Exact exchange-only potentials and the virial relation as microscopic criteria for generalized gradient approximations

1993 ◽  
Vol 47 (20) ◽  
pp. 13164-13174 ◽  
Author(s):  
E. Engel ◽  
S. H. Vosko
Keyword(s):  
Generalized Gradient ◽  
Exact Exchange ◽  
Virial Relation

scholarly journals Dispersion Corrected r2SCAN Based Global Hybrid Functionals: r2SCANh, r2SCAN0, and r2SCAN50

2021 ◽  
Author(s):  
Markus Bursch ◽  
Hagen Neugebauer ◽  
Sebastian Ehlert ◽  
Stefan Grimme
Keyword(s):  
Structural Parameters ◽  
Main Group ◽  
Basis Set ◽  
Generalized Gradient ◽  
Exchange Correlation ◽  
Hartree Fock ◽  
Exact Exchange ◽  
Hybrid Functionals ◽  
London Dispersion

The re-regularized semilocal meta generalized gradient approximation (meta-GGA) exchange-correlation functional r2SCAN [J. W. Furness, A. D. Kaplan, J. Ning, J. P. Perdew, and J. Sun, J. Phys. Chem. Lett. 11, 8208–8215 (2020)] is used to create the three global hybrid functionals with varying admixtures of Hartree–Fock exact exchange (HFX). The resulting exchange-correlation functionals r2SCANh (10% HFX), r2SCAN0 (25% HFX), and r2SCAN50 (50%HFX) are combined with the recent semi-classical D4 London dispersion correction. The new functionals are assessed for molecular geometries, general main-group, and metalorganic thermochemistry at 26 comprehensive benchmark sets including such as the large GMTKN55, ROST61, and IONPI19 sets. It is shown that a moderate admixture of HFX leads to overall mean percentual improvements of −11 (r2SCANh-D4), −16 (r2SCAN0-D4), and −1% (r2SCAN50-D4) regarding thermochemistry compared to the parental meta-GGA. For organometallic reaction energies and barriers, r2SCAN0-D4 even yields a mean improvement of −35%. The computation of structural parameters does not systematically profit from HFX admixture. Overall, the most promising combination r2SCAN0-D4 performs well for both main-group and organometallic thermochemistry. It yields deviations better or on par with other very well-performing global hybrid functionals such as PW6B95-D4 or PBE0-D4. Regarding systems prone to self-interaction errors (SIE4x4), r2SCAN0-D4 shows reasonable performance, reaching the quality of the range-separated ωB97X-V functional. Accordingly, r2SCAN0-D4 in combination with a sufficiently converged basis set (def2-QZVP(P)) represents a robust and reliable choice for general use in the calculation of thermochemical properties of both, main-group and organometallic chemistry.

scholarly journals Quasi-dimensional models applied to kinetic and exchange energy density functionals

2021 ◽  
Vol 94 (7) ◽  
Author(s):  
Vittoria Urso ◽  
Lucian A. Constantin
Keyword(s):  
Quantum Well ◽  
Density Functional ◽  
Local Density ◽  
Three Dimensional ◽  
Energy Functional ◽  
Exchange Energy ◽  
Two Dimensional ◽  
Generalized Gradient ◽  
Quantum Well Width ◽  
Exact Exchange

AbstractWe investigate the behavior of three-dimensional 3D exchange energy functional of density-functional theory in anisotropic systems with two-dimensional 2D character and 1D character. The local density approximation (LDA), the generalized gradient approximation (GGA), and the meta-GGA behave as functions of quantum well width. We use the infinite-barrier model (IBM) for the quantum well. In the first section, we describe the problem of three-dimensional exchange functional, in the second section we introduce the quasi-2D IBM system, in the third section we introduce the quasi-1D IBM system. Using that an exact-exchange functional provides the correct approach to the true two-dimensional limit, we want to show that the 2D limit can be considered as a constraint on approximate functionals. For the 1D limit case we also propose a new functional obtained with methods completely similar to those of 2D limit.

