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F3/F4 Order Parameters

F3 and F4 describe local water ordering. They are order parameters, not cage detectors, and should be interpreted with temperature, water model, cutoff, and sampling conditions.

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F3: Three-Body Oxygen Ordering

For each central oxygen, Clavis forms every unordered pair of oxygen neighbors within the cutoff and evaluates (cos⁡θ ∣cos⁡θ∣+19)2.\left(\cos\theta\,|\cos\theta| + \frac{1}{9}\right)^2. f3_per_atom is the mean of the triplet contributions centered on each water. f3_overall is the mean over all contributing triplets; it is not an unweighted mean of the per-water values. Lower values indicate more tetrahedral local ordering.

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F4: Torsional Ordering

For each neighboring water pair, Clavis selects the hydrogen pair with the largest PBC-aware H–H separation, evaluates the H–O···O–H dihedral angle φ, and averages F4=⟨cos⁡(3ϕ)⟩.F_4 = \langle \cos(3\phi) \rangle. f4_per_atom averages contributing pairs for each water. f4_overall averages each unique water pair once and is bounded by [-1, 1].

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Periodic Geometry and Cutoff

  • The default O–O neighbor cutoff is 0.35 nm (3.5 Å).
  • Orthorhombic and triclinic cells use minimum-image distances.
  • Coordinates are expected in nanometers after input conversion.

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Running F3/F4

  1. Upload a supported structure or trajectory containing waters with oxygen and two hydrogen coordinates.
  2. Open ANALYZE and run F3/F4 for the current frame.
  3. For normal GRO, large streamed GRO, or mapped LAMMPS data, select a sampled trajectory range to obtain one algorithm-owned result per frame.
Normal GRO, streamed GRO, mapped LAMMPS, and native XTC/TRR sessions support selected F3/F4 ranges. Exported trajectory rows include a one-based display frame, zero-based frameIndex, and algorithm: f3f4 so they cannot be mistaken for cage-analysis results.

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Interpretation

Compare values within a controlled series or against a reference produced with the same water model, temperature, cutoff, and frame selection. Static ideal crystals and finite-temperature trajectories can differ substantially, so Clavis does not apply one universal phase threshold.