The Cohesive energy of a silicon

The simplest formation energy is that of silicon.

To do this first, we need to calculate the energy of the unit cell of silicon and an isolated silicon. The calculation below is carried out in vasp and details are given at the bottom of the page.

The basic calculation

$E_{C}={\frac {1}{N}}(E_{B}-2E_{I})$

The bulk unit cell below gives a total energy of -.10842998E+02 (or -10.84 eV) (grep for 'energy w')

The isolated cell below gives

The silicon bulk unit cell

si bulk
1.0
2.715 2.715 0.0
2.715 0.0 2.715
0.0 2.715 2.715
Si
2
Direct
0.0 0.0 0.0
0.25 0.25 0.25

The isolated silicon unit cell

iso
1.0
12.0 0.0 0.0
0.0 12.0 0.0
0.0 0.0 12.0
Si
1
Direct
0.5 0.5 0.5

Key VASP calculation details

The above calculations are run with - the PBE functional - a 9 x 9 x 9 k-point grid (Gamma only for the isolated) - a 600 eV cut off - the POTPAW Potential - zval=4, PAW_PBE Si 05Jan2001 - ISYM=0