4.2 DOS and orbital projections
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.
4.2.1 Question and declared model
How can you distinguish a genuine concentration of states from a peak created by insufficient sampling or arbitrary broadening? Compute silicon DOS from the same accepted LCAO ground state used for bands, but use a dense uniform integration mesh rather than a symmetry path. Resolve orbital contributions without pretending that a chosen local basis is a unique decomposition of chemical bonding.
4.2.2 Physical interpretation
DOS weights each eigenvalue by its Brillouin-zone sampling weight and a representation of the delta function. The nonmagnetic spin degeneracy must be included consistently; in the documented nspin 1 treatment it is already part of the state weighting. Numerical broadening trades visual smoothness against energy resolution.
Projected DOS introduces local-orbital weights and therefore depends on the orbital definition and overlap treatment. Sum all zeta functions belonging to a desired atom and angular channel; a double-zeta basis has more than one radial function for a given angular momentum. Retain the parent's LDA-consistent Si pseudopotential and numerical orbitals. An apparent band-edge tail can be broadening rather than metallicity, and a narrow high peak can be a k-point artifact.
Original course illustration; conceptual geometry and curves, not calculated results.
4.2.3 Worked input and file changes
# Delta to first-lcao-silicon; density exported with out_chg 1 10.
suffix silicon_dos
calculation nscf
init_chg file
read_file_dir ../scf/OUT.silicon_lcao/
gamma_only 0
nbands 12
out_dos 2
dos_sigma 0.05
dos_edelta_ev 0.01
# Separate KPT: first trial, then increase dimensions.
K_POINTS
0
Gamma
8 8 8 0 0 0
This delta inherits complete STRU, PP, orbital paths, basis and accepted cutoff from first LCAO silicon. Point read_file_dir to the actual converged density; the displayed directory name is illustrative. All physical files remain identical. The version 3.9 keyword list explicitly assigns out_dos 2 to LCAO DOS plus PDOS; this value is not portable to the latest beta, which changes that interface. dos_sigma is in eV, whereas occupation smearing_sigma is in Ry: they serve different purposes and must not be equated numerically. The 8 by 8 by 8 grid and 0.05 eV width are first trials only. Twelve bands are a proposed window, and need expansion if the desired high-energy DOS reaches the highest computed band.
4.2.4 Run and inspect the evidence
Verify the density-file precedence described in the bands lesson before launching NSCF. Inspect OUT.silicon_dos/running_nscf.log, then DOS1_smearing.dat and the XML-style PDOS file documented for 3.9. DOS1_smearing.dat lists energy, DOS and a cumulative quantity; inspect the exact file header before treating the third column as a normalized electron number. Reconstruct an integral from the DOS values and energy spacing as an independent check. Read the PDOS orbital entries for atom_index, species, l, m and z, grouping only matching channels. Plot total DOS together with summed Si s and p contributions, stating units of states per eV per unit cell and the chosen energy zero. Preserve the raw energy grid and all projection channels even if the first teaching figure shows only a few.
4.2.5 Observable-specific convergence
Use a two-dimensional convergence matrix: meshes 8, 10 and 12 in every reciprocal direction, crossed with broadening widths 0.10, 0.05 and 0.025 eV. Smaller width needs denser sampling. Compare the integrated state count, band-edge location and a declared peak window; do not require pointwise identity of sharp spectra. A suggested target is band-edge stability within 0.02 eV and stable integrated weight within 1 percent in a preselected window. Check the density parent and orbital quality independently. The finite-band DOS integral over the complete energy window counts computed states, while the occupied integral uses occupations or an explicitly justified zero-temperature limit; do not confuse those two totals.
4.2.6 Acceptance worksheet and provenance
Build a worksheet for mesh size, DOS width, energy spacing, band count and energy-reference policy. Integrate a selected energy window using the actual energy grid, not an assumed spacing copied from INPUT. For nonuniform extracted data use an integration rule that accounts for each interval. Keep the window fixed in physical energy relative to the same reference when comparing widths; moving its limits to follow a peak changes the question.
Read every PDOS orbital tag before grouping. Sum all atoms and radial functions belonging to the selected species/angular channel and retain spin columns separately when present. Compare a grouped integral with the same group reconstructed by explicit orbital indices as a parser sanity check. A missing channel or duplicated atom often produces a visually plausible plot but the wrong integrated weight. For the total finite-band spectrum check the expected number of computed states over a sufficiently complete energy window; for occupied electrons apply the actual occupations or a stated zero-temperature approximation.
| Mesh / sigma (eV) / spacing (eV) | Window integral (states/cell) | Edge position (eV) | Projection grouping checked? |
|---|---|---|---|
| 8 cubed / 0.10 | — | — | — |
| 10 cubed / 0.05 | — | — | — |
| 12 cubed / 0.025 | — | — | — |
The rows are starting comparisons, not accepted settings. Add crossed combinations to distinguish mesh effects from broadening effects, and preserve raw PDOS along with the grouping definition.
4.2.7 Pitfalls and limits
A line path has no appropriate volume weights for a bulk DOS. A broadening-generated tail is not proof of a closed gap. Increasing dos_edelta_ev resolution cannot fix coarse k sampling. Summing only the first zeta omits part of a numerical-orbital channel. Spin-down DOS is sometimes plotted negative for readability; that visual sign must not enter state-count integrals. For PW do not request this LCAO projection route without a separately verified projection method.
4.2.8 Exercises with answer guidance
- Halving dos_sigma makes noisy spikes appear. Should you smooth them manually? Guidance: first densify the k mesh and compare integrals; cosmetic filtering is not a convergence test.
- Does the occupied DOS integral equal the integral over all twelve bands? Guidance: no; the latter includes unoccupied states. Include spin weights and occupations explicitly.
4.2.9 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.