Defect Calculation¶

Calculating the formation energy of a point defect (e.g., vacancy, interstitial).

Workflow¶

1. Perfect Crystal: Calculate the energy of the perfect supercell (\(E_{perf}\)).
2. Defect Supercell: Create a supercell with the defect (remove/add atom).
3. Relaxation: Relax the geometry of the defect supercell using DFT.
4. QMC: Calculate the energy of the relaxed defect supercell (\(E_{def}\)).
5. Formation Energy: $$ E_f = E_{def} - E_{perf} \pm \mu $$ where \(\mu\) is the chemical potential of the removed/added species.

Finite-Size Corrections¶

Defect calculations in QMC are subject to significant finite-size errors (image interactions). Corrections (e.g., Makov-Payne) are often necessary.