EXAMPLE · E5

fcc Al metal

A smearing SCF on metallic fcc Al: the Fermi level, and measured evidence for choosing degauss.

Goal

Your first metal. See why occupations='smearing' is required, where the Fermi level shows up, and measure how the smearing type and degauss change the energy.

New cards and variables

Item Role
occupations='smearing' Partial occupations for a metal
smearing='mv' Marzari-Vanderbilt (cold): the metal default
degauss Smearing width (Ry)
nbnd=8 A generous band count

Input file

Download al.scf.in

! E05: fcc aluminium, the first metal.
! A metal has no gap, so occupations must be smeared around the Fermi level.

&CONTROL
  calculation = 'scf'
  prefix      = 'al'
  outdir      = './tmp/'
  pseudo_dir  = './pseudo/'
  verbosity   = 'high'
/
&SYSTEM
  ibrav       = 2           ! fcc
  celldm(1)   = 7.65        ! bohr (= 4.05 Angstrom, experimental)
  nat         = 1
  ntyp        = 1
  ecutwfc     = 40
  ecutrho     = 320         ! 8x rule
  occupations = 'smearing'  ! mandatory for a metal ('fixed' would abort)
  smearing    = 'mv'        ! Marzari-Vanderbilt cold smearing: free energy ~ E(sigma->0),
                            ! so no extrapolation in degauss is needed
  degauss     = 0.02        ! smearing width in Ry; converge it together with the k-grid
  nbnd        = 8           ! more bands than the default: partial occupations need headroom
/
&ELECTRONS
  conv_thr    = 1.0d-8
  mixing_beta = 0.7         ! simple sp metal: aggressive mixing still works
/

ATOMIC_SPECIES
  Al  26.9815  Al.pbe-n-kjpaw_psl.1.0.0.UPF

ATOMIC_POSITIONS (alat)
  Al  0.00  0.00  0.00

! metals need dense grids to resolve the Fermi surface;
! 12x12x12 here vs the 8x8x8 that sufficed for the Si insulator
K_POINTS (automatic)
  12 12 12  0 0 0

Run

mpirun -np 6 pw.x -nk 6 -in al.scf.in > al.scf.out

What to check

Item Measured (QE 7.5, PAW)
Total energy −39.50323368 Ry
Fermi level the Fermi energy is 7.7450 ev: printed only for metals
smearing contrib. (-TS) The size of the smearing contamination

Where the insulator (E1) printed highest occupied level, the metal prints the Fermi energy is. This line tells you the run converged to a metal; E10 uses it to catch a wrong metallic result.

The degauss scan by smearing type

The same system, scanned over smearing types (gaussian/mv/fd) and degauss (0.005 to 0.05 Ry):

Al total energy vs degauss for three smearing types
Measured fcc Al (QE 7.5, 12×12×12 k). Cold smearing (mv) moves by only 0.3 mRy from 0.01 to 0.05 Ry, while gaussian drifts 3 mRy and Fermi-Dirac 22 mRy. This is why mv needs no extrapolation in practice.

One run in my scan failed: mv at degauss=0.005 on the 12³ grid integrated the charge to 3.003 instead of 3 and stopped with charge is wrong. Narrower smearing demands denser k-grids, so degauss and the k-grid have to be converged together (Chapter 06).

Exercises

  1. Sweep the k-grid from 8³ to 16³ and watch the energy scatter per degauss. Smaller degauss should demand denser grids.
  2. Remove nbnd and find in the output how many bands QE picks by itself.
  3. Set occupations='fixed' and check that you get the error message listed in R3.
Common mistakes

Leaving degauss large because "it converges so nicely". A large smearing contrib. (-TS) means your result sits far from the σ→0 limit. Always check that the property you care about is insensitive to degauss. In magnetic metals an oversized degauss erases the moment (E9).

06 Occupations and smearing · 05 Cutoff and k-point convergence