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Javier Junquera

Exercises on basis set generation Increasing the angular flexibility: polarization orbitals. Javier Junquera. Most important reference followed in this lecture. Converging the basis size: from quick and dirty to highly converged calculations. Radial flexibilization:

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Javier Junquera

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  1. Exercises on basis set generation Increasing the angular flexibility: polarization orbitals Javier Junquera

  2. Most important reference followed in this lecture

  3. Converging the basis size:from quick and dirty to highly converged calculations • Radialflexibilization: • Add more than one radial function within the same angular momentum than SZ • Multiple- • Angular flexibilization: • Add shells of different atomic symmetry (different l) • Polarization • Single- (minimal orSZ) • One single radial function per angular • momentum shell occupied in the free–atom Improving the quality

  4. Example of adding angular flexibility to an atomPolarizing the Si basis set l = 0 (s) l = 1 (p) Si atomic configuration:1s2 2s2 2p63s2 3p2 m = 0 m = -1 m = 0 m = +1 valence core m = -2 m = -1 m = 0 m = +1 m = +2 Polarize: add l = 2 (d) shell New orbitals directed in different directions with respect the original basis

  5. Two different ways of generate polarization orbitals Perturbative polarization Apply a smallelectricfield to the orbital wewant to polarize E s+p s Si 3d orbitals E. Artacho et al., Phys. Stat. Sol. (b), 215, 809 (1999) Elegant and parameter free solution

  6. Bulk Al, a metal that crystallizes in the fcc structure 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 Go to the directory with the exercise on the energy-shift More information at the Siesta web page http://www.icmab.es/siesta and follow the link Documentations, Manual Inspect the input file, Al.per-pol.fdf

  7. 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

  8. Perturbative polarization: They can be included adding a “P” after the standard basis size Or using the PAO.Basis block (see next lecture of the tutorial)

  9. Perturbative polarization: Polarizethep-orbital meansadd a shell of d-orbital L=2 Theextent of thepolarization orbital isdeginedbythat of theorbitalstheypolarize

  10. Search for the free energy Edittheoutput file and searchfor: We are interested in thisnumber Compare the free energywith a DZP basis set withthatobtained in previouslecturesfor SZ and DZ basis sets

  11. Search for the relaxed lattice constant Edittheoutput file and searchfor: Thelatticeconstant in this particular case would be 2.005748 Å × 2 = 4.011496 Å Experimental latticeconstant: 4.05 Å Whenweimprovethequality of thebasis set, wemakethecorrespondingdeviationssmaller. Themostimportantsource of deviations are thenthepseudopotential and thefunctional (the LDA tendstounderestimatethelatticeconstantby 1-3 %)

  12. Perturbative polarization: How to plot the radial part of the atomic orbital Followtheinstructionsgiven in the Tutorial Howtoplotthe radial part of theatomic orbital Rememberthat in the ORB file westore . For Al, thepolarization orbital is a d-shell (l=2) $ gnuplot gnuplot> plot "ORB.S3.1.Al" u 1:($2 * $1**2) w l gnuplot> set terminal postscript gnuplot> set output "perturbative-polarization.ps" gnuplot> replot

  13. Two different ways of generate polarization orbitals Atomic polarization SolveSchrödinger equation for higherangularmomentum (Unoccupiedatomicshells of higher l) unbound in the free atom require short cutoffs (agressive confinement) Perturbative polarization Apply a small electric field to the orbital we want to polarize E s+p s Si 3d orbitals E. Artacho et al., Phys. Stat. Sol. (b), 215, 809 (1999)

  14. Atomicpolarization: They must be included using the PAO.Basis block (see the corresponding lecture of the tutorial) We can includeshells of any angular momenta Thecutoffradiimight be differentfromthat of theorbitalsthat are polarized

  15. Atomicpolarization: Polarizethep-orbital meansadd a shell of d-orbital L=2 Thepolarizationd-orbitals are computed as therest of theshells (solvingthe Schrödinger equation of theisolatedatomforthecorrespondingcomponent of thepseudopotential)

  16. Search for the free energy Edittheoutput file and searchfor: We are interested in thisnumber Theatomicconfinementusuallyperformsvariationalybetterthantheatomicpolarization

  17. Search for the relaxed lattice constant Edittheoutput file and searchfor: Thelatticeconstant in this particular case would be 1.993001Å × 2 = 3.986002Å Experimental latticeconstant: 4.05 Å Whenweimprovethequality of thebasis set, wemakethecorrespondingdeviationssmaller. Themostimportantsource of deviations are thenthepseudopotential and thefunctional (the LDA tendstounderestimatethelatticeconstantby 1-3 %)

  18. Perturbative polarization: How to plot the radial part of the atomic orbital Followtheinstructionsgiven in the Tutorial Howtoplotthe radial part of theatomic orbital Rememberthat in the ORB file westore . For Al, thepolarization orbital is a d-shell (l=2) $ gnuplot gnuplot> plot "ORB.S3.1.Al" u 1:($2 * $1**2) w l gnuplot> set terminal postscript gnuplot> set output ”atomic-polarization.ps" gnuplot> replot

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