How to discriminate between
valence and core electrons
Objectives
Check how the core electrons are chemically inert
Description of the input file of the ATOM code
for an all-electron calculation
ae  All-Electron calculation
N 1s2
A title for the job
core
Chemical
symbol of the
nucleus
2s2 2p3
valence
Number of core
and valence
orbitals
Exchange-and correlation functional
Principal
quantum
number
Occupation
Angular
quantum
number
ca  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)
+s if spin (no relativistic)
+r if relativistic
bl  BLYP Becke-Lee-Yang-Parr (GGA)
am AM05 by Armiento and Mattson (GGA)
vw  van der Waals functional
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)
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
Core electrons are chemically inert
All electron calculation for an isolated N atom
Core charge density
Valence charge density
Core electrons are chemically inert
All electron calculation for an isolated N atom
Core charge density
Valence charge density
Core electrons are chemically inert
All electron calculation for an isolated N atom
Core charge density
Valence charge density
Core electrons are chemically inert
All electron calculation for an isolated N atom
Core charge density
Valence charge density
The core charge density remains
unperturbed
Although there are drastic modifications in
the valence charge density
Peak due to the 2s all-electron orbitals of N, (they
have a node to be ortogonal with the 1s)
To plot the all electron wave functions
$ 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 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
Repeating the exercise for Si…
Core electrons are chemically inert
All electron calculation for an isolated Si atom
Core charge density
Core electrons are chemically inert
All electron calculation for an isolated Si atom
Core charge density
Core electrons are chemically inert
All electron calculation for an isolated Si atom
Core charge density
Core electrons are chemically inert
All electron calculation for an isolated Si atom
Core charge density