4.4 Projection over atomic states, DOS, projected band structure

The code projwfc.x calculates projections of wavefunctions over atomic orbitals. The atomic wavefunctions are those contained in the pseudopotential file(s). The Löwdin population analysis (similar to Mulliken analysis) is presently implemented. The projected DOS (or PDOS: the DOS projected onto atomic orbitals) can also be calculated and written to file(s). More details on the input data are found in file PP/Doc/INPUT_PROJWFC.*. The ordering of the various angular momentum components (defined in routine ylmr2.f90) is as follows: P_{0, 0}(t), P_{1, 0}(t), P_{1, 1}(t)cosφ, P_{1, 1}(t)sinφ, P_{2, 0}(t), P_{2, 1}(t)cosφ, P_{2, 1}(t)sinφ, P_{2, 2}(t)cos2φ, P_{2, 2}(t)sin2φ and so on, where P_{l, m}=Legendre Polynomials, t = cosθ = z/r, φ = atan(y/x).

Data produced by code projwfc.x can be further analysed using auxiliary codes sumpdos.x (sums selected PDOS by specifying the names of files containing the desired PDOS: type sumpdos.x -h or look into the source code for more details) and plotproj.x . A more sophisticated tools is the script PP/tools/sum_states.py, by Julen Larrucea: documentation in http://larrucea.eu/sum_states-py-2/.

The total electronic DOS can also be calculated by code dos.x, whose complete input documentation is in PP/Doc/INPUT_DOS.* See Example 02 for total and projected electronic DOS calculations, -and for projected band structure; see Example 03 for projected and local DOS calculations.

The DOS projected over molecular states (e.g. for a molecule on a surface system) can be computed using code molecularpdos.x (courtesy of Guido Fratesi). See file PP/Doc/INPUT_MOLDOS.* for input documentation and directory PP/examples/MolDos_example/ for an example.

The calculation of magnetic anisotropy using the Force Theorem is described in the following paper: https://journals.aps.org/prb/abstract/10.1103/PhysRevB.90.205409. An example and a README can be found in PP/examples/ForceTheorem_example/