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Calculation of the bandstructure of Si by means of DFT with different settings
ssh -X EMPA-USER@jump1.empa.ch ssh -X hypatia
module load python/2.7.12
go in the directory where you want to put the exercise and do:
cp /home/cpi/exercise_11.tar ./ tar -xvf exercise_11.tar cd exercise_11
You will find a different directory for each TASK
Please have a look at this web page
http://materialscloud.org/sssp/
where pseudopotentials for different elements of the periodic table can be found. For each pseudopotential several convergence test have been made, the use of the data contained in this webpage can be in general trusted, but additional tests are always a good praxis
Please also have a look at the webpage of quantum-espresso to find a detailed description of input parameters
TASK_0
The batch script run contain the instruction to run a quantum-espresso DFT calculaiton for a conventional cell of Si (ibrav=1 for simple cubic cell). As you can see in the file, 8 atoms are included in the cell of parameter a=5.43A. The primitive cell (ibrav=2 for fcc) would contain only 2 atoms and would not be cubic. The scirpt is ment to run a calculation to optimize the wavefuntion of the system and to compute the total energy. A sinlge k point, Gamma, is used for the summation over the Brillouin Zone.
- the lattice parameter is specified
- the type of lattice (ibrav) is specified
- the coordinates of the atoms are provided in crystal coordinates
- the Monkhorst-Pack grid (in this case only Gamma point) is specifyed for the BZ sums
- how many electrons do we have in the system?
- how many occupied egigenvector do we have for each k-point (the occupation is printed in the output for each k-point after the energies of the eigenvalues belonging to the k-point
Submit the calculation to the queue
qsub run
Have a look to th eoutput generated: si.out
- identify where the symmetry operations used by the code are listed
- identify the k-points used during the calculations
- find where the eigenvalues (provided in eV) for each k-point are printed
- find the total energy of teh system
to find the total energy of the system you can also type:
grep "\!" si.out
to find the Fermi energy of the system you can also type:
grep "Fermi" si.out
TASK_0b, TASK_0c, TASK_1
The three tasks repeat the calculation of TASK_0 with a different sampling of the BZ in 0b a non shifted grid of 2x2x2 k-points is used, thus containing high symmetry points (so not ideal to have a accurate integration) in 0c the 2x2x2 grid is shifted and in TASK_1 a non shifted 3x3x3 grid is used.
TASK_2
Here the run script contains teh data to run a calculation for a large Si cell There are 216 atoms corresponding to 3x3x3 of the conventional cell used in the previuos calculations
- why the total energy obtained in TASK_1 is closer to E27/27 compared to the energies obtained in TASKS 0,0b,0c?
- Compare the eigenvalues that you have now at the Gamma k-point with the eigenvalues you had on the different k-points for the calculation of TASK_1. All the eigenvalues obtained in TASK_1, that are subdivided in different k-points are now grouped in a single k-point.
- How many k-points are used in the calculation of TASK_1 as listed in si.out? why not 27?
TASK_3
The script run performs an accurate calculation (Monkhorst-Pack grid 8x8x8) to obtain a accurate estimate of the charge density (thus the hamiltonian) of the system (si.out). Then the datat obtained are used to compute the bandstructure of Si along the symmetry lines L-G and G-X. (the output is written in the file sibands.out, where you will find all the eigenvalues for the 100 k-points specified to sample the symmetry lines)
qsub run
once THE CALCULATION IS COMPLETED plot the bands
grep "Fermi" si.out python bands.py
you will obtain the png file bands.png