The format of filproj

Preliminaries

• The header is written by PP/src/write_io_header.f90
• projections by PP/src/write_proj.f90, in the write_proj_file subroutine.

If the calculation is colinear (no spin polarization) or noncolinear, the filename will be filproj.projwfc_up. If it's spin-polarized colinear, you get a second file filproj.projwfc_down.

Header Format

Header (stuff in {} are just my comments):

{empty line}
nr1x nr2x nr3x nr1 nr2 nr3 nat ntyp
ibrav celldm(1) ... celldm(6)
a1x a1y a1z {only if ibrav=0}
a2x a2y a2z {only if ibrav=0}
a3x a3y a3z {only if ibrav=0}
gcutm dual ecutwfc 9 {last one is always 9}
species_i species_symbol nelect {line repeated ntyp times}
atom_i x y z species_i {line repeated nat times}
natomwfc nkstot nbnd
noncolin lspinorb {only possible combinations: F F, T F, T T}

Parameter	Explanation
nr1x, nr2x, nr3x	Physical dimensions of charge density array
nr1, nr2, nr3	(Dense) FFT grid dimensions/true dimensions of charge density array
nat	Total number of atoms (same as pw.x input)
ntyp	Total number of species (same as pw.x input)
ibrav	Bravais lattice (same as pw.x input)
celldm(1) ... celldm(6)	The lattice constants and angles \((a, b/a, c/a, \cos\alpha, \cos\beta, \cos\gamma)\) in bohr units (same as pw.x input). Only celldm(1) is guaranteed to be nonzero, the rest may be 0 depending on ibrav.
a1x, a1y, a1z	x, y, z components of the first lattice vector in units of alat. Only present if ibrav=0.
a2x, a2y, a2z	x, y, z components of the second lattice vector in units of alat. Only present if ibrav=0.
a3x, a3y, a3z	x, y, z components of the second lattice vector in units of alat. Only present if ibrav=0.
gcutm	\(E_\text{cut}^{\rho}/(2\pi/a)^2\), where \(E_\text{cut}^\rho\) = ecutrho and \(a\) = alat,in units of \(\text{Ry}\times a_0^2\).
dual	ecutrho/ecutwfc
ecutwfc	The wavefunction cutoff in Ry (same as pw.x input)
9	The number 9. It's always there for an unknown reason
species_i	Unique index (1 through ntyp) given to each unique species in the calculation
species_symbol	Symbol for the element given in the input file (O, Fe)
nelect	Number of valence electrons in the pseudopotential file for the species.
atom_i	Unique index (1 through nat) given to each atom in the calculation
x y z	Atom's position in cartesian coordinations, units of alat (regardless of what's in pw.x's input).
species_i	The index giving the type of the atom, see above.
natomwfc	Number of total atomic wave functions (i.e., orbitals) available. Computed from the pseudopotential files
nkstot	Number of total \(k\)-points in the calculation.
nbnd	Number of bands (same as pw.x input).
noncolin	Whether the calculation is noncolinear (T or F, same as pw.x input)
lspinorb	Whether the calculation includes spin-orbit coupling (T or F, same as pw.x input)

Projections

After the header, we end up with natomwfc sets of overlaps that schematically looks like this:

if noncolin and lspinorb:
    state_i atom_i species_symbol orbital_label wfc_i l j mj
elif noncolin and not lspinorb:
    state_i atom_i species_symbol orbital_label wfc_i l m s_z
else:
    state_i atom_i species_symbol orbital_label wfc_i l m 
for k_i in range(k_init, k_final+1):
    for band_i in range(1, nbnd+1):
      k_i band_i overlap

(i.e., there is a total of nkstot*nbnd+1 lines)

Parameter	Explanation
noncolin	Given in the header, see above.
lspinorb	Given in the header, see above.
state_i	A unique index for an atomic state, from 1 to natomwfc. Also written to projwfc.x stdout.
atom_i	Given in the header, see above.
species_symbol	Symbol for the species (e.g., Fe, Sr, etc.). Given in the header, see above.
orbital_label	A label for the atomic orbital, e.g., 4S or 5P or 3D.
wfc_i	A unique index for an atomic wfc of a given atom. A combination (l,j)or just l is considered unique. Prepended to the DOS files.
l	Orbital quantum number \(l\)
j	Orbital quantum number \(j\)
m	Index for the type of orbital, see table below. Not the magnetic quantum number \(m_l\).
s_z	Eigenvalue of \(\hat{S}_z\), \(s_z = \pm 1/2\)
nkstot	Given in the header, see above.
k_init, k_final	The k indices run from 1 to nkstot for colinear spin-unpolarized, noncolinear and SOC calculations. For spin-polarized calculations, the indices run from 1 to nkstot for spin up and nkstot+1 to 2*nkstot for spin down.
nbnd	Given in the header, see above.
overlap	\(\vert\langle \phi_{\alpha}(\boldsymbol{\tau_i})\vert \psi_{n \boldsymbol{k}}^\sigma \rangle\vert^2\) where \(\psi_{n \boldsymbol{k}}^\sigma\) is the Bloch wave of band \(n\)=band_i with \(k\)=kpts[k_i] (possibly with spin \(\sigma\)), and \(\phi_\alpha(\boldsymbol{\tau}_i)\) is an atomic-like wavefunction centered at \(\tau_i\), the position of the atom with \(i\)=atom_i, and \(\alpha\) is the appropriate set of quantum numbers depending on the type of calculation.

The orbitals are given by (from the projwfc.x input description): * \(l=1\):

m	Orbital	Notes
1	\(p_z\)	\(m_l=0\)
2	\(p_x\)	real combination of \(m_l\)=+/-1 with cosine
3	\(p_y\)	real combination of \(m_l\)=+/-1 with sine

• \(l=2\):

m	Orbital	Notes
1	\(d_{z^2}\)	\(m_l=0\)
2	\(d_{zx}\)	real combination of \(m_l=\pm1\) with cosine
3	\(d_{zy}\)	real combination of \(m_l=\pm1\) with sine
4	\(d_{x^2-y^2}\)	real combination of \(m_l=\pm2\) with cosine
5	\(d_{xy}\)	real combination of \(m=\pm2\) with sine
* \(l=3\) (not implemented in projwfc.x)