SQQ

SQQ: Python Joint Toolkit for Water-Shell Topology Analysis.

Current release: 0.4.1

SQQ provides the complete SQQ-Py water-shell topology workflow and the focused SQQ-CPP cage engine. Select the Python workflow with -e py or the C++17 graph/ring/cage/occupancy/F3/F4 workflow with -e cpp. Algorithms are documented in docs/design.md and release notes in docs/update.md.

Acknowledgements

Names are listed alphabetically by family name.

• Liwei Cheng @ Wuhan Institute of Technology
• Bin Fang @ Hainan University
• Yifei Hu @ Fuzhou University
• Jihui Jia @ China University of Petroleum (Beijing)
• Wuquan Li @ Beijing Huairou Laboratory
• Zhenchao Li @ Fuzhou University
• Bo Liao @ China University of Petroleum (East China)
• Yingxu Lu @ Wuhan Institute of Technology
• Fengyi Mi @ Southwest University of Science and Technology
• Yingtao Sun @ The Hong Kong University of Science and Technology
• Zhengcai Zhang @ Laoshan Laboratory

Changed in 0.4.1

• Package, configuration-schema, and native-core versions are synchronized at 0.4.1, released Aug 1, 2026.
• SQQ-Py and SQQ-CPP now use the same exact sparse GROW contract: ring-edge incidence is stored sparsely, each search branch keeps only local edge counts and its open frontier, and all topologically eligible branches are examined without candidate truncation.
• Cage state limits default to 0 (unlimited). A positive diagnostic limit stops the frame with an error instead of returning a partial cage set. The legacy fast-closure fallback is disabled.
• Deterministic final cage ordering makes frame-local cage IDs consistent between the Python and C++ engines without changing cage topology, type, isomer, occupancy, or order-parameter definitions.
• SQQ-CPP validation includes large systems containing up to approximately 10⁶ water molecules.
• Multi-frame reports are collected directly under info/; selected structures use gro/<frame>/. Per-frame and summary publication is transactional, reused output roots clean only known SQQ artifacts, and f3-gro/f4-gro contain complete water molecules with the per-water value on each oxygen.
• Automatic graph selection is resolved before run metadata is shown: the terminal, per-frame reports, summaries, and resolved YAML display only auto -> hbond or auto -> oo.
• After frame analysis reaches 100%, the terminal displays Writing output files; please wait and do not close SQQ... while render, Excel/CSV, and final configuration files are published.

Install

Install the released package from PyPI:

pip install sqq

Upgrade an existing installation:

pip install -U sqq

For local development from a source checkout:

pip install -e .

Building from source compiles the native extension and requires a C++17 compiler, CMake 3.20 or newer, Python development headers, and a platform build tool. Normal releases are intended to install a prebuilt wheel and do not compile C++ on the user's machine.

Then use:

sqq -h
sqq --version
sqq init
sqq analyze -i ./gro -c sqq_config.yaml -o ./result_sqq

Root help prints the SQQ version and release date immediately before the usage line. Use sqq -v or sqq --version for the version line alone.

During source-tree development without installation:

python -m sqq analyze -i ./gro -c sqq_config.yaml -o ./result_sqq

Quick Start

Single GRO file:

sqq analyze -i test1.gro -o ./result_sqq

Directory of GRO files (the default input.pattern in sqq_config.yaml is *.gro):

sqq analyze -i ./gro -o ./result_sqq

For multiple GRO files, SQQ groups compatible frames automatically. Files with one topology share the requested output root; heterogeneous inputs are separated into result_A, result_B, and so on in first-occurrence order. The grouping affects aggregation and paths only, not per-frame analysis.

Glob pattern:

sqq analyze -i "./gro/*.gro" -o ./result_sqq

XTC/TRR trajectory with a topology file; add -dt 100 to analyze an exact 100 ps interval:

sqq analyze -i traj.xtc --top topol.gro -dt 100 -c sqq_config.yaml -o ./result_sqq

A stacked GRO trajectory uses repeated complete GRO blocks in one file and needs no separate topology:

sqq analyze -i frames.gro -dt 100 -o ./result_sqq

LAMMPS dump or DCD with a DATA topology; standard water/methane types are inferred automatically:

sqq analyze -i traj.lammpstrj -t system.data -o ./result_sqq

Input Units and Boxes

GRO and MDAnalysis trajectory coordinates are interpreted in nm. A GRO input may contain one frame or repeated complete GRO blocks in one stacked trajectory. SQQ streams every block, validates atom counts, ordered atom identity, box records, and finite coordinates, and rejects topology changes between stacked frames. A GRO used as --top must still contain exactly one frame. Other trajectory frames also require finite coordinates. XYZ coordinates are multiplied by YAML input.xyz_scale; the default 0.1 assumes angstrom input, while 1.0 keeps nm values. SQQ accepts exactly one declared XYZ frame per file and rejects truncated, extra, malformed, or non-finite atom records. XYZ has no periodic box unless converted through another format.

GRO atom counts and the mandatory box line are validated. A three-value positive box is orthorhombic; an all-zero box is treated as non-periodic. Nine-value GRO boxes with nonzero tilt terms and trajectory frames with non-90-degree angles are rejected because triclinic minimum-image calculations are not implemented. GRO molecules are formed from contiguous residue blocks in source order, preventing wrapped or repeated residue IDs from merging distinct molecules. LAMMPS normally uses DATA molecule IDs; automatic inference can rebuild them from unambiguous Bonds components, and dump atom rows may be interleaved.

