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.

F3: Three-Body Oxygen Ordering

For each central oxygen, Clavis forms every unordered pair of oxygen neighbors within the cutoff and evaluates $\left(\cos\theta\,|\cos\theta| + \frac{1}{9}\right)^2.$ 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.

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 $F_4 = \langle \cos(3\phi) \rangle.$ f4_per_atom averages contributing pairs for each water. f4_overall averages each unique water pair once and is bounded by [-1, 1].

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.

Running F3/F4

1. Upload a supported structure or trajectory containing waters with oxygen and two hydrogen coordinates.
2. Open ANALYZE, tick F3 / F4 in the analysis set, and run it for the current frame or for the trajectory range.
3. For normal GRO, large streamed GRO, or mapped LAMMPS data, set the start, end and step of the range to obtain one algorithm-owned result per frame. See Analysis sets.

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.

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.

Averaged Steinhardt q4/q6 and MCG

Two more published order parameters can be ticked in the same analysis set. Each is computed only when ticked and appears as its own chart with CSV export in RESULTS.

• Averaged Steinhardt q4/q6. This is the frame mean of the locally averaged bond-orientational order of Lechner & Dellago (J. Chem. Phys. 129, 114707, 2008). Neighbours are water oxygens within 0.35 nm, and each water’s q_lm is averaged with its neighbours’ values. Per-water values match freud’s Steinhardt(average=True) within freud’s single precision. q6 separates ice and crystal from liquid well, but separates hydrate from liquid only weakly.
• MCG (Mutually Coordinated Guest). This is the number of guests in the largest MCG-3 cluster, following Barnes, Beckham, Wu & Sum (J. Chem. Phys. 140, 164506, 2014). Two guests within 9 Å are linked when at least 5 waters lie within 6 Å of both and inside the 45° cones along the guest–guest axis. A guest with at least 3 such links is a monomer, and linked monomers form clusters. Fully occupied sI and sII crystals form a single cluster of every guest. MCG needs guest molecules; frames without guests show an empty state.

Both need a cell at least twice as wide as their cutoff (0.7 nm for q4/q6, 1.8 nm for MCG). A frame in a smaller cell reports no value for these two charts, and its F3/F4 values are unaffected. Each chart carries a badge stating how the method was verified. The three levels are: against the authors’ program, against an open reference implementation, or against the paper’s definitions.