1. Numerical Convergence
In density-functional theory (DFT) simulations, numerical convergence refers to the stability of calculated quantities, such as total energy, forces, and band edges with respect to numerical parameters that control the calculation. These parameters include basis set size, real-space grid resolution, Brillouin-zone sampling density, and self-consistent field (SCF) tolerances. [MARTIN], [KRATZER2019]
Numerical convergence is essential regardless of the property of interest. Inadequate convergence can introduce systematic errors that mask real physical effects or lead to incorrect conclusions. For example:
Material trends: Apparent differences between materials may vanish when both are converged to the same accuracy. [LEJAEGHERE2016]
Parameter studies: Band gaps, defect formation energies, or adsorption energies may shift significantly with underconverged settings. [KRATZER2019]
Reproducibility: Published results must be reproducible by others using similar settings. [LEJAEGHERE2016]
For these reasons, convergence testing is a standard prerequisite for any production DFT calculation, whether computing basic structural properties, complex defect energetics, or spectroscopic observables.