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