LAMMPS trajectories require -t system.data (equivalent to --top). A non-empty input.lammps.type_map explicitly maps numeric atom types to resname/atomname or ignore and always takes priority. If the map is absent or empty, SQQ uses DATA masses, type comments, molecule IDs, and Bonds to identify unambiguous water (1 O + 2 H), all-atom methane (1 C + 4 H), and labeled single-site methane. Other bonded components are retained deterministically as environment/other context instead of being mistaken for water or guests; they do not enter the water graph or cage occupancy. Use component.role_map, additive.resname, environment.resname, or an explicit type_map when the automatic role is not the intended one. If molecule IDs do not define valid water/guest molecules but Bonds do, SQQ rebuilds deterministic molecule IDs and reports that decision. Ambiguous reuse of one atom type, insufficient evidence for a requested water/guest role, or topology/trajectory ID mismatch still fails clearly. The resolved mapping and role provenance are recorded in sqq_config_resolved.yaml, per-frame info, and main-summary configuration. This normalization is shared by SQQ-Py and SQQ-CPP. Supported inputs are LAMMPS DATA with full, molecular, bond, or angle atom style, fully periodic pp pp pp orthorhombic dump boxes, and LAMMPS DCD. Tilted boxes, nonperiodic dump boundaries, units lj, duplicate atom IDs, and topology/trajectory ID mismatches fail before analysis. input.delta_time_ps / -dt / --delta-time selects a physical interval in ps for XTC, TRR, LAMMPS dump/DCD, and stacked GRO trajectories. With no delta time, every stored frame is analyzed. For LAMMPS dumps, the native reader interval is passed explicitly as input.lammps.timestep × units-to-ps; this preserves physical time and prevents MDAnalysis from substituting 1 ps without hiding unrelated warnings. The requested interval must be at least, and an integer multiple of, the regular native interval; missing or irregular time metadata is rejected instead of rounded.

Analysis Engines

-e / --engine selects the analysis engine; the default is py:

sqq analyze -i ./gro -e py -o ./result_py
sqq analyze -i ./gro -e cpp -o ./result_cpp

For SQQ-Py, --find-cluster overrides hydrate_cluster.enabled in YAML. Search results enter selected info/main-summary outputs; split cluster structures still require the YAML output type cluster-gro. SQQ-CPP rejects cluster search.

Both documented engines default to one worker. -w / --worker overrides the preset: integer text is a worker count, while 0.5, 1.0, 50%, and 100% are physical-core fractions. Process parallelism supports independent GRO/XYZ files and indexed XTC/TRR/LAMMPS trajectories. At most 3 * workers tasks are submitted at once.

The default chordless/bounded path preserves the established scientific definitions while accelerating neighbor generation, incremental chord pruning, L1 forward checking, cached layer growth, integer-mask subset ownership, and cage target/edge state pruning. Cage DFS also applies exact remaining-edge incidence and parity conditions before expansion. MDAnalysis supplies orthorhombic cutoff candidates when available, but SQQ still rechecks every distance and hydrogen-bond angle with its established float64 logic. F3 and graph-mode Q_l share one graph-vector cache; all Q_l degrees share candidate lists and spherical-angle work. Optional ring.definition: shortest_path applies the Franzblau shortest-path criterion and reuses bounded-BFS distance maps. Optional quasi_cage.search_policy: exact preserves distinct frontiers and enumerates connected L2/L3 subsets; these opt-in modes can change or add results. Quasi-cage candidate and layer-state truncation is reported through frame warnings; the 0.4.1 cage GROW search itself does not truncate candidates or return partial results.

Every cage now passes the same mandatory topology validation in SQQ-Py and SQQ-CPP: each edge belongs to exactly two faces, V - E + F = 2, the face shell is connected, every vertex link is one cycle, and every shell vertex is trivalent. Optional scientific cage validation adds PBC-aware face-planarity and edge-variation limits, nonzero projected area, positive-volume validation, and volume-centroid cage centers. It remains disabled by default, but disabling it no longer bypasses topology validation. SQQ uses an orthorhombic box representation and rejects non-orthogonal/triclinic input explicitly.

The current release uses the same compact three-row stage model for serial and parallel progress: file preparation (reading, settings, selecting), core topology search (graph, ring, optional half/quasi, cage, and optional cluster), and post-processing (filtering, order, ice, output). The half/quasi stage is hidden when both open-patch searches are disabled. In an interactive terminal, one in-place panel highlights the active stage with bold bright-blue ANSI text; redirected or captured output instead emits at most 21 plain 5% checkpoints without ANSI, carriage-return rewrites, or stderr progress. The cluster stage appears only when hydrate-cluster analysis is enabled. Parallel runs also show aggregate stage counts and up to six active files with per-stage and per-file timings. The banner is always the first Analyze output. Nonfatal warnings, when present, are deduplicated into one Diagnostics block after progress and before Run Summary; an ordinary warning-free run adds no empty block.

Native SQQ-CPP Backend

Engine cpp selects the focused native workflow. Python owns input normalization, molecule selection, scheduling, compact VMD output, Markdown, summary CSV, and optional XLSX; C++17 performs graph construction, internal chordless 4/5/6 rings, cage topology/isomers, occupancy, and F3/F4 while releasing the GIL.

It accepts orthorhombic GROMACS/LAMMPS inputs, compatible graph/pair settings, -s within 4/5/6, cage report/validation settings, f3/f4, process or serial scheduling, and info, gro, cage-gro, sqq-render, summary-csv, summary-xlsx, or summary-detail-csv. sqq-render owns the complete visualization package. gro enables the supported classified cage GRO output, but cpp does not select it by default.

