How to discriminate between valence and core electrons Objectives Check how the core electrons are...
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![Page 1: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/1.jpg)
How to discriminate between valence and core electrons
Objectives
Check how the core electrons are chemically inert
![Page 2: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/2.jpg)
Description of the input file of the ATOM code for an all-electron calculation
ae All-Electron calculation
A title for the job
Chemical symbol of the nucleus
Number of core and valence
orbitals
Principal quantum number
Angular quantum number
Occupation
N 1s2 2s2 2p3
core valence
Exchange-and correlation functionalca Ceperley-Alder (LDA) wi Wigner (LDA)
hl Hedin-Lundqvist (LDA) bh von-Barth-Hedin (LDA)
gl Gunnarson-Lundqvist (LDA)
pb Perdew-Burke-Ernzerhof, PBE (GGA)
rv revPBE (GGA)
rp RPBE, Hammer, Hansen, Norvskov (GGA)
ps PBEsol (GGA)
wc Wu-Cohen (GGA)
bl BLYP Becke-Lee-Yang-Parr (GGA)
am AM05 by Armiento and Mattson (GGA)
vw van der Waals functional
+s if spin (no relativistic)+r if relativistic
![Page 3: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/3.jpg)
How to run an all-electron calculation with ATOM
An explanation of the different files can be found in the ATOM User’s Guide (page 4)
![Page 4: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/4.jpg)
Run the code for different atomic configurations (neutral and ionic)
Neutral configuration: 1s2 2s2 2p3 (N.0.ae.inp)
Ionic configuration +1: 1s2 2s2 2p2 (N.+1.ae.inp)
Ionic configuration +2: 1s2 2s2 2p1 (N.+2.ae.inp)
Ionic configuration +3: 1s2 2s2 2p0 (N.+3.ae.inp)
$../Utils/ae.sh N.0.ae.inp
$../Utils/ae.sh N.1.ae.inp
$../Utils/ae.sh N.2.ae.inp
$../Utils/ae.sh N.3.ae.inp
Plot the angularly integrated (multiplied by 4πr2) core and the charge densities
$ gnuplot –persist charge.N-core.gplot
$ gnuplot –persist charge.N-valence.gplot
![Page 5: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/5.jpg)
Core electrons are chemically inert
All electron calculation for an isolated N atom
Core charge density Valence charge density
![Page 6: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/6.jpg)
Core electrons are chemically inert
All electron calculation for an isolated N atom
Core charge density Valence charge density
![Page 7: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/7.jpg)
Core electrons are chemically inert
All electron calculation for an isolated N atom
Core charge density Valence charge density
![Page 8: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/8.jpg)
Core electrons are chemically inert
All electron calculation for an isolated N atom
Core charge density Valence charge density
Although there are drastic modifications in the valence charge density
The core charge density remains unperturbed
Peak due to the 2s all-electron orbitals of N, (they have a node to be ortogonal with the 1s)
![Page 9: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/9.jpg)
$ cd N.0.ae
$ gnuplot –persist ae.gplot (To generate a figure on the screen using gnuplot)
$ gnuplot ae.gps (To generate a postscript file with the figure)
The radial parts that are plotted are the often called u’s in textbooks
The s-wave functions also go to zero at the origin
To plot the all electron wave functions
![Page 10: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/10.jpg)
To identify the positions of the zero and the extrema
$ vi OUT
For each atomic orbital:•Position of the extrema (r extr)•Position of the zeros (r zero)•Position where the norm is 90 and 99% of the norm of the orbital
![Page 11: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/11.jpg)
Repeating the exercise for Si…
![Page 12: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/12.jpg)
Core electrons are chemically inert
All electron calculation for an isolated Si atom
Core charge density
![Page 13: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/13.jpg)
Core electrons are chemically inert
All electron calculation for an isolated Si atom
Core charge density
![Page 14: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/14.jpg)
Core electrons are chemically inert
All electron calculation for an isolated Si atom
Core charge density
![Page 15: How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert.](https://reader030.fdocuments.in/reader030/viewer/2022032722/56649cea5503460f949b510f/html5/thumbnails/15.jpg)
Core electrons are chemically inert
All electron calculation for an isolated Si atom
Core charge density