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exercises:2017_uzh_cmest:pdos

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exercises:2017_uzh_cmest:pdos [2017/10/17 15:47] – jglanexercises:2017_uzh_cmest:pdos [2020/08/21 10:15] (current) – external edit 127.0.0.1
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-======= Projected density of states for graphene and h-BN =======+======= Projected density of states and Band structure for WO$_3$ =======
  
-In the following exercise we are going to look at the density of states of WO$_3$:+In this exercise, you will carry out Density Of States(DOS) and band structure calculation using K-point sampling for Cubic lattice WO$_3$. The reference DOS and band structure you can find in [[http://pubs.acs.org/doi/abs/10.1021/cm3032225|this paper]] 
 + 
 +{{:exercises:2017_uzh_cmest:wo3.jpeg?1200|}} 
 + 
 +====== Getting the PDOS ====== 
 + 
 +In the following exercise we are going to look at the density of states of <chem>WO3</chem>:
  
 Similar to the previous exercise we write the coordinates in term of the unit cell: Similar to the previous exercise we write the coordinates in term of the unit cell:
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  <code>python get-smearing-pdos.py file.pdos</code>  <code>python get-smearing-pdos.py file.pdos</code>
  
-Alternatively, you could also use the [[https://raw.githubusercontent.com/dev-zero/cp2k-tools/master/scripts/cp2k_pdos.py|Python script]] developed by Tiziano.+Alternatively, you could also use the [[https://raw.githubusercontent.com/dev-zero/cp2k-tools/master/scripts/cp2k_pdos.py|Python script]] developed by Tiziano, the parser bug was fixed already.
  
 <note important>Different $\sigma$ values give you different convolution, which mean the lineshape is different. A reasonable $\sigma$ value is required to get a good PDOS plot. When visualize the PDOS, only energy region close to the Fermi level is interesting. One need to adapt the xrange properly.</note> <note important>Different $\sigma$ values give you different convolution, which mean the lineshape is different. A reasonable $\sigma$ value is required to get a good PDOS plot. When visualize the PDOS, only energy region close to the Fermi level is interesting. One need to adapt the xrange properly.</note>
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 While some of the new options to help with convergence are of numerical nature, [[howto:static_calculation#adding_smearing|the smearing is not]]. While some of the new options to help with convergence are of numerical nature, [[howto:static_calculation#adding_smearing|the smearing is not]].
  
