Transcript Document

“SUPERCELLS”
So far we have seen only 3-D crystalline systems. Nature is more complex
than this.
A)Non-periodic systems (e.g. defects, amorphous solids, liquids, etc)
Problem: how can we simulate them with a finite number of atoms?
Solution(s): i) Clusters ✖; ii) Periodic boundary conditions ✔
B) Periodic, but not 3-D (e.g. 0-D (molecules, nanostructures), 1-D
(quantum wires), 2-D (surfaces, graphene)
Problem: plane wave basis set is periodic in 3D
Solution: Add fictitious periodicity in non-periodic directions
The supercell is an artificially constructed, large, periodically repeated,
simulation cell, that allows the simulation of non-3D-periodic systems.
Special care has to be paid to the choice of the supercell lattice parameters
“SUPERCELLS”
Examples:
Defects:
How to construct the supercell:
a)Begin by replicating the crystal unit cell a sufficiently large number times
in all 3 directions
b)Introduce the defect (e.g., for a vacancy, remove one atom)
c)Check convergence of properties with size of supercell by increasing its
size (number of repeat units)
NB1: charged defects may be a challenge
NB2: defect formation energy calculated wrt bulk with same supercell
Surface:
a)Begin by replicating the crystal unit cell a sufficiently large number times
in the direction perp. to the surface.
b)Add vacuum spacing (create a “slab”)
c)Check convergence with respect to vacuum size and slab thickness
NB: surface formation energy calculated wrt bulk with same supercell
NEED TO RELAX!