1. Javier Junquera How to plot the radial part of the atomic orbitals

2. Atomic orbitals: a radial function times an spherical harmonic z y x Index of an atom Angular momentum Possibility of multiple orbitals with the same l,m but different radial dependence

3. s p d f Spherical harmonics: well defined (fixed) objects Size: Number of atomic orbitals per atom Range: Spatial extension of the orbitals Shape: of the radial part Radial part: degree of freedom to play with Atomic orbitals: a radial function times an spherical harmonic

4. The radial part: Numerical atomic orbitals Numerical solution of the Kohn-Sham Hamiltonian for the isolated pseudoatom with the same approximations (xc,pseudos) as for the condensed system This equation is solved in a logarithmic grid using the Numerov method Dense close at the origin where atomic quantities oscillates wildly Light far away from the origin where atomic quantities change smoothly

5. How to plot the radial part of the atomic orbitals After a succesful run, Siesta will generate files with names like ORB.SX.Y.SpeciesLabel X=Number of the shell (to know the corresponding l, edit the file and look at the first line, as indicated in the next slide). Y=Number of the zeta within a given shell Label for the chemical species label

6. Example: Radial part of the first- ζ orbital of the 2s shell of O ORB.S1.1.O Distance from the nuclei (in Bohr) Radial part of the atomic orbital Note of caution: what is printed here is

7. How to plot the radial part of the atomic orbitals Replace here the atomic orbitals of your choice To produce a postscript file Try to plot different atomic orbitals of the examples given in the Tutorial