 +
 +<note>
   * Repeat the above calculation for the different multiple cells 3x3x3, 4x4x4   * Repeat the above calculation for the different multiple cells 3x3x3, 4x4x4
-  * Do you see why it is necessary to do the unit cell replication? Hints: does WO$_3$ have a band gap? Compare the plots for 3x3x3 and 4x4x4.+  * Get the Total DOS and PDOS of O$_2p$ and W$_5d$ orbitals and compare to the literature value. 
 +  * Do you see why it is necessary to do the unit cell replication?   
 +  * What is the value of WO$_3$ band gap? Compare the plots for 3x3x3 and 4x4x4.
   * .. which state ($s$, $p_x$, ..) is mainly responsible for that?   * .. which state ($s$, $p_x$, ..) is mainly responsible for that?
 +  * Change the $\sigma$ value in convolution program, and determine a reasonable value for the PDOS plot
 +</note>
 +
 +====== Getting the band structure of WO$_3$ Lattice ======
 +
 +To get the band structure for <chem>WO3</chem>, only a few changes are required compared to the previous example for [[PDOS|calculating the PDOS]]:
 + 
 +<code - WO3-bs.inp>
 +&GLOBAL
 +   PROJECT WO3-kp-bs
 +   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
 +         &DIAGONALIZATION
 +            ALGORITHM STANDARD
 +            EPS_ADAPT 0.01
 +         &END DIAGONALIZATION
 +         &SMEAR  ON
 +            METHOD FERMI_DIRAC
 +            ELECTRONIC_TEMPERATURE [K] 300
 +         &END SMEAR
 +
 +         &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
 +         WAVEFUNCTIONS REAL
 +         SYMMETRY .FALSE.
 +         FULL_GRID .FALSE.
 +         PARALLEL_GROUP_SIZE -1
 +      &END KPOINTS
 +      &PRINT
 +         &BAND_STRUCTURE
 +            ADDED_MOS 2
 +            FILE_NAME WO3.bs
 +            &KPOINT_SET
 +               UNITS B_VECTOR
 +               SPECIAL_POINT ???   #GAMA
 +               SPECIAL_POINT ???   #X
 +               SPECIAL_POINT ???   #M
 +               SPECIAL_POINT ???   #GAMA
 +               SPECIAL_POINT ???   #R
 +               SPECIAL_POINT ???   #M
 +               NPOINTS ???
 +            &END
 +         &END BAND_STRUCTURE
 +      &END PRINT
 +   &END DFT
 +
 +   &SUBSYS
 +      &CELL
 +         ABC [angstrom] 3.810000 3.810000 3.810000
 +         PERIODIC XYZ
 +         MULTIPLE_UNIT_CELL 1 1 1
 +      &END CELL
 +      &TOPOLOGY
 +         MULTIPLE_UNIT_CELL 1 1 1
 +      &END TOPOLOGY
 +      &COORD
 +         SCALED
 +         W 0.0 0.0 0.0
 +         O 0.5 0.0 0.0
 +         O 0.0 0.5 0.0
 +         O 0.0 0.0 0.5
 +      &END
 +      &KIND W
 +         ELEMENT W
 +         BASIS_SET DZVP-MOLOPT-SR-GTH
 +         POTENTIAL GTH-PBE
 +      &END KIND
 +      &KIND O
 +         ELEMENT O
 +         BASIS_SET DZVP-MOLOPT-SR-GTH
 +         POTENTIAL GTH-PBE
 +      &END KIND
 +   &END SUBSYS
 +
 +&END FORCE_EVAL
 +
 +</code>
 +
 +<note important>At present, it is not possible to get the projected density of states when doing a K-Point calculation. The special points should be given in terms of the b-vectors.</note>
 +
 +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/PRINT/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//.
 +
 +<note tip>You are encouraged to use [[ http://tools.materialscloud.org/seekpath|SeeK-path Tool]] when doing the sampling via K-Points to get a skeleton input file for CP2K with the important paths in the reciprocal space. Give SeeK-path the following as your XYZ file and specify a simple cubic cell with the lattice constant $a$ as specified below as well:
 +<code - WO3-cubic.xyz>
 +4
 +WO3; a=3.810000
 + W    0.000000    0.000000    0.000000
 + O    1.905000    0.000000    0.000000
 + O    0.000000    1.905000    0.000000
 + O    0.000000    0.000000    1.905000
 +</code>
 +</note>
 +
 +
 +Now, when you run this input file you will get in addition the the output file, a file named ''WO3.bs'' which will look similar to the following:
 +
 +<code>
 + SET:       1                 TOTAL POINTS:      26
 +   POINT   1                     ********    ********    ********
 +   POINT   2                     ********    ********    ********
 +   POINT   3                     ********    ********    ********
 +   POINT   4                     ********    ********    ********
 +   POINT   5                     ********    ********    ********
 +   POINT   6                     ********    ********    ********
 +       Nr.    1    Spin 1        K-Point  0.00000000  0.00000000  0.00000000
 +               20
 +           -73.66652408    -38.53370023    -37.80464132    -37.79327769
 +           -16.71308703    -16.11075946    -16.02553853     -1.43495530
 +            -1.34739188     -1.33357408      0.37912017      0.38948689
 +             0.39582882      0.40030859      0.46965212      0.47418816
 +             2.60728842      2.62105342      3.16044140      6.99806305
 +       Nr.    2    Spin 1        K-Point  0.00000000  0.10000000  0.00000000
 +               20
 +           -73.66647294    -38.53337818    -37.80859042    -37.79536623
 +           -16.67479677    -16.09554462    -15.96731960     -1.68492873
 +            -1.44087258     -1.34318045      0.09257368      0.13769271
 +             0.21643888      0.38447849      0.44179002      0.45757924
 +             2.61768501      3.02368022      3.51828287      7.06644645
 +
 +[...]
 +</code>
 +
 +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.
 +
 +<note>
 +Your tasks:
 +
 +  * Lookup the special points for the $\Gamma$, $X$,$M$,$R$ points in the [[http://pubs.acs.org/doi/abs/10.1021/cm3032225|mentioned paper]] (make sure you choose the right lattice). Calculate and plot the band structure for WO3 lattice along $\Gamma$, $X$,$M$,$\Gamma$,$R$,$M$ (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?
 +  * How many orbital energies do you get and why? Try to change the input to get more unoccupied orbitals.
 +</note>
 +
 +
 +To convert the band structure file to a file which can be plotted directly, you can use the script ''cp2k_bs2csv.py'' from below, which when passed a band structure file ''WO3.bs'' as an argument will write files ''WO3.bs-set-1.csv'' for each set containing the K-Point coordinates and the energies in one line.
 +
 +To plot the ''WO3.bs-set-1.csv'' file, you can either load it into $MATLAB$ or use $GNUPLOT$ command line.
 +<code>gnuplot>set yrange [-8:14]
 +gnuplot>plot for [i=4:23] "WO3.bs.set-1.csv" u 0:i w l t ""
 + </code>
 +<file python cp2k_bs2csv.py>
 +#!/usr/bin/env python
 +"""
 +Convert the CP2K band structure output to CSV files
 +"""
 +
 +import re
 +import argparse
 +
 +SET_MATCH = re.compile(r'''
 +[ ]*
 +  SET: [ ]* (?P<setnr>\d+) [ ]*
 +  TOTAL [ ] POINTS: [ ]* (?P<totalpoints>\d+) [ ]*
 +  \n
 +(?P<content>
 +  [\s\S]*?(?=\n.*?[ ] SET|$)  # match everything until next 'SET' or EOL
 +)
 +''', re.VERBOSE)
 +
 +SPOINTS_MATCH = re.compile(r'''
 +[ ]*
 +  POINT [ ]+ (?P<pointnr>\d+) [ ]+ (?P<a>\S+) [ ]+ (?P<b>\S+) [ ]+ (?P<c>\S+)
 +''', re.VERBOSE)
 +
 +POINTS_MATCH = re.compile(r'''
 +[ ]*
 +  Nr\. [ ]+ (?P<nr>\d+) [ ]+
 +  Spin [ ]+ (?P<spin>\d+) [ ]+
 +  K-Point [ ]+ (?P<a>\S+) [ ]+ (?P<b>\S+) [ ]+ (?P<c>\S+) [ ]*
 +  \n
 +[ ]* (?P<npoints>\d+) [ ]* \n
 +(?P<values>
 +  [\s\S]*?(?=\n.*?[ ] Nr|$)  # 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))
  
 +</file>
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