1.2 A convergence laboratory with an error budget

These are unexecuted teaching inputs and starting settings to test. Original figures are schematics, not computed results. Use licensed VASP and PAW data, replace every placeholder, record the executable version and validate convergence.

1.2.1 Model, units and provenance

Use eV for energy, Å for length and eV/Å for force; 1 kbar = 0.1 GPa. State normalization per atom, molecule, primitive cell or simulation cell. Record PAW identifiers, release, ZVAL, ENMAX and permitted hashes; never redistribute POTCAR. SCF convergence addresses the chosen electronic problem; convergence of the target property requires separate tests.

A convergence laboratory with an error budget — original conceptual schematic

Original schematic. Curves explain concepts; blank data areas await verified learner results. No calculation is claimed.

1.2.2 Worked case: procedure, interpretation and checks

Goal and intuition

Convergence is not a badge attached to an INCAR file. It is evidence that a specified observable changes little when a relevant numerical approximation is improved. An adsorption energy, a magnetic-state splitting, a vibrational frequency and a pressure can demand different settings. This laboratory turns “I used a large cutoff” into a defensible statement with a target, a test and an uncertainty estimate.

Choose two systems already understood: H₂ in vacuum and bulk Si or Al. Select one energy difference and one derivative quantity such as a force or stress component. Define a teaching target before running, for example a chosen meV-scale tolerance per molecule or per atom and a separately specified force tolerance. These are project decisions, not universal accuracy standards.

Workflow

Freeze the model. Keep geometry, functional, potential identities, charge and spin treatment fixed during a numerical sweep.

Original input-control sheet

Suggested record fields

Interpreting an error budget

Let Q be the chosen observable. Plot ΔQ relative to the finest tested result, but call that point a reference calculation, not the exact limit. Use successive refinements to detect a plateau, then challenge it with one independent refinement. If the target is an energy difference, calculate every member of the energy cycle consistently at each accuracy level. Testing only one term does not establish the difference's error.

Do not mix numerical and model errors. A converged PBE calculation can still have a functional error, and a well-converged small slab can still model the wrong coverage. Runtime is part of the laboratory: identify a reasonable cost–accuracy compromise after accuracy is demonstrated. Report the approximation you accepted and the evidence, rather than saying “all parameters fully converged” without a tolerance.

Beginner traps

Changing a cell while retaining fractional molecular coordinates may stretch the molecule. Raising PREC does not replace an ENCUT test. Lowering EDIFF does not repair an unconverged k integral. Checking only energy may miss force noise. Comparing inconsistent smearing conventions can imitate a convergence trend. A plot with only two points can show a small accidental difference. A fixed “500 eV for everything” rule is not a convergence argument, especially after adding a harder species or changing the PAW variant.

Exercise and original figure

Deliver an acceptance statement in this format: “For observable Q, within models A and B, these settings changed Q by less than the chosen tolerance under tests X and Y; model limitations Z remain.” Include a matrix showing which settings were changed and which held fixed. The statement must not imply a guarantee outside the tested model family.

1.2.3 Unexecuted inputs and analysis scaffolds

These are unexecuted teaching inputs and starting settings to test. Original figures are schematics, not computed results. Use licensed VASP and PAW data, replace every placeholder, record the executable version and validate convergence.

1.2.3.1 Input block 1

# These are separate experiments, not simultaneous magic settings.
# Experiment A: explicit ENCUT values derived from the licensed POTCAR ENMAX
ENCUT = <TEST_VALUE_EV>
PREC = Accurate
LREAL = .FALSE.
EDIFF = 1E-7

# Experiment B: hold those values fixed and change only KPOINTS for bulk.
# Experiment C: for a molecule change only cell size, recenter coordinates,
#               and preserve the same molecular geometry in Angstrom.

1.2.3.2 Input block 2

run_id, model_id, vasp_version, potential_ids, cutoff_eV,
kmesh, centering, cell_A, EDIFF_eV, energy_label,
observable_value, observable_unit, max_force_eV_A,
stress_kbar, scf_valid, walltime_s, notes