-96ER45571)Massachusetts Institute of Technology. Center for Materials Science and Engineering (Grant No. DMR-819762)Teragrid (Firm) (Grant No. TG-DMR970008S
Orbital nodal surfaces: Topological challenges for density functionals
No full textNodal surfaces of orbitals, in particular of the highest occupied one, play a special role in Kohn-Sham density-functional theory. The exact Kohn-Sham exchange potential, for example, shows a protruding ridge along such nodal surfaces, leading to the counterintuitive feature of a potential that goes to different asymptotic limits in different directions. We show here that nodal surfaces can heavily affect the potential of semilocal density-functional approximations. For the functional derivatives of the Armiento-Kummel (AK13) [Phys. Rev. Lett. 111, 036402 (2013)] and Becke88 [Phys. Rev. A 38, 3098 (1988)] energy functionals, i.e., the corresponding semilocal exchange potentials, as well as the Becke-Johnson [J. Chem. Phys. 124, 221101 (2006)] and van Leeuwen-Baerends (LB94) [Phys. Rev. A 49, 2421 (1994)] model potentials, we explicitly demonstrate exponential divergences in the vicinity of nodal surfaces. We further point out that many other semilocal potentials have similar features. Such divergences pose a challenge for the convergence of numerical solutions of the Kohn-Sham equations. We prove that for exchange functionals of the generalized gradient approximation (GGA) form, enforcing correct asymptotic behavior of the potential or energy density necessarily leads to irregular behavior on or near orbital nodal surfaces. We formulate constraints on the GGA exchange enhancement factor for avoiding such divergences.Funding Agencies|German-Israeli Foundation for Scientific Research and Development; University of Bayreuth Graduate School; Swedish Research Council (VR) [2016-04810]; Swedish e-Science Research Centre (SeRC)</p
Database-Driven High-Throughput Calculations and Machine Learning Models for Materials Design
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