Unsupported requests fail before analysis: public ring output, size 7, shortest-path rings, half/quasi cages, cluster, ice, Q_l/MCG/DHOP, membership/order TSV, legacy per-frame VMD, Python fast closure, thread scheduling, and triclinic boxes. A failed native extension never falls back to Python.

The cpp default layout is:

result/
  sqq_render/
    sqq_cage.gro
    sqq_cage.xtc
    sqq_cage.membership.tsv
    sqq_cage.vmd.tcl
  summary/
    summary.csv
    cage.csv
    cage_occupancy.csv
    cage_isomer.csv
    order_parameter.csv
    detail_index.csv
  sqq_config_resolved.yaml
  frame_name/
    frame_name_info.md

The native engine does not select ordinary/classified GRO by default. Set YAML output.type to include gro or cage-gro when that output is required.

Release CI is configured to build and test precompiled wheels for CPython 3.10-3.14 on Windows x86_64, Linux x86_64, macOS x86_64, and macOS arm64, plus a source distribution. A wheel already contains the platform-native extension; end users installing such a wheel do not compile C++. A source install instead invokes the CMake/scikit-build-core build and therefore needs CMake 3.20 or newer and a local C++17 toolchain.

Common Commands

Write the commented default configuration to sqq_config.yaml. The template includes # section and choices comments, defaults to ring sizes 4/5/6, and refuses to overwrite an existing destination:

sqq init

Use -o only when a different configuration filename is wanted; that destination must also not already exist:

sqq init -o methane.yaml

SQQ does not auto-load a similarly named file from the current directory. Without -c, built-in defaults are used. With -c, the named user file is read but never rewritten.

Select ring search sizes, open-patch searches, hydrate clusters, and order parameters with the retained public overrides:

sqq analyze -i md.gro -e py -s 4,5,6 --find-half on --find-quasi on
sqq analyze -i md.gro --find-cluster on --order-parameter f3,f4,q6

Analyze an explicit pair map:

sqq analyze -i md.gro -b pairs --pair water_pairs.txt

--pair overrides YAML graph.pair_file. A CLI-relative pair path is resolved from the working directory; a YAML-relative path is resolved from the directory containing the user configuration. graph.mode: pairs without either source fails before frame analysis.

Parallelize independent files or indexed trajectory frames with the default process backend:

sqq analyze -i ./gro -w 4 -o ./result_sqq
sqq analyze -i traj.xtc -t topol.gro -w 50% -o ./result_sqq

Integer worker text is an explicit count. Decimal text and percentages are physical-core fractions, so -w 1 is one worker while -w 1.0 and -w 100% request all detected physical cores before the reserve-one-core and task-count clamps.

Configuration

The generated file uses YAML # comments and canonical singular keys. The main settings are:

schema_version: "0.4.1"
engine: py  # choices: py, cpp

run:
  strict: false  # choices: true, false

input:
  pattern: "*.gro"
  recursive: false  # choices: true, false
  delta_time_ps: null
  xyz_scale: 0.1
  lammps:
    unit: real  # choices: real, metal, nano
    timestep: 1.0
    atom_style: full  # choices: full, molecular, bond, angle
    coordinate_convention: auto  # choices: auto, x, xs, xu, xsu
    type_map: {}

component:
  auto_classify: true
  unknown_role: other
  unknown_action: warn
  role_map: {}

water:
  resname: [SOL, TIP, WAT, HOH]
  oxygen_name: [OW, O, OH2]
  hydrogen_name: [HW1, HW2, H1, H2, HW, HT1, HT2]

guest:
  resname: [CH4, CO2, MET, ETH]
  center_atom:
    CH4: [C]
    CO2: [C]
    MET: [C]
  center_mode: center_atom

additive:
  resname: []

environment:
  resname: []

graph:
  mode: auto  # choices: auto, hbond, oo, pairs
  oo_cutoff_nm: 0.35
  hbond_distance_nm: 0.35
  hbond_angle_deg: 30.0
  pair_file: null
  pair_id: resid  # choices: resid, oxygen_index, atomid

ring:
  size: [4, 5, 6]
  report_size: auto
  definition: chordless  # choices: chordless, shortest_path

half_cage:
  enabled: auto  # choices: auto, true, false

quasi_cage:
  enabled: auto  # choices: auto, true, false
  base_size: auto
  side_size: auto
  max_layer: 1
  search_policy: bounded  # choices: bounded, exact

cage:
  enabled: true
  report_type: auto
  max_face: 20
  search_mode: grow
  seed_mode: ring
  max_state_per_seed: 0  # 0 = unlimited
  max_total_state: 0  # 0 = unlimited
  max_boundary_candidate: 8  # compatibility setting; never truncates exact search
  fast_closure: false  # legacy compatibility key
  fast_closure_max_state: 20000  # ignored by the exact sparse search
  scientific_validation: false
  max_face_planarity_rms_nm: 0.06
  max_face_edge_cv: 0.35
  min_cage_volume_nm3: 1.0e-6
  occupancy_mode: polyhedron

hydrate_cluster:
  enabled: false
  min_cage: 2

hydrate_order:
  mcg_guest_resname: [CH4, MET]
  mcg_guest_cutoff_nm: 0.90
  mcg_water_cutoff_nm: 0.60
  mcg_cone_half_angle_deg: 45.0
  mcg_min_water: 5
  dhop_neighbor_cutoff_nm: 0.35
  dhop_planar_count: [11, 12]
  dhop_min_qualified_neighbor: 3

order_parameter:
  enabled: [f3, f4]
  q_neighbor_mode: graph  # choices: graph, cutoff, nearest, lammps
  q_cutoff_nm: 0.35
  q_n_neighbor: null


parallel:
  backend: process  # choices: process, thread, serial
  worker: auto
  math_thread: 1

output:
  type: [info, sqq-render, summary-xlsx]
  summary_csv_dir: summary
  cage_isomer_row: nonzero  # choices: nonzero, all
  write_empty_file: false
  structure_layout: grouped  # choices: grouped, flat
  gro_atom_mode: cage_oxygen_guest
  context_role: []

