3.1 A two-dimensional grid-convergence experiment
These are unexecuted teaching inputs and starting models. Original diagrams are schematics, not calculated results. Validate version-specific syntax, licensed or authorized data, numerical convergence and the scientific model before using this workflow.
3.1.1 Model, units and provenance
Keep basis/potential files and executable versions traceable. Grid controls use Ry; common energy/force outputs use hartree and hartree/bohr. Read the unit in each output heading.
Shared inputs, conventions and evidence
3.1.2 Unexecuted inputs and explicit deltas
Use the accompanying instructions to identify the parent calculation and placement of every delta; a snippet is not automatically a standalone input. Preserve all blank-line and file-provenance requirements.
3.1.2.1 Input block 1
3.1.3 Worked investigation
Intuition. CUTOFF sets the finest auxiliary grid; REL_CUTOFF influences how Gaussian products are assigned among grid levels. They solve related but distinct representation problems. A one-dimensional cutoff sweep with an inadequate relative cutoff can produce a misleading plateau. Use distorted water and a strained silicon cell, because a grid adequate for a smooth molecular energy may be inadequate for stress.
Original delta and design. Replace A or B's MGRID section using the template below. Test CUTOFF = 300, 400, 500, 700 Ry and REL_CUTOFF = 40, 60, 80 Ry. This is an experimental matrix, not a recommendation that 700/80 is universally converged. Hold NGRIDS=4, basis, geometry and EPS_SCF fixed.
See input block 1 above.
Workflow. 1. Define target tolerances on ΔE, maximum force component and, for a cell problem, pressure or stress. 2. Start with tight SCF so electronic noise does not dominate. 3. Run the matrix, extracting final energies, force arrays, stress if requested, grid information and timing. 4. Use the most stringent tested pair as a provisional reference, not mathematical truth. 5. At the selected economical pair, change one value beyond the original matrix to test whether the apparent plateau survives. 6. Repeat on a displaced geometry or representative liquid snapshot rather than validating only a high-symmetry structure.
Interpretation. Differences between adjacent columns measure one source of sensitivity; differences between rows measure another. Nonmonotonic variations can arise from discrete grid changes and assignment between levels. Plot error on a log scale only for nonzero absolute differences, and distinguish numerical zero from missing data. Convergence of total energy per atom does not guarantee convergence of stress, which involves differentiation with respect to strain. For reaction energies, evaluate the difference with the same grid policy on both sides, but do not use cancellation as an excuse to ignore large force noise.
Pitfalls and limits. CUTOFF is in Ry in this section, unlike a plane-wave code whose cutoff keyword may be expressed in eV. Its role also differs from the orbital plane-wave cutoff of a pure PW representation. A large box increases grid cost even for only three atoms. Harder potentials or contracted core regions can require different settings. A variable-cell trajectory continuously changes grid geometry, so it needs checks more stringent than one static snapshot.
Exercise. Choose a setting that passes a predeclared force tolerance, then test whether it also passes the pressure tolerance. If the choices differ, explain the additional scientific cost of using the force-only setting for NpT. Include a heatmap of measured errors with an explicit “not run” state.
Diagram. Original 4×3 parameter matrix, axes CUTOFF/Ry and REL_CUTOFF/Ry, with blank tiles reserved for measured error and a highlighted validation point outside the initial grid. EN labels: finest grid, assignment threshold, provisional reference, independent validation.