Exercises on basis set generation Control of the range: the energy shift

Javier Junquera

Most important reference followed in this lecture

How to control the range of the orbitals in a balanced way: the energy shift Particle in a confinement potential: Imposing a finite + Continuous function and first derivative



E

is quantized (not all values allowed) Increasing

E



and tends to -



has a node when

x



+



Complement M III

“

Quantum Mechanics

”

, C. Cohen-Tannoudji et al.

How to control de range of the orbitals in a balanced way: the energy shift Energy increase



Energy shift PAO.EnergyShift (energy) Cutoff radius, r c , = position where each orbital has the node A single parameter for all cutoff radii The larger the Energy shift, the shorter the r c ’s Typical values: 100-200 meV E. Artacho et al. Phys. Stat. Solidi (b) 215, 809 (1999)

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 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

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

The energy shift: Variables to control the range of the basis set

The energy shift: Run S IESTA for different values of the PAO.EnergyShift

Edit the input file and set up PAO.EnergyShift

0.002 Ry Then, run S IESTA $siesta < Al.energy-shift.fdf > Al.0.002.out

For each energy shift, search for the range of the orbitals Edit each output file and search for:

For each energy shift, search for the free energy Edit each output file and search for: We are interested in this number

For each energy shift, search for the free energy Edit each output file and search for: We are interested in this number

For each energy shift, search for the relaxed lattice constant Edit each output file and search for: The lattice constant in this particular case would be 2.108073 Å

×

2 = 4.216146 Å

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

The energy shift: Run S IESTA for different values of the PAO.EnergyShift

Edit the input file and set up PAO.EnergyShift

0.002 Ry Then, run S IESTA $siesta < Al.energy-shift.fdf > Al.0.002.out

Try different values of the PAO.EnergyShift

PAO.EnergyShift

PAO.EnergyShift

PAO.EnergyShift

PAO.EnergyShift

PAO.EnergyShift

PAO.EnergyShift

PAO.EnergyShift

PAO.EnergyShift

0.005 Ry 0.010 Ry 0.015 Ry 0.020 Ry 0.025 Ry 0.030 Ry 0.035 Ry 0.040 Ry $siesta < Al.energy-shift.fdf > Al.0.005.out

$siesta < Al.energy-shift.fdf > Al.0.010.out

$siesta < Al.energy-shift.fdf > Al.0.015.out

$siesta < Al.energy-shift.fdf > Al.0.020.out

$siesta < Al.energy-shift.fdf > Al.0.025.out

$siesta < Al.energy-shift.fdf > Al.0.030.out

$siesta < Al.energy-shift.fdf > Al.0.035.out

$siesta < Al.energy-shift.fdf > Al.0.040.out

Analyzing the results Edit in a file (called, for instance, cutoff-ef.dat) the previous values as a function of the Energy shift

Analyzing the results: range of the orbitals as a function of the energy shift $ gnuplot $ gnuplot> plot "cutoff-ef.dat" u 1:2 w l, "cutoff-ef.dat" u 1:3 w l $ gnuplot> set terminal postscript color $ gnuplot> set output “range.ps” $ gnuplot> replot

Analyzing the results: lattice constant as a function of the energy shift $ gnuplot $ gnuplot> plot "cutoff-ef.dat" u 1:4 w l $ gnuplot> set terminal postscript color $ gnuplot> set output “latcon.ps” $ gnuplot> replot

Analyzing the results: free energy as a function of the energy shift $ gnuplot $ gnuplot> plot "cutoff-ef.dat" u 1:5 w l $ gnuplot> set terminal postscript color $ gnuplot> set output “freener.ps” $ gnuplot> replot

Analyzing the results: time per SCF step as a function of the energy shift $ gnuplot $ gnuplot> plot "cutoff-ef.dat" u 1:6 w l $ gnuplot> set terminal postscript color $ gnuplot> set output “timer.ps” $ gnuplot> replot