Unknown keys and duplicate YAML keys are errors. Canonical public collections are singular, units appear in names such as _ps, _nm, and _deg, engine-related three-state switches use auto/true/false, and ordinary booleans use true/false. Legacy top-level mode, graph.bond_mode, and order.parameter migrate with warnings to engine, graph.mode, and order_parameter.enabled. Former 0.3.x plural keys also remain readable for migration; generated and resolved files use only the canonical form.

Configuration priority is:

built-in defaults < engine preset < sqq_config.yaml < retained command-line overrides

Every run writes the final effective state to sqq_config_resolved.yaml in its result root, including the requested engine, effective sqq-py/sqq-cpp backend, requested and effective graph modes, requested and resolved workers, output selection, input/LAMMPS provenance, automatic adjustments, run status, failures, and summary-write timing. This file is separate from the user-owned sqq_config.yaml.

Parallel Execution

Public YAML uses singular collection keys such as water.resname, ring.size, order_parameter.enabled, output.type, and parallel.worker. Configurations from 0.3.x that use former plural spellings are migrated on read; sqq init and the resolved runtime file use the singular schema.

half_cage.enabled: auto and quasi_cage.enabled: auto resolve to on for SQQ-Py and off for SQQ-CPP. If an older YAML explicitly enables either Python-only search under C++, SQQ disables the unsupported work, deactivates quasi layer controls, removes incompatible half/quasi outputs, records the adjustment in sqq_config_resolved.yaml, and continues. Missing required inputs or settings that prevent the native cage calculation remain hard errors.

parallel.backend: process is the default for two or more independent GRO/XYZ inputs. SQQ uses the spawn start method on every supported platform. Each worker receives run configuration once, reads and writes its own frame, and sends only small stage events plus one summary row to the main process. This avoids the Python GIL limitation of the compatibility thread backend.

Before dispatching two or more GRO files, SQQ reads only their topology records and assigns topology groups in first-occurrence order. The fingerprint contains the atom count and ordered contiguous residue blocks, represented by each block's residue name and ordered atom-name sequence. Titles and time labels, coordinates, velocities, boxes, and numeric atom/residue IDs do not affect grouping. A supplied GRO -t / --top is checked against every input fingerprint; any mismatch fails before analysis and identifies the exact source file.

All accepted groups use one shared worker pool and one global progress index. Each task also carries a group-local frame index and output root, so group summaries and annotated bundles remain correctly ordered without running groups serially. Requested graph.mode: auto remains recorded as auto, but its effective hbond or oo mode is resolved once from a representative frame in each topology group and reused by both SQQ-Py and SQQ-CPP for every frame in that group.

With parallel.worker: auto, the documented py and cpp engines resolve to one worker. Physical-core detection for explicit fractional requests prefers optional psutil, then platform probes such as Windows CIM, macOS sysctl, or Linux /proc/cpuinfo; if physical cores cannot be detected, SQQ falls back to the CPU count visible to the process. --worker / -w accepts either a fraction (50%, 0.5, or 1.0 for 100%) or an explicit positive integer worker count (1 means one worker). Windows ProcessPoolExecutor runs are capped at 61 workers; Linux workstations can use larger explicit values such as -w 100, subject to the reserve-one-core rule, task count, memory, and storage throughput.

One XTC/TRR or supported LAMMPS trajectory with --top is frame-parallel when the process backend resolves to more than one worker. Every worker opens a private MDAnalysis Universe once and seeks small contiguous batches of selected raw frame indexes; batch size is automatically bounded from 1 to 8, and complete coordinate arrays are not serialized between processes. Parent and worker trajectory readers are explicitly closed. Multiple trajectory files and the compatibility thread backend use the serial trajectory reader.

Process submission uses a bounded rolling queue of at most 3 * workers tasks. This is a queue-depth limit, not a CPU limit: with 100 effective workers SQQ may keep up to 300 tasks submitted while still running as many as 100 workers concurrently. Results are restored to original file/frame order before main-summary writing.

The parent preserves original input order globally and group-local order in every selected group summary and annotated bundle. Output-name collisions are resolved deterministically within each topology group. Process runs set OMP_NUM_THREADS, OPENBLAS_NUM_THREADS, MKL_NUM_THREADS, VECLIB_MAXIMUM_THREADS, NUMEXPR_NUM_THREADS, and BLIS_NUM_THREADS to parallel.math_thread while workers are spawned, then restore the parent environment.

The scheduling and search-cache refinements themselves do not change existing scientific definitions or values. Before the new hydrate descriptors were enabled, they reduced the local 1200ns.gro serial run from about 26.6 s to 18.2 s. A 0.2.3 benchmark that also selected MCG-1 and DHOP35 completed in about 21.6 s on the same host; every overlapping pre-existing analysis column matched the earlier workbook. Performance depends on data, configuration, CPU, memory, and storage.

