exercises:2016_uzh_cmest:band_structure_calculation
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Getting the band structure of graphene
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
specifies the tiling of the brillouin zone. - After the basic calculation, CP2K calculates the energies along certain lines, denoted as
KPOINT_SET
(when you check [https://manual.cp2k.org/trunk/CP2K_INPUT/FORCE_EVAL/DFT/KPOINTS/BAND_STRUCTURE/KPOINT_SET.html|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 specifies 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 of [http://www.sciencedirect.com/science/article/pii/S0927025610002697|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. Calculate and plot the band structure for graphene from $\Gamma$ over $M$, $K$ back to $\Gamma$.
- 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.
exercises/2016_uzh_cmest/band_structure_calculation.1478444065.txt.gz · Last modified: 2020/08/21 10:15 (external edit)