Bands and DOS: different sampling tasks
The inputs on this page are educational templates that have not been executed for this course. Use an authorized installation, verify version-specific options and establish your own convergence.
Establish density before eigenvalue analysis
An SCF finds density on an integration mesh. Bands evaluate selected path eigenstates at the fixed potential; DOS requires dense volume sampling. Neither bands.x nor dos.x performs a missing pw.x stage. Use independent branches, each with its own converged SCF and tmp directory:
04-bands: SCF -> pw.x calculation='bands' -> bands.x -> plot
05-dos: SCF -> pw.x calculation='nscf' -> dos.x -> plot
A short explicit silicon path
For the exact vectors in the first lesson, reciprocal vectors are \(\mathbf b_1=(-1,1,1)2\pi/a\), \(\mathbf b_2=(1,-1,1)2\pi/a\), \(\mathbf b_3=(1,1,-1)2\pi/a\). A fraction q gives \(\mathbf k=\sum_iq_i\mathbf b_i\). Our Γ–X–L–Γ takes X=(1/2,0,1/2), Cartesian \((0,1,0)2\pi/a\), and L=(1/2,1/2,1/2). It teaches path sampling, not all extrema or conventional fcc segments.
In 04-bands complete SCF, copy full input as si.bands.in, set calculation='bands', keep from_scratch, prefix='si' and outdir='./tmp/', add nbnd=8 for this four-valence nonmagnetic example, keep occupations='fixed', and replace the automatic card:
K_POINTS crystal_b
4
0.0000000000 0.0000000000 0.0000000000 30
0.5000000000 0.0000000000 0.5000000000 30
0.5000000000 0.5000000000 0.5000000000 30
0.0000000000 0.0000000000 0.0000000000 1
With crystal_b the fourth column controls segment interpolation, not integration weights. Consult release-specific endpoint counting and actual generated list. Standard path generators must use their returned standardized cell consistently; changing cell orientation/basis without transforming fractions changes actual k. Increase empty bands for the desired window.
Create si.bands.pp.in:
Run sequentially only after parent SCF succeeds. SCF/bands/NSCF distinction; bands.x reference.
Uniform-mesh DOS
In 05-dos run independent SCF, copy full input to si.nscf.in, set calculation='nscf', nbnd=12, occupations='tetrahedra', and use:
This is a trial mesh, not established convergence. Check k sampling and empty bands: finer plotted energy steps cannot recover missing states. Create si.dos.in:
With no degauss, this intends tetrahedron integration using saved NSCF data and an appropriate automatic uniform grid. DeltaE uses eV; Gaussian-workflow degauss uses Ry. Do not confuse units. dos.x reference.
Plot reference and exercise
Declare an energy zero. For an insulator a justified valence maximum can be clearer than a Fermi energy placed within the gap. A short path can miss global maxima/minima; align compatible bands/DOS references before overlay. Semilocal Kohn–Sham gaps are not automatically optical/quasiparticle gaps; convergence does not remove functional error.
Explain why even dense Γ–X sampling cannot give total DOS. Repeat a denser uniform mesh, separate stable features from artifacts and convert X using the stated basis. Save data/plot scripts, reciprocal basis, reference and normalization. Further reading: Materials Cloud silicon workshop; QE input generator.
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