Compare Multiple Starts and Stationary Candidates

Use multiple physically motivated starting structures to expose distinct stationary candidates, preserve every basin, and avoid calling an accepted relaxation endpoint a verified minimum without curvature evidence.

A local optimizer answers a basin-dependent question: which stationary structure is reached from this starting point under this state evaluator and active subspace? It does not generally search the full configurational landscape.

Compare real starts and endpoints before ranking candidates

Open every credible starting structure side by side with the same cell, orientation, and periodic-image settings. Compare coordination, symmetry, stacking or registry, defect environment, cell volume, and any magnetic or charge label. Record where each candidate came from: database record, experiment, literature structure, prototype, previous calculation, or an intentional distortion. Use visual and symmetry tools for the comparison, and keep one clearly named directory per candidate.

Run the candidates independently with the same declared numerical setup unless a documented physical reason requires otherwise. During each run, inspect its trajectory rather than waiting only for the final energy. Reopen the start, representative intermediate frames, and endpoint; note reconstruction, state changes, constraint violations, or optimizer stalls. Then inspect complete SCF, free-force, stress, displacement, and warning histories.

Build a comparison table only from scientifically comparable and numerically accepted endpoints. Include state identity and geometry descriptors as well as energy; retain distinct stationary candidates rather than silently discarding higher-energy branches. Force, stress, displacement, and solver criteria can support an accepted stationary candidate, but they do not establish positive curvature. Call an endpoint a local minimum only when a Hessian, phonon, vibrational, or other appropriate curvature test supports that classification in the active subspace. A lower printed energy does not repair a wrong model, an incompatible state, or an unconverged trajectory.

Before using the synthetic helper, inspect the candidate directories that belong to the real study. This read-only shell pass inventories inputs, trajectories, outputs, and endpoint structures without ranking them:

: "${CANDIDATE_ROOT:?Set CANDIDATE_ROOT to the directory containing independent starts}"
find "$CANDIDATE_ROOT" -mindepth 1 -maxdepth 2 -type f \
  \( -name '*.in' -o -name '*.out' -o -name '*.traj' -o -name '*.xyz' -o -name '*.cif' \) \
  -printf '%12s %p\n' | sort
find "$CANDIDATE_ROOT" -mindepth 1 -maxdepth 2 -type f -size 0 -print
for output in "$CANDIDATE_ROOT"/*/*.out; do
  printf '\n%s\n' "$output"
  head -n 20 -- "$output"
  tail -n 40 -- "$output"
  grep -niE 'warning|error|stopping|not converged|no convergence' -- "$output" || true
done

Open each retained endpoint and trajectory beside this inventory, then build the comparable candidate ledger described above. The double-well script below is a bounded synthetic teaching fixture for bookkeeping. It is optional automation, not a real material calculation and not evidence that a chosen set of starts is complete. Consult the learning resources and the original literature to identify physically motivated candidates before automating a larger search.

Run the bounded basin exercise

python3 examples/practical-guides/optimization_multiple_starts.py

The script starts the same deterministic local minimizer from four coordinates, reports which of two synthetic basins each start reaches, and retains both minima. It does not run DFT or prove that the lower fixture basin is globally lowest.

For a material study, prepare one directory and stable candidate ID per physically motivated start. Preserve each input, trajectory, final geometry, final state, termination evidence, and fresh final energy-and-gradient check. Deduplicate only after structure, cell, atom mapping, state identity, and numerical tolerances agree. Send every distinct accepted stationary candidate to the same fixed-geometry reference-state protocol; do not rank raw last-step relaxation energies. Record which candidates have separate curvature evidence before describing them as minima.

Identify why multiple minima are plausible

Multiple starts are especially important when the model admits alternatives such as:

crystal polymorphs or symmetry-lowered distortions;
layer stackings and interface registries;
adsorption sites and molecular orientations;
defect reconstructions or charge-localization patterns;
magnetic orders or spin directions;
molecular conformers;
ferroelectric orientations;
disordered or compositionally ordered arrangements.

Generate candidates from scientific hypotheses, symmetry, enumeration, perturbations, prior data, or a declared global-search method. Random displacement alone is not a substitute for covering known configurational alternatives.