Search and Report Scope

-s / --size defines the ring-face sizes used during detection and, by default, reporting. YAML ring.report_size and cage.report_type can narrow user-facing output without changing the shared search universe:

ring:
  size: [4, 5, 6]
  report_size: [5, 6]

cage:
  report_type: [I, II]

sqq analyze -i md.gro -c sqq_config.yaml -s 4,5,6

cage.report_type accepts auto, all, I, II, H, HS-I, TS-I, and I2II; group names may be listed together. auto follows the selected search sizes, while all reports every detected cage composition in scope. Do not combine auto or all with named groups.

Repeated cage types contributed by several groups are reported once. All detected cages still participate in half-cage, quasi-cage, free-ring filtering, and hydrate-cluster topology. A report filter changes user-facing cage counts and files, not topology ownership. Cage detection supports 4/5/6 faces; ring and quasi-cage detection also support size 7 in SQQ-Py.

Exact Sparse Cage Search and Scientific Validation

SQQ-Py and SQQ-CPP use the same exact frame-local cage-search contract. The shared topology stores compact ring-to-edge and edge-to-ring incidence. A search branch stores only its selected ring IDs, local edge-use counts, and open-edge frontier; it does not allocate a frame-wide bit mask per ring, edge, or state. Ring centers, normals, and adjacency are built only when another enabled analysis actually needs them.

GROW starts from each canonical seed ring, chooses a constrained open edge, and visits every topologically eligible neighboring ring in deterministic order. Candidate count is never used to prune the search. Per-seed duplicate-state detection is exact and released when that seed finishes. cage.max_boundary_candidate is retained only so older configuration files remain readable; it does not truncate candidates or change the cage set.

cage.max_state_per_seed: 0 and cage.max_total_state: 0 are the defaults and mean unlimited exact search. Positive values are diagnostic safety guards. Reaching either guard aborts the frame with a clear error and publishes no partial result. The former half-cage fast-closure recovery path is disabled; older configurations that request it are normalized to false and record an adjustment in sqq_config_resolved.yaml.

Topology validation is always enabled. Every candidate must use each edge exactly twice, satisfy V - E + F = 2, form one edge-connected face shell, have one cyclic face link around every vertex, and have only trivalent shell vertices. These checks reject disconnected, pinched, branched, and non-manifold false cages before type/isomer assignment in both engines. Accepted cages receive a deterministic final order from cage type, water membership, and face topology, so SQQ-Py and SQQ-CPP assign the same frame-local IDs to the same cage set.

cage.scientific_validation: false is the default. When set to true in YAML, a topologically valid cage must additionally satisfy the configured PBC-aware face-planarity RMS and edge-length coefficient-of-variation limits, nonzero projected face area, and positive minimum triangulated volume. Accepted cages then use the volume centroid instead of the mean cage-water position. Enabling it can therefore remove geometrically distorted cages and can change guest occupancy or geometry-resolved hydrate-cluster edges. Raw ring and half/quasi searches remain unchanged; ownership-filtered free-ring and free-patch outputs can increase when a rejected cage no longer consumes them.

Guest occupancy uses the configured center atom when available. The defaults select CH4, CO2, MET, and ETH as guests and map CH4, CO2, and MET to atom name C, so these residues use their carbon atom under the default guest.center_mode: center_atom. Otherwise, guest atoms are PBC-unwrapped around one molecular anchor before calculating the centroid; the same helper is used by MCG.

Hydrate Cluster

--find-cluster on analyzes every detected cage in the selected search scope. Cages become graph nodes and are connected through complete shared ring faces. When several detected cages reference the same face, ring-plane geometry keeps at most one cage on each physical side. YAML cage.report_type filters user-facing cage tables and files only; it does not remove cages from cluster connectivity or phase evidence.

SQQ classifies hydrate type, domains, and boundaries on a cage-connection graph using labelled shared-face fingerprints, strict local evidence, distributed spatial cores, mutually compatible expansion, and exclusive per-frame domains.

YAML hydrate_cluster.min_cage sets the minimum connected-component size; the default is 2. Smaller components are counted as isolated cages.

Within each cluster, SQQ builds labelled first-shell fingerprints from neighboring cage types and shared-face sizes. Exact sI/sII/sH fingerprints remain high-confidence seeds. In addition, partial but phase-pure fingerprints can form a distributed spatial core: candidates require at least 50% template coverage, 50% phase purity, and a harmonic support score of 0.55; the compatible cage graph must retain a degree-2 core of at least three cages, mean support of 0.60, and the phase-defining hexagonal large-cage connection. The core is anchored by phase-specific cages (5^12 6^2 for sI, 5^12 6^4 for sII, and 4^3 5^6 6^3/5^12 6^8 for sH). All three phases then expand through mutually compatible face-labelled edges when a candidate has at least two accepted phase contacts. Cages claimed exclusively by one phase form deterministic per-frame domains.

After the exclusive sI/sII/sH domains are finalized, SQQ partitions the remaining cluster cages. A cage enters the generic boundary only when it is outside every phase domain and directly shares a complete cage face with at least one domain cage. Boundary search stops at this first external non-phase layer. Domain cages are never relabelled as boundary, and a direct shared-face contact between different phase domains leaves both endpoint cages in their original phases.

The resulting classified_cage_ids, boundary_cage_ids, ambiguous_cage_ids, and unclassified_cage_ids are mutually exclusive and together cover every cage in a reported cluster. Competing phase claims without boundary membership remain ambiguous; all other residual cages are unclassified. There are no sI-boundary, sII-boundary, sH-boundary, transition, or boundary-context categories. Neighboring cages can still share face-water coordinates in structure views, so cage ownership should be verified from cage IDs or detected cage/ring edges rather than coordinate-set overlap.

