1. Javier Junquera Exercises on basis set generation Control of the range of the second-ς orbital: the split norm

2. Most important reference followed in this lecture

3. Default mechanism to generate multiple-  in SIESTA: “Split-valence” method Starting from the function we want to suplement

4. Default mechanism to generate multiple-  in SIESTA: “Split-valence” method The second-  function reproduces the tail of the of the first-  outside a radius r m

5. Default mechanism to generate multiple-  in SIESTA: “Split-valence” method And continuous smoothly towards the origin as (two parameters: the second-  and its first derivative continuous at r m

6. Default mechanism to generate multiple-  in SIESTA: “Split-valence” method The same Hilbert space can be expanded if we use the difference, with the advantage that now the second-  vanishes at r m (more efficient)

7. Default mechanism to generate multiple-  in SIESTA: “Split-valence” method Finally, the second-  is normalized r m controlled with PAO.SplitNorm

8. Meaning of the PAO.SplitNorm parameter PAO.SplitNorm is the amount of the norm (the full norm tail + parabolla norm) that the second-ς split off orbital has to carry (typical value 0.15)

9. Bulk Al, a metal that crystallizes in the fcc structure Go to the directory with the exercise on the energy-shift Inspect the input file, Al.energy-shift.fdf More information at the Siesta web page http://www.icmab.es/siesta and follow the link Documentations, Manual http://www.icmab.es/siesta As starting point, we assume the theoretical lattice constant of bulk Al FCC lattice Sampling in k in the first Brillouin zone to achieve self-consistency

10. For each basis set, a relaxation of the unit cell is performed Variables to control the Conjugate Gradient minimization Two constraints in the minimization: - the position of the atom in the unit cell (fixed at the origin) - the shear stresses are nullified to fix the angles between the unit cell lattice vectors to 60°, typical of a fcc lattice

11. The splitnorm: Variables to control the range of the second-ς shells in the basis set

12. The splitnorm: Run S IESTA for different values of the PAO.SplitNorm PAO.SplitNorm0.10 Edit the input file and set up Then, run S IESTA $siesta Al.splitnorm.0.10.out

13. For each splitnorm, search for the range of the orbitals Edit each output file and search for:

14. We are interested in this number For each splitnorm, search for the range of the orbitals

15. Edit each output file and search for: The lattice constant in this particular case would be 2.037521 Å × 2 = 4.075042 Å For each splitnorm, search for the range of the orbitals

16. For each energy shift, search for the timer per SCF step We are interested in this number

17. The SplitNorm: Run S IESTA for different values of the PAO.SplitNorm PAO.SplitNorm 0.15 Edit the input file and set up Then, run S IESTA $siesta Al.splitnorm.0.15.out Try different values of the PAO.EnergyShift PAO.SplitNorm 0.20$siesta Al.splitnorm.0.20.out PAO.SplitNorm 0.25$siesta Al.splitnorm.0.25.out PAO.SplitNorm 0.30$siesta Al.splitnorm.0.30.out PAO.SplitNorm 0.10$siesta Al.splitnorm.0.10.out

18. Analyzing the results Edit in a file (called, for instance, splitnorm.dat) the previous values as a function of the SplitNorm

19. Analyzing the results: range of the orbitals as a function of the split norm $ gnuplot $ gnuplot> plot ”splitnorm.dat" u 1:2 w l, ”splitnorm.dat" u 1:3 w l $ gnuplot> set terminal postscript color $ gnuplot> set output “range-2zeta.ps” $ gnuplot> replot The larger the SplitNorm, the smaller the orbitals