Exercises on basis set generation
Control of the range of the second-ς
orbital: the split norm
Javier Junquera
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
Edit the input file and set up
PAO.SplitNorm
0.10
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:
For each splitnorm,
search for the range of the orbitals
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 be
2.037521 Å × 2 = 4.075042 Å
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
Edit the input file and set up
PAO.SplitNorm
0.15
Then, run SIESTA
$siesta < Al.splitnorm.fdf > Al.splitnorm.0.15.out
Try different values of the PAO.EnergyShift
PAO.SplitNorm 0.10
$siesta < Al.splitnorm.fdf > Al.splitnorm.0.10.out
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
$siesta < Al.splitnorm.fdf > Al.splitnorm.0.30.out
0.30
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