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# Cd Si volume relaxation

## Contents

Relaxation of the internal coordinates, volume and cell shape in cd Si.

## Input

### POSCAR

```cubic diamond
5.5
0.0    0.5     0.5
0.5    0.0     0.5
0.5    0.5     0.0
2
Direct
-0.125 -0.125 -0.125
0.125  0.125  0.125
```

### INCAR

```System = diamond Si
ISMEAR = 0; SIGMA = 0.1;
ENMAX  =  240
IBRION = 2; ISIF=3 ; NSW=15
EDIFF  = 0.1E-04
EDIFFG = -0.01
```
• ISIF=3 change of internal parameter, shape and volume simultaneously.

### KPOINTS

```k-points
0
Monkhorst Pack
11 11 11
0  0  0
```

## Calculation

• To determine the equilibrium volume we can:
• Fit the energz over a certain volume range to an equation of state (see cd_Si).
• Alternatively we relax the structure with VASP "on the fly" (IBRION=2 and ISIF=3)
• From equation of states we determine lattice parameter of ${\displaystyle a=5.4687}$ Å (volume scan plus Murnaghan EOS using ENMAX=400).
• From relaxations using IBRION=2 and ISIF=3 we get ${\displaystyle a=5.4684}$ Å.
• Difference can be due to pulay stress (especially when the relaxation starts far away from equilibrium):
```-------------------------------------------------------------------------------------
Total       0.00155     0.00155     0.00155    -0.00000     -0.00000      0.00000
in kB       0.06056     0.06056     0.06056    -0.00000     -0.00000      0.00000
external pressure =        0.06 kB  Pullay stress =          0.00 kB

VOLUME and BASIS-vectors are now :
-----------------------------------------------------------------------------
energy-cutoff :      400.00
volume of cell :      40.88
direct lattice vectors                 reciprocal lattice vectors
0.000000000  2.734185321  2.734185321    -0.182869828  0.182869828  0.182869828
2.734185321  0.000000000  2.734185321     0.182869828 -0.182869828  0.182869828
2.734185321  2.734185321  0.000000000     0.182869828  0.182869828 -0.182869828
```

• To remedy this increase the plane wave cutoff by at least 30% (here we used ENMAX=400 instead of 240) and use a small EDIFF.

### Summary

• Calculation of the equilibrium volume:
• FIt the energy over a certain volume range to an equation of state.
• When internal degrees of freedom exist (e.g. c/a), the structure must be optimized. Use a conjugate-gradient algorithm (IBRION=2) and at each volume do e.g. 10 ionic steps (NSW=10) and allow change of internal parameters and shape (ISIF=4).
• Simpler but less reliable: relaxing all degrees of freedom including volume.
• To relax all degrees of freedom use ISIF=3 (internal coordinates, shape and volume).
• Mind pulay stress problem. Increase plane wave cutoff by 25-30% when the volume is allowed to change.