Higher-order gradient corrections for exchange-correlation functionals

1997 ◽  
Vol 266 (1-2) ◽  
pp. 16-22 ◽  
Author(s):  
Ralf Neumann ◽  
Nicholas C. Handy
Keyword(s):  
Higher Order ◽  
Exchange Correlation ◽  
Gradient Corrections

scholarly journals Thomas–Fermi-like and average atom model equations of state for highly compressed matter at any temperature

1992 ◽  
Vol 10 (2) ◽  
pp. 263-275 ◽  
Author(s):  
P. Friomy ◽  
C. Deutsch ◽  
G. Maynard
Keyword(s):  
Equations Of State ◽  
Temperature Behaviour ◽  
Thomas Fermi ◽  
Exchange Correlation ◽  
Analytic Approximations ◽  
Atomic Properties ◽  
Atom Model ◽  
Gradient Corrections ◽  
Model Equations ◽  
Average Atom Model

We develop a systematic comparison of thermodynamical and atomic properties computed within the three (TF, TFD, and TFDW) Thomas-Fermi modellings with results obtained from the average atom model. A special emphasis is placed on using the same analytic approximations for exchange, correlation, and gradient corrections. Analogies and discrepancies with respect to temperature behaviour are also stressed.

HYDROGEN ADSORPTION ON THE (100) SURFACES OF RHODIUM, PALLADIUM AND SILVER

1997 ◽  
Vol 04 (06) ◽  
pp. 1297-1303 ◽  
Author(s):  
A. EICHLER ◽  
J. HAFNER ◽  
G. KRESSE
Keyword(s):  
Density Functional Calculations ◽  
Atomic Hydrogen ◽  
Density Functional ◽  
Hydrogen Adsorption ◽  
Face Centered Cubic ◽  
Generalized Gradient ◽  
Exchange Correlation ◽  
Gradient Corrections ◽  
Face Centered ◽  
Chemical Trends

The adsorption of atomic hydrogen on the (100) surfaces of face-centered-cubic rhodium, palladium and silver has been studied using ab-initio density-functional calculations (including generalized gradient corrections). At the example of Rh(100) we present detailed investigations of the influence of the nonlocal corrections to the exchange-correlation functional on the stable geometries and the energies of adsorption. We also study the influence of the adsorbate on the relaxation of the substrate. Chemical trends are studied along the series Rh–Pd–Ag.

The Effect of Gradient Correctionsin Calculating the Energy of Electron Gas on Metal Surface

2020 ◽  
pp. 14-27
Author(s):  
V.L. Glushkov ◽  
O.S. Erkovich
Keyword(s):  
Surface Energy ◽  
Electron Density ◽  
Metal Surface ◽  
Fourth Order ◽  
Correlation Energy ◽  
Electron Gas ◽  
Energy Functional ◽  
Exchange Correlation ◽  
Gradient Corrections ◽  
Experimental Values

The paper describes the results of studying the effect of gradient corrections to the kinetic and exchange-correlation energy functional in calculating the surface energy of a metal surface; the calculations are performed within the framework of the density functional theory. The electron density distribution profile near the metal surface was calculated by the variational method for two test functions, which differ by taking into account the electron density oscillations. The exact form of the kinetic and exchange-correlation energy functional is unknown; therefore, to calculate the surface energy of the selected metals, various gradient corrections for the second and fourth order electron gas inhomogeneity are used. The effect of the discreteness of the ionic lattice and the orientation of the crystallographic planes on the spatial distribution of the electron gas is taken into account within the framework of perturbation theory; the Ashcroft pseudopotential is taken as the one to describe the electron-ion interaction. The use of a fourth-order gradient correction for the exchange-correlation and kinetic energies has little effect on the calculated values of the surface energy of alkali metals. The calculation results do not always agree well with the experimental values of the selected metals. This may be due to the fact that the relaxation of the metal surface is not taken into consideration and because of the large error in obtaining the experimental values of the surface energy

Dual systems for all: Higher-order, role-based relational reasoning as a uniquely derived feature of human cognition

2019 ◽  
Vol 42 ◽  
Author(s):  
Daniel J. Povinelli ◽  
Gabrielle C. Glorioso ◽  
Shannon L. Kuznar ◽  
Mateja Pavlic
Keyword(s):  
Temporal Reasoning ◽  
Higher Order ◽  
Important Case ◽  
Human Cognition ◽  
Relational Reasoning ◽  
Dual Systems ◽  
First Order ◽  
Reasoning System ◽  
Role Based

Abstract Hoerl and McCormack demonstrate that although animals possess a sophisticated temporal updating system, there is no evidence that they also possess a temporal reasoning system. This important case study is directly related to the broader claim that although animals are manifestly capable of first-order (perceptually-based) relational reasoning, they lack the capacity for higher-order, role-based relational reasoning. We argue this distinction applies to all domains of cognition.

Inelastic scattering at surfaces and interfaces

1986 ◽  
Vol 44 ◽  
pp. 392-393
Author(s):  
R. H. Ritchie ◽  
A. Howie
Keyword(s):  
Inelastic Scattering ◽  
Surface Properties ◽  
Correlation Energy ◽  
Condensed Matter ◽  
Charged Particles ◽  
Condensed Matter Physics ◽  
Optical Phonons ◽  
Exchange Correlation ◽  
Surfaces And Interfaces ◽  
Inelastic Interactions

An important part of condensed matter physics in recent years has involved detailed study of inelastic interactions between swift electrons and condensed matter surfaces. Here we will review some aspects of such interactions.Surface excitations have long been recognized as dominant in determining the exchange-correlation energy of charged particles outside the surface. Properties of surface and bulk polaritons, plasmons and optical phonons in plane-bounded and spherical systems will be discussed from the viewpoint of semiclassical and quantal dielectric theory. Plasmons at interfaces between dissimilar dielectrics and in superlattice configurations will also be considered.

Quantitative EPMA of nitrogen : A tricky element in the electron-probe microanalyzer

1992 ◽  
Vol 50 (2) ◽  
pp. 1622-1623
Author(s):  
G.F. Bastin ◽  
H.J.M. Heijligers
Keyword(s):  
Background Subtraction ◽  
Electron Probe ◽  
Detection System ◽  
Higher Order ◽  
Light Elements ◽  
Strong Suppression ◽  
Electron Probe Microanalyzer ◽  
Quantitative Epma ◽  
Peak Count ◽  
Lead Stearate

Among the ultra-light elements B, C, N, and O nitrogen is the most difficult element to deal with in the electron probe microanalyzer. This is mainly caused by the severe absorption that N-Kα radiation suffers in carbon which is abundantly present in the detection system (lead-stearate crystal, carbonaceous counter window). As a result the peak-to-background ratios for N-Kα measured with a conventional lead-stearate crystal can attain values well below unity in many binary nitrides . An additional complication can be caused by the presence of interfering higher-order reflections from the metal partner in the nitride specimen; notorious examples are elements such as Zr and Nb. In nitrides containing these elements is is virtually impossible to carry out an accurate background subtraction which becomes increasingly important with lower and lower peak-to-background ratios. The use of a synthetic multilayer crystal such as W/Si (2d-spacing 59.8 Å) can bring significant improvements in terms of both higher peak count rates as well as a strong suppression of higher-order reflections.

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