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

2. 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 1s 2 2s 2 2p 3 corevalence Exchange-and correlation functional 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) 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

3. 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)

4. Run the code for different atomic configurations (neutral and ionic) Neutral configuration: 1s 2 2s 2 2p 3 (N.0.ae.inp) Ionic configuration +1: 1s 2 2s 2 2p 2 (N.+1.ae.inp) Ionic configuration +2: 1s 2 2s 2 2p 1 (N.+2.ae.inp) Ionic configuration +3: 1s 2 2s 2 2p 0 (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 4πr 2 ) core and the charge densities $ gnuplot –persist charge.N-core.gplot $ gnuplot –persist charge.N-valence.gplot

5. Core electrons are chemically inert All electron calculation for an isolated N atom Core charge densityValence charge density

6. Core electrons are chemically inert All electron calculation for an isolated N atom Core charge densityValence charge density

7. Core electrons are chemically inert All electron calculation for an isolated N atom Core charge densityValence charge density

8. Core electrons are chemically inert All electron calculation for an isolated N atom Core charge densityValence 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)

9. $ 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

10. 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

11. Repeating the exercise for Si…

12. Core electrons are chemically inert All electron calculation for an isolated Si atom Core charge density

13. Core electrons are chemically inert All electron calculation for an isolated Si atom Core charge density

14. Core electrons are chemically inert All electron calculation for an isolated Si atom Core charge density

15. Core electrons are chemically inert All electron calculation for an isolated Si atom Core charge density