CHILL+ versus cages

Two classifiers live in libyodaLib. They answer different questions and they do not imply each other.

Four-neighbour star

CHILL (seams chill, chill::getCorrel / getIceTypeNoPrint) and CHILL+ (seams chill-plus, chill::getCorrelPlus / getIceTypePlusNoPrint) look at the four-neighbour star. Both stay on the host. They compute bond-order correlations c_ij on the four nearest neighbours of each oxygen (or each mW site) and label the atom cubic, hexagonal, interfacial, clathrate, or water from the staggered and eclipsed pattern of that star.

A molecule is cubic or hexagonal when its four bonds look like ice, even if those neighbours do not close a cage.

CHILL+: Nguyen and Molinero, J. Phys. Chem. B 2015 (10.1021/jp510289t). CHILL: Moore et al., Phys. Chem. Chem. Phys. 2010.

Cage membership

The ice score (seams cages, ring::seededCageAffiliation by default) is cage membership. A molecule in a hexagonal cage (HC) is ice Ih. A molecule in a double-diamond cage (DDC) is ice Ic. A molecule in neither is water. The cages are assembled from six-membered primitive rings on a chosen bond graph, not from the four-neighbour star.

This is topological unit matching (TUM). The methods paper is the 2020 JCIM article (see Citation).

The GPU path (gpu::analyzeResident) is that TUM ice score only: linkcell::gpu k-nearest, the mutual four-nearest graph, primitive six-rings, and HC/DDC affiliation. CHILL, CHILL+, and \(q_{lm}\) stay on the host. Only cage labels come back.

Why they disagree

A configuration can agree exactly on the closed star of a vertex (same induced graph, same coordinates on those five atoms) and still disagree on that vertex’s cage label, because the cage predicates read a larger neighbourhood of six-rings. The Catch2 suite encodes that fact: cage membership is not a function of the four-neighbour star.

On the in-tree mixed TIP4P dump (input/traj/exampleTraj.lammpstrj), CHILL+ reports 12 interfacial clathrate and 238 water. Seeded cages report zero HC and zero DDC. A three-eclipsed star is not cage membership. Walk through the commands in the mixed TIP4P tutorial.

Bond graph

seams cages --graph chooses the bond graph those rings are found on:

value	graph
cutoff	pairs inside the distance cutoff
knn	mutual k-nearest (default k=4)
knn-union	union k-nearest (completion graph of the seeded rule)
seeded	mutual seeds, union completions (CLI default)

On a perfect cubic crystal the four graphs coincide. On a mixed nucleation dump they do not have to.

Ring-adjacent completion

ring::seededCageAffiliation takes a fifth argument, ringAdjacentCompletion, default false. When the flag is true, the accepted labels pass through ring::ringAdjacentCompletion: a permissive six-ring with all but one vertex labelled fills that last vertex, iterated to a fixed point. Hexagonal cage (HC) flags and double-diamond cage (DDC) flags run as two walks.

seams cages --complete sets the flag. The rule, the least-fixed-point claim, and the Lean build live on Ring-adjacent completion.