Interstitial vs. Substitutional Metal Insertion in V2O5 as Post-Lithium Ion Battery Cathode: A Comparative GGA/GGA+U Study with Localized Bases

2020 ◽  
Author(s):  
Daniel Koch ◽  
Sergei Manzhos
Keyword(s):  
Electronic Structure ◽  
Plane Wave ◽  
Transition Metal Oxides ◽  
Reasonable Agreement ◽  
Correction Term ◽  
Lithium Ion ◽  
Generalized Gradient ◽  
Main Group Metals ◽  
Generalized Gradient Approximation ◽  
Metal Insertion

<p></p><p>The generalized gradient approximation (GGA) often fails to correctly describe the electronic structure and thermochemistry of transition metal oxides and is commonly improved using an inexpensive correction term with a scaling parameter <i>U</i>. We tune <i>U</i> to reproduce experimental vanadium oxide redox energetics with a localized basis and a GGA functional. We find the value for <i>U</i> to be significantly lower than what is generally reported with plane-wave bases, with the uncorrected GGA results being in reasonable agreement with experiments. We use this computational setup to calculate interstitial and substitutional <a>insertion energies of main group metals in vanadium pentoxide</a> and find <a>interstitial doping to be thermodynamically favored</a>.</p><p></p>

Ab initio calculation on the Optical Properties of AA- Stacked two dimensional Graphene, Silicene, Germanene, and Stanene

2018 ◽  
Vol 1 (1) ◽  
pp. 46-50
Author(s):  
Rita John ◽  
Benita Merlin
Keyword(s):  
Optical Properties ◽  
Band Structure ◽  
Density Functional ◽  
Electronic Band Structure ◽  
Complex Refractive Index ◽  
Single Layer ◽  
Generalized Gradient ◽  
Electronic Band ◽  
Wide Range ◽  
Optical Region

In this study, we have analyzed the electronic band structure and optical properties of AA-stacked bilayer graphene and its 2D analogues and compared the results with single layers. The calculations have been done using Density Functional Theory with Generalized Gradient Approximation as exchange correlation potential as in CASTEP. The study on electronic band structure shows the splitting of valence and conduction bands. A band gap of 0.342eV in graphene and an infinitesimally small gap in other 2D materials are generated. Similar to a single layer, AA-stacked bilayer materials also exhibit excellent optical properties throughout the optical region from infrared to ultraviolet. Optical properties are studied along both parallel (||) and perpendicular ( ) polarization directions. The complex dielectric function (ε) and the complex refractive index (N) are calculated. The calculated values of ε and N enable us to analyze optical absorption, reflectivity, conductivity, and the electron loss function. Inferences from the study of optical properties are presented. In general the optical properties are found to be enhanced compared to its corresponding single layer. The further study brings out greater inferences towards their direct application in the optical industry through a wide range of the optical spectrum.

scholarly journals Performance of SCAN Meta-GGA Functionals on Nonlinear Mechanics of Graphene-Like g-SiC

Crystals ◽  
2021 ◽  
Vol 11 (2) ◽  
pp. 120
Author(s):  
Qing Peng
Keyword(s):  
Mechanical Properties ◽  
Density Functional ◽  
Large Strains ◽  
Two Dimensional ◽  
Nonlinear Mechanics ◽  
Generalized Gradient ◽  
Mechanics Of Materials ◽  
Nonlinear Mechanical ◽  
Direct Band ◽  
Simulations And Modeling

Although meta-generalized-gradient approximations (meta-GGAs) are believed potentially the most accurate among the efficient first-principles calculations, the performance has not been accessed on the nonlinear mechanical properties of two-dimensional nanomaterials. Graphene, like two-dimensional silicon carbide g-SiC, has a wide direct band-gap with applications in high-power electronics and solar energy. Taken g-SiC as a paradigm, we have investigated the performance of meta-GGA functionals on the nonlinear mechanical properties under large strains, both compressive and tensile, along three deformation modes using Strongly Constrained and Appropriately Normed Semilocal Density Functional (SCAN) as an example. A close comparison suggests that the nonlinear mechanics predicted from SCAN are very similar to that of Perdew-Burke-Ernzerhof (PBE) formulated functional, a standard Density Functional Theory (DFT) functional. The improvement from SCAN calculation over PBE calculation is minor, despite the considerable increase of computing demand. This study could be helpful in selection of density functionals in simulations and modeling of mechanics of materials.