The default py engine leaves cluster search off unless YAML hydrate_cluster.enabled or explicit --find-cluster on enables it. Engine cpp does not support cluster search. Explicit --find-cluster on|off has highest priority. Cluster search does not alter ring, patch, cage, occupancy, order-parameter, or ice results. Classification is per-frame and independent of the cage reporting filter. Spatial consensus uses only the current frame: it performs no temporal smoothing, so analyzing a frame alone or inside a compatible batch gives the same phase assignment. Temporal grain tracking and crystallographic orientation matching are not implemented.

Cluster search populates every selected info and main-summary output. Split category structures are written only when YAML output.type includes cluster-gro; no documented engine preset includes it by default. The selected main summary output gains its per-frame hydrate_cluster table, while native category structures are written under grouped layout as <frame>/hydrate_cluster/<frame>_cluster_sI.gro, <frame>_cluster_sII.gro, <frame>_cluster_sH.gro, and <frame>_cluster_boundary.gro. Flat layout places the same filenames directly in the frame directory. All same-category domains and clusters are aggregated into one file per frame. An absent category is omitted unless output.write_empty_file: true.

Cluster GRO files contain only complete water molecules belonging to the selected cage IDs; guests and CNT atoms are excluded. Ambiguous, unclassified, and isolated cages are not exported. Every atom keeps the exact wrapped coordinate from the analyzed frame, and every file keeps the original box; categories are never moved or unwrapped independently. Periodic or percolating networks may therefore still show bonds crossing a box face because no single-copy GRO representation can remove every periodic seam.

Cage IDs are mutually exclusive across sI, sII, sH, and boundary, but adjacent category files can contain the same face-water molecules because neighboring cages physically share them. When resolved cluster search is on and info is selected, Frame Information records find_cluster as on and the report adds one compact Hydrate Cluster hierarchy. Domain rows may be sI, sII, or sH; boundary and compact unclassified rows are subdivided by cage type. The compact unclassified count is the deduplicated unresolved set: stored ambiguous and unclassified IDs plus any uncategorized residual cluster cages. Main summary and cluster-detail output preserve the distinct scientific fields. Counts use unique cage IDs, zero-count rows are omitted, multiple clusters appear sequentially, and isolated appears once as the final top-level row without subtype children.

## Hydrate Cluster

| item               | type         | cage_qty |
| ------------------ | ------------ | -------- |
| cluster_00001      | mixed        | 334      |
| ├ domain_00001     | sI           | ├ 66     |
|   ├ 5¹²            |              |   ├ 13   |
|   └ 5¹²6²          |              |   └ 53   |
| ├ domain_00002     | sII          | ├ 194    |
|   ├ 5¹²            |              |   ├ 131  |
|   └ 5¹²6⁴          |              |   └ 63   |
| ├ boundary         | boundary     | ├ 69     |
|   ├ 5¹²            |              |   ├ 24   |
|   └ 5¹²6³          |              |   └ 45   |
| └ unclassified     | unclassified | └ 5      |
|   ├ 5¹²6³          |              |   ├ 2    |
|   └ 4¹5¹⁰6²        |              |   └ 3    |
| isolated           | isolated     | 5        |

The compact table does not include exact IDs, seeds, confidence values, water/guest membership, or domain adjacency. Add cluster-detail to YAML output.type for summary/hydrate_domain.csv and one-row-per-cluster summary/hydrate_cluster_detail.csv. Explicit cluster-detail or cluster-gro selection requires cluster search. Turning search off writes neither cluster-detail nor cluster-gro and removes stale generated cluster GRO files. Public motif output is not generated.

Hydrate Nucleation Order Parameters

MCG-1 and DHOP35 were introduced as defaults in 0.2.5. Since 0.2.7, every MCG/DHOP variant is selected explicitly through --order-parameter; the package default is only f3,f4. These descriptors are independent of the optional cage-topology hydrate_cluster classifier: MCG works on selected methane-like guest centers and surrounding waters, while DHOP works on a dedicated O-O neighbor graph. They do not change graph, ring, patch, cage, occupancy, F3/F4/Q_l, hydrate-cluster, or ice results.

MCG follows the mutually coordinated guest definition. Guest pairs within 0.90 nm are connected when at least five waters lie within 0.60 nm of both guests and inside both 45-degree opposing cones. The threshold is at least five, not exactly five. MCG-1 keeps guest nodes with at least one qualifying MCG edge; optional MCG-3 applies a one-pass degree-at-least-three filter to the same qualifying graph. Connected components are measured only through qualifying MCG edges. The default guest residue names are CH4 and MET; change hydrate_order.mcg_guest_resname for another methane naming convention. If no configured guest type is present, MCG is reported as N/A, not zero.

DHOP builds its own orthorhombic-PBC oxygen graph with hydrate_order.dhop_neighbor_cutoff_nm: 0.35. This 0.35 nm default follows the all-atom TIP4P/Ice implementation used by Li et al.; use 0.325 in YAML when reproducing the original mW-water definition. For each central O-O bond, SQQ counts neighboring plane-normal pairs within 35 degrees (or 30 degrees for DHOP30), selects waters with counts 11 or 12, requires at least three similarly qualified neighbors, includes their first oxygen shell, and reports the largest connected water cluster. DHOP35 and DHOP30 name the angular thresholds, not the O-O cutoff. No transition-state value such as DHOP35=57 is hard-coded; such values are system- and condition-dependent.

Select any combination with names such as --order-parameter mcg1,mcg3,dhop35,dhop30. Selection is separate from the numerical hydrate_order cutoff settings. All cutoff searches use deterministic cell lists and exact float64 minimum-image rechecks; there are no fixed neighbor-array limits.

