The Generalized Gradient of a Marginal Function in Mathematical Programming

1979 ◽  
Vol 4 (4) ◽  
pp. 458-463 ◽  
Author(s):  
Jacques Gauvin
Keyword(s):  
Mathematical Programming ◽  
Marginal Function ◽  
Generalized Gradient

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.

Sign in / Sign up

Export Citation Format

Share Document