Comparison of projwfc.x output files

This document compares the output files of projwfc.x for the same calculation. The files are projwfc.out (just the stdout of projwfc.x redirected to a file), filproj, and atomic_proj.xml.

	projwfc.out	filproj	atomic_proj.xml
Structure	❌	✅	❌
\(k\)-points\(^\text{[\small{Note 1}]}\)	✅	❌	✅
Eigenvalues	✅	❌	✅
\(\langle \psi_{nk} \vert \phi \rangle\)\(^{[\small{\text{Note 2}]}}\)	❌	❌	✅
\(\vert \langle\psi_{nk} \vert \phi\rangle \vert^2\)	✅\(^{\text{\small{3 decimal places}}}\)	✅	✅\(^\text{\small{from above}}\)
Principle quantum number \(n\) for \(\vert\phi\rangle\)\(^{\small{[\text{Note 3}]}}\)	❌	✅	❌
Orbital quantum numbers for \(\vert\phi\rangle\)\(^{\small{[\text{Note 3}]}}\)	✅	✅	❌
Partial Parsing\(^{\small{[\text{Note 4}]}}\)	❌	❌	✅
Same file for spin up/down\(^{\small{[\text{Note 5}]}}\)	✅	❌	✅
Overlaps	✅	❌	❌
Lowdin Charges	✅	❌	❌
\(E_{\text{Fermi}}\)	❌	❌	✅
Other Info\(^{\small{[\text{Note 6}]}}\)	❌	✅	❌

Note 1: the \(k\)-points in projwfc.out and atomic_proj.xml are in cartesian coordinates in units of alat, and there's no way to convert them without reading the header of filproj Note 2: It is necessary to know these if you want to obtain projections in the \((l, m_l, s_z)\) (or linear combinations thereof, e.g., \(p_x\) spin up orbitals) for calculations with SOC. Note 3: projwfc.out contains the quantum numbers (\((l, m)\) or \((l,m,s_z)\) or \((l, j, m_j)\)) of the atomic states in the header, so it's easy to extract them. It doesn't contain \(n\). They are spread throughout the file in filproj (which does contain \(n\), so you have to parse the entire file to extract them. They are absent from atomic_proj.xml, only a numerical index for the atomic state is present and must be matched against one of the other files. Note 4: You can extract only specific atomic states from atomic_proj.xml using an iterative XML parsing implementation. This can be a huge time save for large structures if you only care about certain orbitals (\(O(10)\) minutes vs seconds to parse). Note 5: For spin polarized calculations, you need filproj.projwfc_up and filproj.projwfc_down. However, projwfc.out in that case will include twice as many k-points, the first half of which is spin-up and the second half is spin-down, and it's not explicitly stated anywhere in the file that it's for a spin-polarized calculation (but you can tell because the Lowdin charges will mention spin up/down but the states won't have s_z) Note 6: filproj contains other information such as the number of valence electrons (useful), cutoffs and FFT grids (might be useful for working with Lowdin charges?).

Actual Data in the Files

Comparing the projection data in filproj and projwfc.out, they are quite similar but in general filproj is better since it has more precision. I noticed they more or less agree to within 5e-3 for non-spin polarized, LSDA (spin down only), noncolinear and SOC calculations. For the case of LSDA (spin up), there are some discrepancies but they are not that large. I don't understand why.

Another note from my code:

psi2 = float(band_dict["psi2"])
psi2_sum = np.sum(projections[:, k_i, band_i])
# The precision is so low in projwfc.out
# that they differ by 10-20%
if not np.isclose(psi2, psi2_sum, atol=1e-1):
     raise ValueError(
     "Sum of squared projections not "             "equal to |psi|^2 in projwfc.out "           f"file. {psi2} != {psi2_sum}"
     )

Note that the data in the XML is not symmetrized. Further, see this note about orthogonalization.