4.2 Cell optimization and an independent equation of state
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.
4.2.1 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
4.2.2 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.
4.2.2.1 Input block 1
&MOTION
&CELL_OPT
TYPE DIRECT_CELL_OPT
OPTIMIZER BFGS
MAX_ITER 150
EXTERNAL_PRESSURE [bar] 0.0
PRESSURE_TOLERANCE [bar] 50.0
KEEP_SYMMETRY T
MAX_FORCE 1.0E-4
&END CELL_OPT
&END MOTION
4.2.3 Worked investigation
Intuition. Atomic relaxation minimizes internal coordinates; cell relaxation also asks how energy changes under strain. A stress-sensitive problem needs more demanding grid and k-point checks. Use B with converged k sampling, analytical stress for a supported method, and the cubic symmetry deliberately retained. A zero-temperature optimized cell is not a room-temperature experimental cell.
Input delta. Set GLOBAL/RUN_TYPE CELL_OPT, add STRESS_TENSOR ANALYTICAL under FORCE_EVAL, and set SYMMETRY CUBIC in SUBSYS/CELL. Add:
See input block 1 above.
The 50 bar threshold is an example chosen for an experiment, not evidence that the discretized stress is accurate to 50 bar. Explicitly setting external pressure avoids inheriting an unnoticed default.
Workflow. 1. Run a stress-converged static calculation before allowing the cell to move. 2. Optimize while recording volume, pressure, energy and forces. 3. Extract the final cell and recheck at a tighter grid and denser k mesh. 4. Independently evaluate five to seven isotropically strained cells around the candidate volume, keeping fractional coordinates fixed for ideal silicon or relaxing internal coordinates consistently where needed. 5. Fit a local equation of state with a documented external fitter, declaring volume normalization and energy units. 6. Compare the fitted minimum to the optimization result and inspect fit residuals.
Interpretation. At nonzero pressure the relevant stationary quantity involves E+pV, not E alone. Bulk modulus derives from curvature, so fitting a noisy or narrow dataset can make it much less stable than the minimum volume. A numerically precise fit can still reflect a poor functional. If allowing full cell shape, a symmetry-lowering distortion may be physical or numerical; investigate instead of forcing it back silently.
Tests, pitfalls and exercise. Check pressure convergence under cutoff, relative cutoff and k mesh. Keep a consistent mesh policy across volume scans to avoid discontinuous changes in sampling. A slab's vacuum direction should not be optimized as if it were a bulk compressible material. Compare two fitting windows and show how the minimum and curvature respond. Explain why the narrower uncertainty of a least-squares fit does not include functional error.
Diagram. Energy versus volume with discrete placeholders and a local fit region, paired with a cubic cell under isotropic arrows. EN: strain, volume, pressure derivative, curvature, independent check. Mark the line schematic until real data exist.