Javier Junquera
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Transcript of Javier Junquera
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Javier Junquera
Exercises on basis set generationControl of the range: the energy shift
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Most important reference followed in this lecture
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How to control the range of the orbitals in a balanced way: the energy shift
Complement M III “Quantum Mechanics”, C. Cohen-Tannoudji et al.
Increasing E has a node and tends to - when x +
Particle in a confinement potential:
Imposing a finite +
Continuous function and first derivative
E is quantized (not all values allowed)
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Cutoff radius, rc, = position where each orbital has the node
A single parameter for all cutoff radiiThe larger the Energy shift, the shorter the rc’s
Typical values: 100-200 meV
E. Artacho et al. Phys. Stat. Solidi (b) 215, 809 (1999)
How to control de range of the orbitals in a balanced way: the energy shift
Energy increase Energy shift PAO.EnergyShift (energy)
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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.fdfMore 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
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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
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The energy shift:
Variables to control the range of the basis set
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The energy shift:
Run SIESTA for different values of the PAO.EnergyShift
PAO.EnergyShift 0.002 Ry
Edit the input file and set up Then, run SIESTA
$siesta < Al.energy-shift.fdf > Al.0.002.out
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For each energy shift, search for the range of the orbitals
Edit each output file and search for:
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For each energy shift, search for the free energy
Edit each output file and search for:
We are interested in this number
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For each energy shift, search for the free energy
Edit each output file and search for:
We are interested in this number
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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 be2.108073 Å × 2 = 4.216146 Å
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For each energy shift, search for the timer per SCF step
We are interested in this number
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The energy shift:
Run SIESTA for different values of the PAO.EnergyShift
PAO.EnergyShift 0.002 Ry
Edit the input file and set up Then, run SIESTA
$siesta < Al.energy-shift.fdf > Al.0.002.out
Try different values of the PAO.EnergyShift
PAO.EnergyShift 0.010 Ry $siesta < Al.energy-shift.fdf > Al.0.010.outPAO.EnergyShift 0.015 Ry $siesta < Al.energy-shift.fdf > Al.0.015.outPAO.EnergyShift 0.020 Ry $siesta < Al.energy-shift.fdf > Al.0.020.outPAO.EnergyShift 0.025 Ry $siesta < Al.energy-shift.fdf > Al.0.025.out
PAO.EnergyShift 0.005 Ry $siesta < Al.energy-shift.fdf > Al.0.005.out
PAO.EnergyShift 0.030 Ry $siesta < Al.energy-shift.fdf > Al.0.030.out
PAO.EnergyShift 0.040 Ry $siesta < Al.energy-shift.fdf > Al.0.040.outPAO.EnergyShift 0.035 Ry $siesta < Al.energy-shift.fdf > Al.0.035.out
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Analyzing the results
Edit in a file (called, for instance, cutoff-ef.dat) the previous values as a function of the Energy shift
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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
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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
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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
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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