3.3 Diagonalization and finite-temperature occupations
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.
3.3.1 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
3.3.2 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.
3.3.2.1 Input block 1
&SCF
SCF_GUESS ATOMIC
EPS_SCF 1.0E-7
MAX_SCF 200
ADDED_MOS 20
&DIAGONALIZATION
ALGORITHM STANDARD
&END DIAGONALIZATION
&MIXING
METHOD BROYDEN_MIXING
ALPHA 0.10
NBROYDEN 8
&END MIXING
&SMEAR
METHOD FERMI_DIRAC
ELECTRONIC_TEMPERATURE [K] 300
&END SMEAR
&END SCF
3.3.3 Worked investigation
Intuition. Near a Fermi level, many states can exchange occupation during SCF. Fixed occupied-subspace optimization is then an awkward default. Diagonalization plus density mixing and finite electronic temperature offers a controlled alternative, but electronic smearing is not the ionic thermostat. Use B initially to learn the syntax, then a separately validated metallic structure and element-specific data. No metal coordinates or potential are silently inferred from silicon.
Original replacement. Replace the entire SCF section, including removal of OT. The following is a teaching starting point for a small cell; ADDED_MOS 20 is a count of extra orbitals, not a universal adequacy criterion. Electronic temperature is in kelvin. Inspect occupation of the highest computed states and increase the count if necessary.
See input block 1 above.
Workflow. 1. Validate geometry and electron count before switching the solver. 2. Run at fixed k mesh and electronic temperature; track residual, occupations and final energy terms. 3. Increase extra orbitals until the top of the computed manifold is sufficiently unoccupied for the target accuracy. 4. Test a smaller mixing amplitude if charge oscillates, while keeping the physical model fixed. 5. Converge electronic temperature jointly with the k mesh, for example comparing 150, 300 and 600 K as a diagnostic sweep rather than asserting any value is correct. 6. Compare like energy quantities, recording entropy-related terms and the intended zero- or finite-temperature interpretation.
Interpretation and tests. A smooth SCF is not a convergence study of metallic energetics. Smearing can smooth poor k sampling and conceal an insufficient mesh. The Fermi level, fractional occupations and entropy contribution are parts of the numerical/thermodynamic description; do not report a smeared energy as an isolated zero-temperature ground-state energy without qualification. For magnetic metals, spin initialization and competing magnetic states add an independent search dimension.
Pitfalls and exercise. Too few empty states truncates the occupation tail. Aggressive mixing can create charge sloshing, especially in large or elongated cells. Metallic slab convergence cannot be inferred from bulk silicon. Design a two-axis temperature/mesh study and decide which observable will determine sufficiency: energy difference, force, stress or density of states near EF. Explain why “300 K electrons” does not automatically mean a 300 K nuclear trajectory.
Diagram. Draw two occupation curves against ε−EF, one sharp and one smooth, with an upper-orbital boundary visibly beyond the occupied tail. EN: Fermi level, fractional occupation, extra orbitals, electronic temperature. Curves are conceptual.
3.3.4 Related calculations
- 3.2 Orbital transformation as a controlled solver choice
- 3.4 Brillouin-zone sampling and supercell logic