References: Barnes et al., MCG (DOI 10.1063/1.4871898); Knott et al., MCG nucleation coordinate (DOI 10.1021/jp507959q); DeFever and Sarupria, DHOP (DOI 10.1063/1.4996132); Li et al., all-atom DHOP nucleation pathway (DOI 10.1073/pnas.2011755117).

Public CLI

Analyze exposes this intentionally compact interface:

Migration errors

The former mode spelling is not silently converted:

$ sqq analyze -i md.gro --mode py
Error: --mode has been replaced by --engine.
Use: --engine py

$ sqq analyze -i md.gro -m py
Error: -m has been replaced by -e.
Use: -e py

Likewise, the former plural pair option stops with an actionable error:

$ sqq analyze -i md.gro --pairs water_pairs.txt
Error: --pairs has been replaced by --pair.
Use: --pair water_pairs.txt

These errors exit with status 2. The deprecated spellings are not hidden aliases.

Former advanced CLI settings now belong only in YAML:

The former --cage-fast-closure option is removed. Legacy YAML fast-closure keys remain readable but are normalized to the exact 0.4.1 search with fast_closure: false.

The legacy compatibility names --workers, --no-q, -q, --q-degree, --mcg3, --dhop30, and --topology are removed. Use -w / --worker, --order-parameter, and -t / --top as applicable.

Bond Mode and Pair Files

Use -b / --bond-mode to override YAML graph.mode:

sqq analyze -i md.gro -b auto
sqq analyze -i md.gro --bond-mode hbond
sqq analyze -i md.gro -b oo
sqq analyze -i md.gro -b pairs --pair pairs.txt

--pair PAIRS.txt alone is shorthand for pairs mode. Combining it with explicit -b auto, -b hbond, or -b oo is rejected. Pairs mode requires either --pair or YAML graph.pair_file; the identifier convention is YAML graph.pair_id.

Output Selection

Output selection can be set with --output-type or YAML output.type. Engine py defaults to:

output:
  type: [info, sqq-render, summary-xlsx]

SQQ-Py accepts info, membership-tsv, order-tsv, f3-gro, f4-gro, sqq-render, gro, ring-gro, half-gro, quasi-gro, cage-gro, ice-gro, cluster-gro, summary-xlsx, summary-csv, summary-detail-csv, and cluster-detail, plus default, all, and none. gro expands to ordinary ring/half/quasi/cage/ice GRO categories. sqq-render writes the complete four-file visualization package; its files cannot be selected independently.

SQQ-CPP accepts info, gro, cage-gro, f3-gro, f4-gro, sqq-render, summary-csv, summary-xlsx, and summary-detail-csv, plus default, all, and none. default may be combined with extra types, for example --output-type default,summary-detail-csv; duplicate types are removed. all and none remain exclusive. Removed types sqq-cage-gro and vmd are rejected with a message to use sqq-render. The cpp preset does not select gro or cage-gro by default. Cluster-specific output requires SQQ-Py with resolved cluster search on. sqq_config_resolved.yaml is always written regardless of output.type.

Per-water F3/F4 GRO

--output-type f3-gro and --output-type f4-gro are explicit, non-default outputs supported by both engines. The matching parameter must also be selected, for example --order-parameter f3,f4 --output-type f3-gro,f4-gro. Each file contains only waters with a defined per-water value, but retains every atom of each selected water in source order. Only the oxygen record is annotated (; SQQ F3=<value> or ; SQQ F4=<value>); hydrogen and virtual-site records are unannotated. GRO coordinate columns and available velocity columns remain fixed-width, and the annotation begins after the velocity field. Grouped output is written below <frame>/order/; in separated multi-frame/multi-file output it is below gro/<frame>/order/. Empty files follow output.write_empty_file. These files expose existing per-water values and do not change their calculation.

Output Structure

The layout decision is based on the complete job rather than a particular reader or scheduler. A single ordinary one-frame GRO or XYZ keeps the compact frame-root layout. Every trajectory-like input, including one or more XTC/TRR/LAMMPS/DCD paths or a stacked GRO, and every multi-file GRO/XYZ job uses the separated info/ plus gro/<frame>/ layout in serial, thread, and process execution.

For two or more independent GRO files, topology grouping controls only the aggregation root. If every GRO has one compatible topology, all selected outputs are written directly under the requested result directory:

result/
  sqq_config_resolved.yaml
  summary.xlsx                 # when summary-xlsx is selected
  summary/                     # summary-csv/detail/cluster-detail CSVs
    summary.csv
    cage.csv
    ...
  info/
    frame_001_info.md
    frame_002_info.md
  gro/                         # when any per-frame GRO output is selected
    frame_001/
      order/                   # explicit f3-gro/f4-gro
        frame_001_f3.gro
        frame_001_f4.gro
    frame_002/
  sqq_render/
    sqq_cage.gro              # stable topology and first selected frame
    sqq_cage.xtc              # every selected render frame
    sqq_cage.membership.tsv   # typed frame/center/guest/membership metadata
    sqq_cage.vmd.tcl          # VMD loader and commands

When 2-26 distinct topologies are found, groups are assigned letters by first occurrence and each group gets a complete independent result root. No summary, GRO, or VMD bundle combines incompatible systems:

result/
  sqq_config_resolved.yaml              # batch manifest and source-to-group mapping
  result_A/
    sqq_config_resolved.yaml
    summary.xlsx               # and/or summary/
    info/
    gro/                       # when selected
    sqq_render/                # when selected
      sqq_cage.gro
      sqq_cage.xtc
      sqq_cage.membership.tsv
      sqq_cage.vmd.tcl
  result_B/
    sqq_config_resolved.yaml
    summary.xlsx               # and/or summary/
    info/
    gro/                       # when selected
    sqq_render/                # when selected
      sqq_cage.gro
      sqq_cage.xtc
      sqq_cage.membership.tsv
      sqq_cage.vmd.tcl

If more than 26 topologies are found, SQQ warns and switches the whole multi-GRO run to information-only output. It still analyzes every readable GRO, but writes only the root sqq_config_resolved.yaml and result/info/*_info.md; summary XLSX/CSV/detail files, ordinary GRO files, and the complete sqq_render/ bundle are suppressed. This safety override has precedence over engine defaults and configured output requests.

