DOS and projected DOS

DOS from EIG file using Eig2DOS

Given the set of eigenvalues \(\epsilon_n({\bf k})\), the DOS can be estimated as:

\[DOS(\omega) = \sum_{n{\bf k}} { \delta(\epsilon_n({\bf k}) - \omega)}\]

replacing the delta function with some suitable gaussian broadening.

The advantage of this method is that is very simple, and the EIG file containing the BZ eigenvalues is always available after the end of the scf cycle.

Since the algorithm is very simple minded (just sum over energy points with some smearing, the DOS might be spiky (coarse k-sampling, small broadening) or too broad. It is possible to increase the number of k-points in the sampling of the BZ, but then a new scf cycle is needed.

Projected DOS from PDOS and PDOS.xml files

When a Projected-Density-of-States block is used in Siesta, such as:

%block Projected-density-of-states
-26.00 4.00 0.200 500 eV
%endblock Projected-density-of-states

Siesta will compute a full decomposition of the DOS over all orbitals, in the energy range provided (above: -26.00 to 4.00 eV), using a given broadening (0.2 eV above), and a given number of energy points in the range (500 in the above example). The output is placed, for historical reasons, in two files: SystemLabel.PDOS and SystemLabel.PDOS.xml. Both contain the same (XML) data, but the first one is formatted so that the data items appear in separate lines. The second is more compact. We have kept the original .PDOS file since it can be processed by the fmpdos program by Andrei Postnikov, which does not really parse the XML, and depends on the special format.

The program pdosxml uses an XML parser to process either file, and is therefore more robust. However, it currently has a drawback: the specification of which orbitals to take into account for the projection of the DOS is done in the code, so the program must be recompiled for each use. It is thus not very convenient in practice.

Both fmpdos and `pdosxml are installed when Siesta is built.

The shortcomings of pdosxml and fmpdos can be avoided by using a new python-based utility pdos-select, which offers a fully flexible orbital specification syntax and a host of other features. Some examples:

# Select all oxygen orbitals
pdos-select h2o.PDOS --select "species == 'O'" > oxygen_dos.dat

# Multiple selections (OR logic)
pdos-select input.PDOS --select "species == 'O'" --select "species == 'H'"

# Complex query
pdos-select input.PDOS --select "atom_index in range(1, 6) and l in [0, 1]"

# List all orbitals without processing
pdos-select input.PDOS --list-orbitals

# Export as CSV
pdos-select input.PDOS --select "l == 0" --format csv -o output.csv

# Get help on selection syntax
pdos-select --help-selectors

Note

pdos-select is not yet included in the Siesta distribution. To install it, assuming you have a modern Python interpreter installed, just execute:

pip install --index-url https://gitlab.com/api/v4/projects/27621639/packages/pypi/simple pdos-tools

The package has no extra dependencies.

The PDOS file can also be processed by sisl, using ???.

Note that if a different energy range, smearing, or number of points is desired, a new Siesta run must be used. And since the PDOS information is computed internally from the coefficients of the wave functions, the program needs the Hamiltonian, which cannot currently be read from a file. So even if a converged density-matrix file is used to restart the calculation, some substantial computing is still involved to get the new projected DOS data.

One can specify a denser BZ sampling for the PDOS calculation by using a special block:

%block PDOS.kgrid_Monkhorst_Pack
 8  0  0  0.5
 0  8  0  0.5
 0  0  8  0.5
%endblock PDOS.kgrid_Monkhorst_Pack

Projected DOS from stored wavefunctions

An alternative way to process the projected DOS is to use explicitly the equation (see the theoretical background to the tutorial on the analysis of the electronic structure):

\[g_{\mu} (\varepsilon) = \sum_i { \sum_{\nu} { c_{i\mu}c_{i\nu} S_{\mu\nu} \delta(\varepsilon - \varepsilon_i) } }\]

which involves the overlap matrix and the wavefunctions associated to a full sampling of the BZ. These can be output to file by Siesta if the option:

COOP.write T

is used. The name of the option is related to the framework for the analysis of the crystal-overlap populations (COOP/COHP), which includes the processing of the pDOS as a by-product.

This framework allows the interactive control of all the parameters (energy range, broadening, orbitals involved, etc), at the expense of having potentially large wavefunction files around.