Aluminum in the fcc structure

In this tutorial how to perform the total energy calculation of a metallic system is described by taking Al as an example. We use von Barth-Car normconserving pseudopotential as distributed in the Quantum-ESPRESSO web page.

Optimizing the cell parameter

In this example, the cell is optimized by using 'vc-relax.' Cutoff energy of 30 Ry and nonshifted 12 x 12 x 12 are used. In the metallic systems, the smearing technique is used with the keywords "occupation='smearing'", "smearing", and "degauss" with the number of bands ("nbnd") slightly larger than the half of the number of bands to accomodate partially unoccupied bands. How to determine the parameters for the smearing technique is discussed below.

&control
 calculation  = 'vc-relax'
 restart_mode = 'from_scratch',
 pseudo_dir   =  '/home/ikutaro/QE/pseudo/'
 outdir       = './tmp'
 prefix       = 'al'
 tprnfor      = .true.
 tstress      = .true.
/
&system
 ibrav       = 2
 A           = 4.020
 nat         = 1
 ntyp        = 1
 ecutwfc     = 30.0
 ecutrho     = 120.0
 occupations = 'smearing'
 smearing    = 'mp'
 degauss     = 0.01
 nbnd        = 12
/
&electrons
 diagonalization = 'cg'
 conv_thr        = 1.0e-12
 mixing_beta     = 0.5
/
&ions
 ion_dynamics='bfgs'
/
&cell
 cell_dynamics='bfgs'
/
ATOMIC_SPECIES
 Al 0.0000 Al.pz-vbc.UPF
ATOMIC_POSITIONS (crystal)
Al      0.000000000000      0.000000000000      0.00000000000
K_POINTS (automatic)
16 16 16 0 0 0

Determining the smearing width

Now let us examine the smearing function and width. We use the Fermi-Dirac (smearing='fd'), Gaussian (smearing='gaussian'), Methfessel-Paxton (smearing='mp'), and Marzari-Vanderbilt (smearing='mv') and vary smearing width (degauss) from 0.05 to 0.10. An example input is the following. Only difference from the previous one is "calculation='scf'"

&control
 calculation  = 'scf'
 restart_mode = 'from_scratch',
 pseudo_dir   =  '/home/ikutaro/QE/pseudo/'
 outdir       = './tmp'
 prefix       = 'al'
 tprnfor      = .true.
 tstress      = .true.
/
&system
 ibrav       = 2
 A           = 4.020
 nat         = 1
 ntyp        = 1
 ecutwfc     = 30.0
 ecutrho     = 120.0
 occupations = 'smearing'
 smearing    = 'mp'
 degauss     = 0.01
 nbnd        = 12
/
&electrons
 diagonalization = 'cg'
 conv_thr        = 1.0e-12
 mixing_beta     = 0.5
/
&ions
 ion_dynamics='bfgs'
/
&cell
 cell_dynamics='bfgs'
/
ATOMIC_SPECIES
 Al 0.0000 Al.pz-vbc.UPF
ATOMIC_POSITIONS (crystal)
Al      0.000000000000      0.000000000000      0.00000000000
K_POINTS (automatic)
16 16 16 0 0 0

The results for the Fermi-Dirac and Methfessel-Paxton are shown below. (Fermi-Dirac)

#smearing width (Ry) total energy (Ry)
0.005 -4.19003452
0.010 -4.19061414
0.015 -4.19165619
0.020 -4.19317708
0.030 -4.19764208
0.040 -4.20395723
0.050 -4.21209681
0.060 -4.22205685
0.070 -4.23383710
0.080 -4.24743412
0.090 -4.26283926
0.100 -4.28003855

(Methfessel-Paxton)

#smearing width (Ry) total energy (Ry)
0.005 -4.18988203
0.010 -4.18986582
0.015 -4.18984568
0.020 -4.18982833
0.030 -4.18978271
0.040 -4.18971203
0.050 -4.18962976
0.060 -4.18956040
0.070 -4.18951623
0.080 -4.18949432
0.090 -4.18948574
0.100 -4.18948238
ftot_Al_smearing.png

We can see that with the Fermi-Dirac function, total energy descrease significantly as the smearing width increases, while with the Methfessel-Paxton scheme, the change is insignificant, and therefore it is possible to use relatively large smearing width with the MP scheme. Note that the smearing width is to treat the Fermi surface efficiently and it is desirable to use small smearing width. Alternatively, one can use the tetrahedron method for the Brillouin zone integration without smearing. In this case the number of k-points tends to be large.

Exercise

  • Perform the convergence study on the smearing width by changing the number of k-points.
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Last-modified: 2019-11-28 (木) 12:11:23 (12d)