How to calculate the Total DOS of Silicon with Elk alone

Silicon's total density of states, computed with Elk alone -- a type 1, independent calculation with the QELK suite (no Quantum ESPRESSO involved here; for the direct Elk-vs-QE overlay, see the Si_tdos_elk_vs_qe example).

 

The input file

 

We need only the input file

Si_tdos_elk.qelk

version 1

cell bohr
  -5.1   0.0   5.1
   0.0   5.1   5.1
  -5.1   5.1   0.0
end

atoms crystal
  Si  0.00  0.00  0.00
  Si  0.25  0.25  0.25
end

species Si
  elk_file   Si.in
  qe_pseudo  Si.pz-vbc.UPF
  qe_mass    28.086
end

step dos elk
  from initial
  task    0 10
  rgkmax  7.0
  ngridk  8 8 8
  xctype  2
end

Note: task 0 10 is a LIST, both in the SAME step -- not two separate steps. Elk's task 10 (DOS) does not run its own SCF; it reads a converged STATE.OUT written by a prior task 0 in the same Elk invocation. Since qelk gives every step its own clean directory, splitting these into two qelk steps would leave task 10 with no density to read -- the same reasoning as the band-structure example. xctype 2 (LDA) matches Si.pz-vbc.UPF's functional.

 

Calculation

 

algerien1970@linux-ml0a:~/abinitio/QELK/examples/Si_dos_elk> qelk Si_dos_elk.qelk

Elk runs task 0 then task 10 in one invocation. From dos.elk.stdout:

Info(elk): current task :      0
Info(checkmt): reduced muffin-tin radius of species   1 (Si) from   2.2000 to   2.1834

Info(elk): current task :     10

Info(writedos):
 Total density of states written to TDOS.OUT
 ...
 Fermi energy is at zero in plot
 DOS units are states/Hartree/unit cell

Every step's files land in run/NN_<step>/, and the important ones are also copied next to the .qelk file, prefixed with the step id: dos.TDOS.OUT, dos.INFO.OUT, dos.TOTENERGY.OUT, dos.elk.stdout.

 

SCF result

 

grep -A1 "Convergence targets achieved" dos.INFO.OUT
grep " total energy" dos.INFO.OUT | tail -1
grep " Fermi " dos.INFO.OUT | tail -1
grep "Estimated" dos.INFO.OUT | tail -2

Convergence targets achieved

 total energy                :     -578.076938663     (Hartree)
 Fermi                       :     0.213191193976     (Hartree)
 Estimated indirect band gap :   0.1806684094E-01     (from k-point 1 to k-point 18)
 Estimated direct band gap   :   0.9362392480E-01     (at k-point 1)

Converged in 19 SCF iterations on the 8x8x8 mesh (29 irreducible k-points after symmetry reduction), matching the exact ground state Si_band_elk and Si_band_dos_elk already established for this cell.

 

Plot

 

plot_elk_dos.py dos.TDOS.OUT -o elk_dos.png

Note: Elk writes TDOS.OUT energies already relative to the Fermi level, so 0 eV on the plot below IS the Fermi level -- don't pass --efermi here, exactly the same caveat as Si_band_elk.

 

Analysis

 

Reading dos.TDOS.OUT directly (500 points, energies converted Hartree -> eV, DOS in states/eV):

Window        : -13.61 eV to +13.55 eV -- Elk's own default DOS window
                (roughly +-13.6 eV around E_Fermi), the same default
                the Si_band_dos_elk tutorial's TDOS.OUT already showed.

Gap           : DOS is essentially zero from about -0.11 to +0.16 eV
                around E_Fermi, with a faint thermal tail extending a
                little further either side -- expected, since this run
                uses Fermi-Dirac smearing (width 0.001 Hartree, an
                effective electronic temperature of ~316 K), not a
                hard cutoff.

Valence peaks : -9.96 eV (0.93 states/eV) -- the single, narrow 3s-
                derived bonding band Si_band_elk found flat and
                isolated along L-G-X-W-G.
                -6.91, -4.30, -3.97, -2.99, -2.29, -1.69 eV (1.1-1.7
                states/eV) -- the p-derived valence manifold, matching
                the -7 to 0 eV range Si_band_elk's band structure
                already mapped out; DOS shows more structure here than
                that single band-path cut did, because it sums the
                heavy-hole/light-hole splitting over the WHOLE
                Brillouin zone, not just one path through it.

Conduction    : 2.07, 2.29, 3.37 eV (2.20, 2.37, 2.90 states/eV) -- the
peaks           tallest feature in the whole curve, then 5.12, 7.02,
                9.69-10.99, 13.06 eV (1.5-1.75 states/eV) further up,
                broadening as expected for increasingly free-electron-
                like conduction states away from the gap.

Note: the gap this DOS shows (roughly a few tenths of an eV wide on the raw grid) lines up with Elk's own internal estimate from this same SCF run -- indirect band gap 0.01806684 Hartree = 0.4916 eV -- MUCH closer to the usual quoted LDA silicon gap (0.5-0.6 eV) than the ~2.3 eV read directly off Si_band_elk's plot. The difference is entirely down to sampling: Si_band_elk's estimate came from a band structure plotted along a handful of high-symmetry lines, which can miss the true conduction-band minimum sitting off those lines; Elk's own gap estimator here scans every eigenvalue at all 29 irreducible k-points of the SCF mesh and finds the true minimum (k-point 1 to k-point 18), which is exactly the kind of check the band-structure tutorial's own notes flagged as needed. The direct gap at k-point 1 is 0.09362 Hartree = 2.548 eV -- k-point 1 is the zone-centre G point for this zero-offset mesh.

Note: sanity check: integrating dos.TDOS.OUT up to E_Fermi (0 eV) gives exactly 8.000 states per cell -- 2 Si atoms x 4 valence electrons (3s²3p²), confirming the DOS is internally consistent with the valence electron count Si_band_elk already verified band-by-band. The DOS AT E_Fermi itself is 0.00404 states/Hartree/cell (about 1.5x10^-4 states/eV) -- vanishingly small, as expected for a semiconductor, and nonzero only because of the finite-temperature smearing rather than any real states in the gap.

This is the DOS counterpart of Si_band_elk: same cell, same functional, same converged ground state (-578.077 Hartree total energy, E_Fermi = 5.801 eV) -- just integrated over the whole Brillouin zone instead of sampled along one path, which is why the same bonding/valence/gap story shows up in both, in slightly different clothing, and why this run's own internal gap estimate is the more trustworthy one of the two.