I have a unit cell consisting of 8 atoms of CO with their position in cartesian coordinate and given lattice vector. How can i translate it into a supercell mathematically.
You need to assign a orbital index to each atom belonging to your super-cell and a super cell index.
Let's say you label your atoms within your super-cell from 0 to 8 with positions r_0 to r_8. For simplicity, lets put the atom 0 at the origin so that r_0 = {0,0,0}. Then you need to translate your unit cell and construct a larger one, lets call this translational vectors a_0, a_1 and a_2. The position for any atom in your lattice will be given by
r( io, i0, i1) = r_{io} + i0*a_0+ i1*a_1
where i0 and i1 are the unit cell indexes and io is the inner orbital index.