Javier Junquera

Javier Junquera

Exercises on basis set generationControl of the range: the energy shift

Most important reference followed in this lecture

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)

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)

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

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 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

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 be2.108073 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 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

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