Tutorial:Particle in an octopus

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Octopus can actually run 2D systems where the shape of the simulation box is defined by what is white in an image file. Here is an example of a "particle in an octopus", in which we have a constant potential and an octopus-shaped quantum dot. To run it, you will need to have built the code with the optional library GDLIB.

Needed files

inp

CalculationMode = gs
FromScratch = yes
Dimensions = 2

%Species
"null" | species_user_defined | potential_formula | "0" | valence | 1
%

%Coordinates
"null" | 0 | 0
%

BoxShape = box_image
BoxShapeImage = "gdlib.png"

ff = 20
%Lsize
 135 / ff | 95 / ff
%

TheoryLevel = independent_particles
ConvEigenError = yes

Make this file available in the run directory: gdlib.png (also available in PREFIX/share/octopus from your octopus installation)

Gdlib.png

Plotting

You can obtain the wavefunction by adding this to the input file:

Output = wfs
OutputFormat = plane_z

and rerunning. View it in gnuplot with

plot 'static/wf-st0001.z=0' u 1:2:3 linetype palette

or

splot 'static/wf-st0001.z=0' u 1:2:(0):($3*500) with pm3d

Where does the wavefunction localize, and why?

Exercises

  • See how the total energy scales with the size of the system (controlled by the ff parameter in the input file). How does it compare to the formula for a particle in a box?
  • Look at the wavefunctions of the unoccupied states.
  • Think of a serious application that would use the ability to define the simulation box by an image!

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