In this example, we will calculate band-projected density matrices to study charge densities associated with individual electronic bands of Cu2O.
- You need to be in the
propdirectory that we used in the section Electronic band structure and density of states for Cu2O (DFT-PBE0/TZVP level of theory).
- You should already have calculated and studied the electronic band structure of the material.
PBAN/ECH3 for occupied bands
We run a
PBAN calculation to get a band-projected density matrix and then plot the charge density associated with the band using keyword
ECH3. Let's focus on the band 66, which is the highest occupied band (it is threefold degenerate at Γ-point, however). Note that
PBAN only works for occupied bands and for unoccupied bands, one has to use
PGEOMW (see below).
Create a new copy the wavefunction file
cp Cu2O_Pn-3m_PBE0_TZVP_band.w Cu2O_Pn-3m_PBE0_TZVP_b66.w
Create the following property calculation input file
Cu2O_Pn-3m_PBE0_TZVP_b66.d3 in the directory:
NEWK: Request CRYSTAL to calculate the Fock/Kohn-Sham eigenvectors at a number of k-points in the reciprocal space. The lines
0 8 and
8 8 8 are equal to the original
SHRINK values (see the chapter on geometry optimization), the original k-mesh is enough to obtain the band widths. Line
1 0 requests CRYSTAL to calculate the Fermi energy using this k-mesh (1) and tells that no additional printing is required (0).
PBAN: Request CRYSTAL to calculate band-projected density matrix for one band, labeled 66. All properties requested after this keyword are calculated using this band-projected density matrix.
ECH3: Request charge density plotted on a 3D grid in Gaussian Cube format. 75 is the number of grid points in each direction of the cube. The more ponts, the higher the resolution of the plot, and larger the resulting file.
Running the calculation will produce
Cu2O_Pn-3m_PBE0_TZVP_band66.DENS.cube that can be visualized with VESTA (see below).
PGEOMW/ECH3 for unoccupied bands
In the case of unoccupied bands, one cannot use the
PBAN keyword as these bands do not correspond to any density. In this case, the
PBAN keyword is replaced with
PGEOMW keyword, which has otherwise identical syntax. This keyword sets full occupation for every band.
Visualization of charge densities in VESTA
(work in progress, more screenshots and explanations coming)
Cube files can be directly opened in VESTA, but this usually does not produce good enough result.
- It is better to first open a CIF file correspongind to the cube file. Note that this CIF must correspond to the optimized structure of the primitive cell. The CIF must also be in the same orientation as the cube file produced by CRYSTAL. This is normally simple for primitive lattices, but more tricky for centered lattices.
- Next, the calculated density can be added from Edit → Edit Data → Volumetric Data.
- Click Isosurfaces → Import... and open the cube file
- The following dialog opens, keep the defaults (Add to current data and Raw Data)
Next, VESTA will show the following warning:
Typically, the best option is to click "No". If the CIF and cube really do not match, you will see it from the resulting plot (isodensities are completely wrong places compared to the atoms).
Now you can start adjusting the properties of the isodensity (Properties → Isosurfaces → Isosurface level). A reasonable starting point for band-projected charge densities could be 0.002 e–. Please remember always to report the isovalue in publications. Either separately in each plot or in the computational details.