======= 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_pdos|calculating the PDOS]]: &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 [(http://journals.aps.org/prb/abstract/10.1103/PhysRevB.13.5188)] 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 [[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 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 [[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 (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 ''cp2k_bs2csv.py'' from below, 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. #!/usr/bin/env python """ Convert the CP2K band structure output to CSV files """ import re import argparse SET_MATCH = re.compile(r''' [ ]* SET: [ ]* (?P\d+) [ ]* TOTAL [ ] POINTS: [ ]* (?P\d+) [ ]* \n (?P [\s\S]*?(?=\n.*?[ ] SET|$) # match everything until next 'SET' or EOL ) ''', re.VERBOSE) SPOINTS_MATCH = re.compile(r''' [ ]* POINT [ ]+ (?P\d+) [ ]+ (?P\S+) [ ]+ (?P\S+) [ ]+ (?P\S+) ''', re.VERBOSE) POINTS_MATCH = re.compile(r''' [ ]* Nr\. [ ]+ (?P\d+) [ ]+ Spin [ ]+ (?P\d+) [ ]+ K-Point [ ]+ (?P\S+) [ ]+ (?P\S+) [ ]+ (?P\S+) [ ]* \n [ ]* (?P\d+) [ ]* \n (?P [\s\S]*?(?=\n.*?[ ] Nr|$) # match everything until next 'Nr.' or EOL ) ''', re.VERBOSE) if __name__ == '__main__': parser = argparse.ArgumentParser(description=__doc__) parser.add_argument('bsfilename', metavar='bandstructure-file', type=str, help="the band structure file generated by CP2K") args = parser.parse_args() with open(args.bsfilename, 'r') as fhandle: for kpoint_set in SET_MATCH.finditer(fhandle.read()): filename = "{}.set-{}.csv".format(args.bsfilename, kpoint_set.group('setnr')) set_content = kpoint_set.group('content') with open(filename, 'w') as csvout: print(("writing point set {}" " (total number of k-points: {totalpoints})" .format(filename, **kpoint_set.groupdict()))) print(" with the following special points:") for point in SPOINTS_MATCH.finditer(set_content): print(" {pointnr}: {a}/{b}/{c}".format( **point.groupdict())) for point in POINTS_MATCH.finditer(set_content): results = point.groupdict() results['values'] = " ".join(results['values'].split()) csvout.write("{a} {b} {c} {values}\n".format(**results))