“ SUPERCELLS ”

1. “SUPERCELLS” • So far we have seen only 3-D crystalline systems. Nature is more complex than this. • 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

2. “SUPERCELLS” • Examples: • Defects: • How to construct the supercell: • Begin by replicating the crystal unit cell a sufficiently large number times in all 3 directions • Introduce the defect (e.g., for a vacancy, remove one atom) • 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: • Begin by replicating the crystal unit cell a sufficiently large number times in the direction perp. to the surface. • Add vacuum spacing (create a “slab”) • Check convergence with respect to vacuum size and slab thickness • NB: surface formation energy calculated wrt bulk with same supercell • NEED TO RELAX!