4.1 Bands from a converged charge density
These educational templates have not been executed and contain no fabricated numerical results. Inputs and filenames follow ABACUS 3.9.0 documentation; recheck every interface when changing version.
4.1.1 Question and declared model
What does silicon's Kohn-Sham dispersion look like along a declared reciprocal-space path, and what must be held fixed when computing it? Begin with the accepted first LCAO silicon calculation. A uniform SCF mesh establishes the ground-state density. A separate NSCF path samples eigenvalues in that fixed potential. The path is not a replacement for Brillouin-zone integration and its apparent gap is not automatically the fundamental gap.
4.1.2 Physical interpretation
The same self-consistent density defines a Hamiltonian for every sampled k point. With numerical atomic orbitals, solve a generalized eigenproblem involving the overlap matrix. Changing orbitals between SCF and NSCF changes the representation and undermines a controlled comparison.
The extrema in that expression extend over the full Brillouin zone. A chosen line can miss either extremum. Retain the two-atom primitive diamond cell and the parent's LDA-consistent pseudopotential/orbitals; this lesson does not silently switch it to PBE. The number of unoccupied bands controls the displayed conduction window but not a quasiparticle correction. A semilocal Kohn-Sham band gap should not be labelled an experimental optical gap.
Original course illustration; conceptual geometry and curves, not calculated results.
4.1.3 Worked input and file changes
# SCF: add this to the accepted parent INPUT and rerun if needed.
out_chg 1 10
# NSCF: replace matching parent keys in a separate directory.
suffix silicon_bands
calculation nscf
init_chg file
read_file_dir ../scf/OUT.silicon_lcao/
gamma_only 0
symmetry 0
nbands 8
out_band 1
out_proj_band 1
# Separate KPT: path coordinates tied to the parent's primitive cell.
K_POINTS
6
Line
0.5 0.0 0.5 20
0.0 0.0 0.0 20
0.5 0.5 0.5 20
0.5 0.25 0.75 20
0.375 0.375 0.75 20
0.0 0.0 0.0 1
This is a delta to the complete first LCAO silicon deck. Adjust read_file_dir to the actual accepted SCF directory and suffix; the path shown is an explicit example, not an assumed file location. Retain identical STRU, PP, orbital files, cutoff and functional. The reciprocal coordinates are fractions of the reciprocal vectors of that same primitive cell; changing lattice-vector order changes their Cartesian meaning. The six rows are vertices, not six uniformly weighted integration points. Each final integer specifies sampling to the next vertex, with 1 on the terminal row. Labels X-Gamma-L-W-K-Gamma follow the documented example convention; verify labels against your actual reciprocal cell before plotting.
4.1.4 Run and inspect the evidence
First confirm the SCF density converged before exporting it. Version 3.9 init_chg file checks charge-density.dat before falling back to SPIN1_CHG.cube, so do not leave a stale binary density in read_file_dir and assume the newer cube will win. Archive exactly which file was read. In the NSCF directory inspect OUT.silicon_bands/running_nscf.log for successful initialization and eigenvalue solution. Version 3.9 out_band produces BANDS_1.dat; out_proj_band produces XML-format PBAND_1. Read its orbital indices, species and angular labels rather than treating the first projection as a universal s channel. Build the horizontal axis from cumulative Cartesian reciprocal distance and mark each segment boundary. Reference energies to a declared SCF Fermi level or valence maximum and retain the unshifted eigenvalues.
4.1.5 Observable-specific convergence
Increase path density from 20 to 40 points per segment to check interpolation and extrema on the chosen lines. Independently tighten the SCF mesh and orbital quality; a denser plotting path cannot repair an inaccurate potential. Proposed teaching targets are less than 0.02 eV change in selected band energies and stable band ordering in the energy window of interest. For PW, the eigenvalue solver threshold also matters; do not copy pw_diag_thr into an LCAO accuracy argument because the documented LCAO solver ignores that PW control. If the gap is the target, search extrema on a dense uniform mesh or a validated local search, and report a path-only gap as such.
4.1.6 Acceptance worksheet and provenance
Prepare a band worksheet that identifies every plotted vertex in both fractional and Cartesian reciprocal coordinates. Compute each Cartesian reciprocal vector from the inverse-transpose lattice matrix with the declared 2 pi convention, then accumulate segment distances. Equal point counts do not imply equal physical segment lengths. A plot indexed only by row number can misrepresent slopes and relative widths.
Keep two energy arrays: raw eigenvalues and values shifted by a declared reference. For a valence-maximum plot, subtract the accepted reference value once from every band; do not independently reset each k point to its local valence edge, which destroys dispersion. If comparing two numerical setups, use the same reference policy and compare a common set of k coordinates. Record whether a reported gap comes from this path or from a separate Brillouin-zone search. Explicitly mark degeneracies where individual band indices can swap; compare the corresponding subspace rather than an arbitrary color label.
| Density parent / band test | Read density identity | Reference zero (eV) | Selected eigenvalue change (eV) |
|---|---|---|---|
| Accepted SCF, 20-point segments | — | — | — |
| Same SCF, 40-point segments | — | — | — |
| Tighter SCF mesh / improved orbitals | — | — | — |
Archive KPT and the exact BANDS_1.dat/PBAND_1 pair with each plot. The listed filenames apply to the versioned stable interface, not to every future release.
4.1.7 Pitfalls and limits
Do not recompute SCF on a line-mode mesh and call it a bulk ground state. gamma_only 1 can overwrite KPT and erase the intended path. Reusing a density with a different cell or valence count is invalid. VASP's ICHARG is not an ABACUS control. The beta's eig.txt naming must not be imposed on the stable example. Projection color is basis-dependent weight, not a directly measured probability of a chemical oxidation state.
4.1.8 Exercises with answer guidance
- Can doubling path density improve the SCF charge density? Guidance: no; NSCF fixes it. Converge the parent uniform mesh separately.
- You permute lattice vectors but retain the old Line coordinates. Is the same physical path guaranteed? Guidance: no; transform reciprocal coordinates or regenerate the path, checking Cartesian reciprocal positions.
4.1.9 Versioned references
The university-authored guide provides teaching context; older pages can predate 3.9. Use the linked official version for exact syntax. This is original instructional synthesis, and reference outputs are not presented as results of this course.