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Javier Junquera Exercises on basis set generation Control of the range of the second-ς orbital: the split norm

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Most important reference followed in this lecture

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Default mechanism to generate multiple- in SIESTA: “Split-valence” method Starting from the function we want to suplement

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Default mechanism to generate multiple- in SIESTA: “Split-valence” method The second- function reproduces the tail of the of the first- outside a radius r m

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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 r m

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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 r m (more efficient)

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Default mechanism to generate multiple- in SIESTA: “Split-valence” method Finally, the second- is normalized r m controlled with PAO.SplitNorm

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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)

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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.fdf More information at the Siesta web page 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 splitnorm: Variables to control the range of the second-ς shells in the basis set

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The splitnorm: Run S IESTA for different values of the PAO.SplitNorm PAO.SplitNorm0.10 Edit the input file and set up Then, run S IESTA $siesta Al.splitnorm.0.10.out

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For each splitnorm, search for the range of the orbitals Edit each output file and search for:

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We are interested in this number For each splitnorm, search for the range of the orbitals

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Edit each output file and search for: The lattice constant in this particular case would be Å × 2 = Å For each splitnorm, search for the range of the orbitals

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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 SplitNorm: Run S IESTA for different values of the PAO.SplitNorm PAO.SplitNorm 0.15 Edit the input file and set up Then, run S IESTA $siesta Al.splitnorm.0.15.out Try different values of the PAO.EnergyShift PAO.SplitNorm 0.20$siesta Al.splitnorm.0.20.out PAO.SplitNorm 0.25$siesta Al.splitnorm.0.25.out PAO.SplitNorm 0.30$siesta Al.splitnorm.0.30.out PAO.SplitNorm 0.10$siesta Al.splitnorm.0.10.out

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Analyzing the results Edit in a file (called, for instance, splitnorm.dat) the previous values as a function of the SplitNorm

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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

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