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--- exercises:common:pdos [2022/09/08 15:26] – created jglan
+++ exercises:common:pdos [2022/09/08 15:29] (current) – jglan
@@ Line 1: / Line 1: @@
-======= Projected density of states and Band structure for WO$_3$ =======
+======= Projected density of states for 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]]
+In this exercise, we 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|}}
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 </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 3
-         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>
-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
-           -73.66652408    -38.53370023    -37.80464132    -37.79327769
-           -16.71308703    -16.11075946    -16.02553853     -1.43495530
-            -1.34739188     -1.33357408      0.37912017      0.38948689
-.39582882      0.40030859      0.46965212      0.47418816
-.60728842      2.62105342      3.16044140      6.99806305
-       Nr.    2    Spin 1        K-Point  0.00000000  0.10000000  0.00000000
-           -73.66647294    -38.53337818    -37.80859042    -37.79536623
-           -16.67479677    -16.09554462    -15.96731960     -1.68492873
-            -1.44087258     -1.34318045      0.09257368      0.13769271
-.21643888      0.38447849      0.44179002      0.45757924
-.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>