Solution LAB1 diamond lattice parameter

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Lattice parameter of diamond

Given the convergence study of the total energy as a function of the k-point grid (as done in previous exercises), here we set the k-grid to a converged value, say


and perform a series of total energy calculations at different lattice parameters, for several values of the kinetic energy cutoff.

Here we consider the following values:

 ecutwfc_list="20 30 40 50 60 80 100 120 140 160"
 for cutwfc in $ecutwfc_list
    # run scf calculations for multiple alat values

For each cutoff, Etot vs alat is fit (eg using a python script provided) and the minimum is extracted.

For instance, once data are extracted and cast in the form:

 $> cat results_50Ry.dat
 # calculations using ecutwfc=50 Ry
 # alat [bohr]    etot [Ry]
 6.5388      -22.75492438
 6.6062      -22.75814079
 6.6736      -22.75965543
 6.7410      -22.75832711
 6.8084      -22.75526586
 6.8758      -22.75029450
 6.9432      -22.74340707

The script


can be used to extract the position of the minimum of the curve as well as to plot the behaviour of etot vs alat, e.g.:

 ./  results_50Ry.dat

The scripts developed in previous exercises can be used to run multiple calculations and to extract the data.

Results as a function of the cutoff

At first, it is important to inspect the behaviour of the total energy as a function of the lattice parameter.

Some plots for ecutwfc = 20, 30, 40 Ry and ecutwfc=50, 60, 80 Ry are reported below:

Ecutwfc=20 Ry Ecutwfc=30 Ry Ecutwfc=40 Ry

Ecutwfc=50 Ry Ecutwfc=60 Ry Ecutwfc=80 Ry

In the following you can find the fitted lattice parameter as a function of the kinetic energy cutoff used in the calculations.

 # Ecut     alat
   20      6.8354274
   30      6.686406
   40      6.727857
   50      6.6744762
   60      6.6694212
   80      6.664164
  100      6.6647706
  120      6.6639618
  140      6.6639618
  160      6.6639618

A decent convergence can be already obtained using values of the kinetic energy cutoff as low as 60-80 Ry.