Keep each start and state lineage independent

Assign every initial candidate a stable identity and preserve its parent model and transformation, initial geometry and cell checksum, initial electronic or magnetic state, constraints and symmetry treatment, optimizer and evaluator identity, complete trajectory, final structure and state, and separate termination and verification result.

Do not reuse one candidate’s wavefunction or optimizer Hessian in another branch unless the scientific intent and compatibility are explicit. Such reuse can bias nominally independent starts toward the same metastable state.

Demonstrate basin dependence with a synthetic landscape

The companion script minimizes a one-dimensional tilted double-well from four initial coordinates:

import sys

sys.path.insert(0, "examples/practical-guides")
from optimization_multiple_starts import run

report = run()
for result in report["starts"]:
    print(result["start"], result["minimum_label"], result["final_energy"])

The potential and numerical settings are deterministic teaching fixtures. Two starts reach the left basin and two reach the right basin. The analysis retains both stationary families and identifies the lower fixture energy without claiming that a local optimizer proved the global solution.

Compare final objects before deduplication

Two relaxed files may represent the same basin under translation, atom permutation, cell choice, symmetry operation, or small numerical noise. Conversely, similar total energies do not make two geometries equivalent.

A deduplication record may use:

composition and atom mapping;
periodic cell equivalence;
symmetry and Wyckoff or local-environment information;
displacement or distance metrics after optimal mapping;
magnetic or charge-state identity;
declared numerical tolerances;
a method-compatible final energy-and-gradient check.

Preserve the mapping and tolerance used. Do not delete the original branches after clustering them.

Classify stationary candidates before calling them minima

When multiple accepted stationary candidates remain, compare them with a consistent reference-state protocol. A candidate becomes a supported local minimum only after an appropriate curvature test excludes unstable directions within the declared active subspace. The lowest computed energy under one method may be the leading zero-temperature candidate, but higher stationary candidates can remain scientifically relevant; classify them as metastable phases, reconstructed defects, stackings, conformers, or kinetic intermediates only when the additional evidence required by that label is present.

Do not relabel all non-leading minima as “unconverged.” Distinguish:

optimization failure;
a stopped but unverified path;
a stationary candidate satisfying the declared optimization criteria;
a local minimum supported by a separate curvature test;
a candidate that is higher in a declared energy comparison;
a candidate rejected by a separate physical or experimental criterion.

Use global-search methods as separate workflows

Basin hopping, minima hopping, evolutionary searches, random structure search, and related methods alternate candidate generation with local minimization. They can explore more basins, but their stopping rules and completeness claims require separate evidence.

A global-search algorithm returning one lowest candidate does not prove that no lower basin exists unless the search protocol provides a defensible coverage or probability argument. Keep global-search configuration, random seeds, accepted and rejected candidates, and local-minimization settings.

Perturb high-symmetry candidates deliberately

A high-symmetry start can remain trapped because imposed symmetry excludes an unstable direction or because exact coordinates produce zero first-order force along a symmetry-breaking mode. Use small physically motivated perturbations, lower-symmetry supercells, alternative magnetic starts, or known soft-mode directions where justified.

Turning off all symmetry without constructing relevant candidates may increase cost without improving coverage. The perturbation family and its scientific rationale should be recorded.

Rank only after comparable final verification

Before comparing energies of different stationary candidates or supported minima, ensure that each candidate uses a compatible model, method, numerical setup, state definition, and final verification. Cell sizes, formula units, charge states, magnetic branches, and constraints may require normalization or separate reference terms.

Energy ranking is a later reference-state or target-calculation task. This guide establishes candidate and basin lineage; it does not define formation energies, phase stability, or finite-temperature populations.

What this guide verifies

The companion script confirms that a deterministic local minimizer reaches two distinct basins from different starts, groups converged fixture coordinates, and retains both minima before reporting their relative fixture energies.

It does not run DFT, validate any material, prove global optimality, prescribe a number of starting structures, or establish thermodynamic or dynamic stability.

Common mistakes

Optimizing one start and calling it the ground state. Local minimization is basin dependent.

Using only random noise around one structure. Cover known polymorph, registry, magnetic, and reconstruction hypotheses.

Deleting higher stationary candidates. Preserve candidate lineage, curvature status, and rejection reasons.

Deduplicating by energy alone. Compare structure, cell, mapping, and state identity.

Calling a global-search best-so-far candidate proven. Search completeness needs its own evidence.