how to discriminate between valence and core electrons objectives check how the core electrons are...

How to discriminate between valence and core electrons Objectives Check how the core electrons are chemically inert

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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

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

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

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

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

$ 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

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

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

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