Projected density of states for WO$_3$
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 this paper
Getting the PDOS
In the following exercise we are going to look at the density of states of WO3:
Similar to the previous exercise we write the coordinates in term of the unit cell:
- WO3-PDOS.inp
&GLOBAL PROJECT WO3-pdos 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 &SCF SCF_GUESS ATOMIC EPS_SCF 1.0E-6 MAX_SCF 300 ADDED_MOS 100 &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 &PRINT &PDOS # print all projected DOS available: NLUMO -1 # split the density by quantum number: COMPONENTS &END &END PRINT &END DFT &SUBSYS &CELL ABC [angstrom] 3.810000 3.810000 3.810000 PERIODIC XYZ MULTIPLE_UNIT_CELL 2 2 2 &END CELL &TOPOLOGY MULTIPLE_UNIT_CELL 2 2 2 &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
The replication of the unit cell is necessary since the program samples only at the $\Gamma$ point unless instructed otherwise and we will otherwise do get a meaningful sampling of the density of states (e.g. the grid over the Brillouin Zone will be too coarse). Another option (which we will look into in the next exercise) is to sample over k-points instead.
What you will get in addition to the output file is a file named WO3_pdos-k1-1.pdos (to be precise, you will get one such file per atom kind but here we only have one, carbon) with a content similar to:
# Projected DOS for atomic kind W at iteration step i = 0, E(Fermi) = 0.144475 a.u.
# MO Eigenvalue [a.u.] Occupation s py pz px d-2 d-1 d0 d+1 d+2 f-3 f-2 f-1 f0 f+1 f+2 f+3
1 -2.621088 2.000000 0.87115225 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000256 0.00000000 0.00000256 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000 0.00000000
2 -2.621080 2.000000 0.85006340 0.00131878 0.00166813 0.00134861 0.00000000 0.00000000 0.00515023 0.00000000 0.00441289 0.00006412 0.00000000 0.00003847 0.00012977 0.00003934 0.00000000 0.00006557
[...]
The columns correspond to the orbitals present in the basis set (hence projected DOS). You would now do a convolution plot using a gaussian to get a smooth DOS
To the convoluted DOS, you may want to check this website. Here, it is provided two Python script to do the convolution. Download two files pdos.py and get-smearing-pdos.py to your folder. And execute the Python script using
python get-smearing-pdos.py file.pdos
Alternatively, you could also use the Python script developed by Tiziano:
python cp2k_pdos.py -h
Please also note the unit of the energy, it is in $E_h$. When looking at DOS plots you may want to convert it to Electronvolt instead. In the convolution program, this has been done in the code.
While some of the new options to help with convergence are of numerical nature, the smearing is not.
- Repeat the above calculation for the different multiple cells 3x3x3, 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?
- Change the $\sigma$ (or $width$) value in convolution program, what effect does it have on the PDOS plot ?