javier junquera exercises on basis set generation control of the range of the second-ς orbital: the...
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Javier Junquera
Exercises on basis set generation
Control of the range of the second-ς orbital: the split norm
Most important reference followed in this lecture
Default mechanism to generate multiple- in SIESTA: “Split-valence” method
Starting from the function we want to suplement
Default mechanism to generate multiple- in SIESTA: “Split-valence” method
The second- function reproduces the tail of the of the first- outside a radius rm
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 rm
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 rm (more efficient)
Default mechanism to generate multiple- in SIESTA: “Split-valence” method
Finally, the second- is normalized
rm controlled with PAO.SplitNorm
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)
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 splitnorm:
Variables to control the range of the second-ς shells in the basis set
The splitnorm:
Run SIESTA for different values of the PAO.SplitNorm
PAO.SplitNorm 0.10
Edit the input file and set up Then, run SIESTA
$siesta < Al.splitnorm.fdf > Al.splitnorm.0.10.out
For each splitnorm, search for the range of the orbitals
Edit each output file and search for:
Edit each output file and search for:
We are interested in this number
For each splitnorm, search for the range of the orbitals
Edit each output file and search for:
The lattice constant in this particular case would be2.037521 Å × 2 = 4.075042 Å
For each splitnorm, search for the range of the orbitals
For each energy shift, search for the timer per SCF step
We are interested in this number
The SplitNorm:
Run SIESTA for different values of the PAO.SplitNorm
PAO.SplitNorm 0.15
Edit the input file and set up Then, run SIESTA
$siesta < Al.splitnorm.fdf > Al.splitnorm.0.15.out
Try different values of the PAO.EnergyShift
PAO.SplitNorm 0.20 $siesta < Al.splitnorm.fdf > Al.splitnorm.0.20.out
PAO.SplitNorm 0.25 $siesta < Al.splitnorm.fdf > Al.splitnorm.0.25.out
PAO.SplitNorm 0.30 $siesta < Al.splitnorm.fdf > Al.splitnorm.0.30.out
PAO.SplitNorm 0.10 $siesta < Al.splitnorm.fdf > Al.splitnorm.0.10.out
Analyzing the results
Edit in a file (called, for instance, splitnorm.dat) the previous values as a function of the SplitNorm
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