Dissociation of dinitrogen on iron clusters: A detailed study of the Fe16 + N2 case.

2020 ◽  
Author(s):  
Bole Chen ◽  
Gennady L. Gutsev ◽  
Weiguo Sun ◽  
Xiao-Yu Kuang ◽  
Cheng Lu ◽  
...  
Keyword(s):  
Density Functional Theory ◽  
Density Functional ◽  
Basis Set ◽  
Generalized Gradient ◽  
Functional Theory ◽  
Iron Clusters ◽  
Generalized Gradient Approximation

The coalescence of two Fe8N as well as the structure of the Fe16N2 cluster were studied using density functional theory with the generalized gradient approximation and a basis set of...

scholarly journals Calculation of Band Offsets of Mg(OH)2-Based Heterostructures

2021 ◽  
Vol 2 (3) ◽  
pp. 274-283
Author(s):  
Masaya Ichimura
Keyword(s):  
Solar Cells ◽  
Valence Band ◽  
Dye Sensitized Solar Cells ◽  
Band Alignment ◽  
First Principles Calculation ◽  
Band Edge ◽  
Level Energy ◽  
Type I ◽  
Valence Band Edge ◽  
Generalized Gradient

The band alignment of Mg(OH)2-based heterostructures is investigated based on first-principles calculation. (111)-MgO/(0001)-Mg(OH)2 and (0001)-wurtzite ZnO/(0001)-Mg(OH)2 heterostructures are considered. The O 2s level energy is obtained for each O atom in the heterostructure supercell, and the band edge energies are evaluated following the procedure of the core-level spectroscopy. The calculation is based on the generalized gradient approximation with the on-site Coulomb interaction parameter U considered for Zn. For MgO/Mg(OH)2, the band alignment is of type II, and the valence band edge of MgO is higher by 1.6 eV than that of Mg(OH)2. For ZnO/Mg(OH)2, the band alignment is of type I, and the valence band edge of ZnO is higher by 0.5 eV than that of Mg(OH)2. Assuming the transitivity rule, it is expected that Mg(OH)2 can be used for certain types of heterostructure solar cells and dye-sensitized solar cells to improve the performance.

Thermal Properties of Divalent Metal Oxides: CaO as a Prototype

2013 ◽  
Vol 209 ◽  
pp. 190-193
Author(s):  
Nisarg K. Bhatt ◽  
Brijmohan Y. Thakore ◽  
P.R. Vyas ◽  
A.Y. Vahora ◽  
Asvin R. Jani
Keyword(s):  
Density Functional ◽  
Tight Binding ◽  
Mean Field ◽  
Field Potential ◽  
Theoretical Data ◽  
Test Case ◽  
Generalized Gradient ◽  
Core Electrons ◽  
Vibrational Free Energy ◽  
Semi Empirical

Commonly employed quasiharmonic approximation (QHA) is inadequate to account for intrinsic anharmonism such as phonon-phonon interaction, vacancy contribution, etc. Though anharmonic contributions are important at high temperatures and low pressure, complete ab initio calculations are scanty due largely to laborious computational requirements. Nevertheless, some simple semi-empirical schemes can be used effectively to incorporate the anharmonism. In this regards, in the present study we have proposed a simple computational scheme to include the effect of vacancy directly into the description within the mean-field potential approach, which calculates vibrational free energy of ions. Validity of the scheme is verified by taking calcium oxide as a test case. Equilibrium properties at (T,P) = (0,0) condition is obtained within the tight-binding second-moment approximation (TB-SMA), whose parameters were determined through first principles density functional theory. Kohn-Sham equations for core electrons were solved using ultrasoft plane-wave pseudopotential employing the generalized gradient approximation for exchange and correlation. Present findings for thermal expansion and high-T EOS clearly show perceptible improvement over the case when vacancy contribution was not included. Some related thermodynamic properties are also calculated and compared with the available experimental and theoretical data.

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