Lattice constant, DOS, and band structure of Si

Lattice constant of Si

For bulk materials it is a common task in DFT calculations, given an atomic structure, to find the equilibrium volume of the unit cell. Here we study Silicon which has diamond lattice structure shown in the Figure below:

Diamond cubic crystal structure of silicon.

To determine the equilibrium volume and thereby the lattice constant $a$, a series of calculations is made where $a$ is swept over a range around some initial guess (below we start from Failed to parse (syntax error): {\displaystyle a = 5.43 \text{\AA} } and sweep the lattice parameter �5% in five steps).