exercises:2016_uzh_cmest:band_structure_calculation

To get the band structure for graphene (or h-BN), only a few changes are required compared to the previous example for calculating the PDOS:

- graphene_kp_dos.inp
&GLOBAL PROJECT graphene_kp_dos RUN_TYPE ENERGY PRINT_LEVEL MEDIUM &END GLOBAL &FORCE_EVAL METHOD Quickstep &DFT BASIS_SET_FILE_NAME BASIS_MOLOPT POTENTIAL_FILE_NAME POTENTIAL &POISSON PERIODIC XYZ &END POISSON &QS EXTRAPOLATION USE_GUESS ! required for K-Point sampling &END QS &SCF SCF_GUESS ATOMIC EPS_SCF 1.0E-6 MAX_SCF 300 ADDED_MOS 2 &SMEAR ON METHOD FERMI_DIRAC ELECTRONIC_TEMPERATURE [K] 300 &END SMEAR &DIAGONALIZATION ALGORITHM STANDARD EPS_ADAPT 0.01 &END DIAGONALIZATION &MIXING METHOD BROYDEN_MIXING ALPHA 0.2 BETA 1.5 NBROYDEN 8 &END MIXING &END SCF &XC &XC_FUNCTIONAL PBE &END XC_FUNCTIONAL &END XC &KPOINTS SCHEME MONKHORST-PACK 3 3 1 SYMMETRY OFF WAVEFUNCTIONS REAL FULL_GRID .TRUE. PARALLEL_GROUP_SIZE 0 &BAND_STRUCTURE ADDED_MOS 2 FILE_NAME graphene.bs &KPOINT_SET UNITS CART_BOHR ! work around a bug in CP2K, should be B_VECTOR SPECIAL_POINT 0.0 0.0 0.0 SPECIAL_POINT 1./2. 0.0 0.0 NPOINTS 5 &END &END BAND_STRUCTURE &END KPOINTS &END DFT &SUBSYS &CELL ABC [angstrom] 2.4612 2.4612 8 ALPHA_BETA_GAMMA 90. 90. 60. SYMMETRY HEXAGONAL PERIODIC XYZ MULTIPLE_UNIT_CELL 1 1 1 &END CELL &TOPOLOGY MULTIPLE_UNIT_CELL 1 1 1 &END TOPOLOGY &COORD SCALED C 1./3. 1./3. 0. C 2./3. 2./3. 0. &END &KIND C ELEMENT C BASIS_SET TZVP-MOLOPT-GTH POTENTIAL GTH-PBE &END KIND &END SUBSYS &END FORCE_EVAL

At present (CP2K 4.1) it is not possible to get the projected density of states when doing a K-Point calculation. Plus there is currently an issue with the

`UNITS`

specification for the special point coordinates: even though the unit is set to Cartesian coordinates (in Bohr), the special points are multiplied by the reciprocal vectors and must therefore be given in terms of the b-vectors.
Some notes on the input file:

- By specifying the
`KPOINT`

section you are enabling the K-Point calculation. - While you could specify the K-Points directly, we are using the Monkhorst-Pack scheme
^{1)}to generate them. The numbers following the keyword`MONKHORST-PACK`

specify the tiling of the brillouin zone. - After the basic calculation, CP2K calculates the energies along certain lines, denoted as
`KPOINT_SET`

(when you check the documentation you will note that this section can be repeated). - The keyword
`NPOINTS`

specifies how many points (in the addition to the starting point) should be sampled between two special points. - The
`SPECIAL_POINT`

keyword is used to specify the start-, mid- and endpoints of the line. Those points usually denote special points in the reciprocal lattice/unit cell, like the $\Gamma$, $M$ or $K$ point. You can find the definition for these in the appendix section of this paper. This keyword can also be specified multiple times, making it possible to directly get the band structure for a complete*path*.

Now, when you run this input file you will get in addition the the output file, a file named `graphene.bs`

which will look similar to the following:

SET: 1 TOTAL POINTS: 6 POINT 1 0.000000 0.000000 0.000000 POINT 2 0.500000 0.000000 0.000000 Nr. 1 Spin 1 K-Point 0.00000000 0.00000000 0.00000000 8 -15.30752034 -3.31285773 0.93143545 1.03651421 8.71874068 12.74920179 12.83785311 15.50144316 Nr. 2 Spin 1 K-Point 0.02500000 0.00000000 0.00000000 8 -15.29453364 -3.29547462 0.87472486 1.00321991 8.31998068 12.81500348 12.93001933 15.45108207 Nr. 3 Spin 1 K-Point 0.05000000 0.00000000 0.00000000 [...]

For each set there is a block named `SET`

with the special points listed as `POINT`

, followed by sub-blocks for each K-Point containing the energies for each MO.

Your tasks:

- Lookup the special points for the $\Gamma$, $M$, $K$ points in the mentioned paper (make sure you choose the right lattice). Calculate and plot the band structure for graphene from $\Gamma$ over $M$, $K$ back to $\Gamma$ (you are free to decide whether to use multiple K-Point sets are multiple special points in a single set). Mark the special points. Choose an appropriate number of interpolation points to get a smooth plot.
- Compare your plot with plots from literature. What is different?
- Why do you get 8 orbital energies? Try to change the input to get more unoccupied orbitals.

To convert the band structure file to a file which can be loaded directly into MATLAB for example, you can use the script `/users/tiziano/bin/cp2k_bs2csv.py`

which when passed a band structure file `graphene.bs`

as an argument will write files `graphene.bs-setN.csv`

for each set containing the K-Point coordinates and the energies in one line.

exercises/2016_uzh_cmest/band_structure_calculation.txt · Last modified: 2016/11/06 16:06 by tmueller

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