For every normal multi-frame or multi-file result root, Markdown and optional membership/order TSV reports are placed under info/; selected per-frame structure files are placed under gro/<frame>/. Serial, thread, and process execution use the same placement. No per-frame directory is created merely to hold one Markdown file.

The four files in sqq_render/ form one visualization package. sqq_cage.gro contains the stable atom topology and first selected frame only. sqq_cage.xtc contains the coordinates and box for every selected render frame, with the original physical frame times when available. sqq_cage.membership.tsv uses four record types: F maps render frames to source frames, time, and effective graph mode; C stores every frame-local cage center after orthorhombic PBC wrapping in explicit angstrom coordinates; G stores every complete guest-molecule atom group, including guests outside cages; and M stores cage/guest membership atoms with cage type and optional phase, domain, and cluster identifiers. “Sparse” applies only to the membership metadata: the XTC still contains every selected atom coordinate in every selected frame. Shared waters and guests assigned to several cages retain all memberships.

SQQ permits only one active Analyze run per output root. A concurrent run stops before modifying results and asks for another --output directory. Worker fragments use a private run workspace; final render files are replaced atomically. Temporary-directory removal retries transient Linux/shared-filesystem ENOTEMPTY, EBUSY, and permission delays. If cleanup still fails, SQQ prints the retained temporary path but does not turn an otherwise completed analysis into a failure.

Each frame stages its Markdown, TSV, and selected GRO files privately and publishes the complete frame bundle only after every selected writer succeeds. Summary XLSX/CSV/detail files use the same recoverable publication rule. A failed write removes its staging data rather than exposing empty directories or a mixture of old and new generated files. Reusing an output root clears known SQQ artifacts from previous source names, grouped/flat layouts, and obsolete lettered topology roots, including F3/F4 output; unknown user files remain untouched.

Keep all four files together in sqq_render/, then source only the script from the VMD Tk Console:

source {path/to/result/sqq_render/sqq_cage.vmd.tcl}

Sourcing sets the VMD display background to white, prints a compact welcome, reports SQQ graph: <effective-mode> once, and starts from the default opaque sqq show cage all view. The graph line is printed again only if the effective mode changes. Use any of these equivalent commands for the full guide:

sqq help
sqq -h
sqq --help

The command grammar is explicit:

sqq show <family> <target...> [<family> <target...>]...
sqq color <family> <target...> <color>
sqq clear
sqq show label [on|off]
sqq pick center|guest|off

Supported families are cage, guest, phase, cluster, and domain. Examples:

sqq show cage all
sqq show cage 512
sqq show cage 512 51264
sqq show cage 512 guest 512
sqq show cage 512 51264 guest 512 phase sI

sqq show guest all
sqq show guest 512

sqq show phase all
sqq show phase sI boundary
sqq show cluster all
sqq show cluster cluster_00001
sqq show domain all
sqq show domain domain_00001

sqq color cage 512 green
sqq color cage 51262_00053 yellow
sqq color guest 512 yellow
sqq color phase boundary orange
sqq color cluster cluster_00001 cyan
sqq color cage all default

sqq show label
sqq pick center
sqq pick off

The startup sqq show cage all view is a replaceable default. The first sqq show ... command after sourcing the script or after sqq clear replaces that default; later show commands add independent layers without removing earlier selections. One show may contain several family/target groups, and an exact repeated family/target selection is ignored rather than creating another VMD representation. sqq show label toggles labels; optional on or off sets an explicit state, and the historical misspelling lable is accepted. Labels are off by default and remain independent of picking. sqq pick center makes active objects transparent and creates yellow cage-center spheres/pick points; VMD automatically enters Atom Label mode for graphics picking; click a yellow center to make exactly that cage opaque. Do not manually select Query mode: Query only prints VMD information and does not send the callbacks SQQ needs. Water-atom clicks are ignored in center mode. sqq pick guest automatically enters VMD Pick mode, accepts a click on any guest atom, and highlights the complete guest plus every cage containing it. Cage highlights are yellow and guest highlights are orange. Both pick paths update persistent highlight representations instead of deleting the representation being clicked. Guests with no cage membership are reported without highlighting. Center and guest modes are mutually exclusive. A frame change clears the transient selection and rebuilds the current-frame targets without disabling the chosen mode. sqq pick off exits pick mode but does not restore a previous VMD mouse mode; sqq clear removes custom show/color/label/pick state and restores the initial opaque cage-all view.

Each family token in show starts a new group and consumes the following targets until the next family token. For cage, a target is all, a registered cage type, or an exact frame-local cage ID such as 51262_00053; generic types such as 4^1-5^10-6^2 also accept 4151062. For guest, the same target identifies guests assigned to all cages, to a cage type, or to one frame-local cage ID. Phase targets are all, sI, sII, sH, boundary, ambiguous, unclassified, or isolated; cluster/domain targets are all or exact frame-local IDs. Multiple targets are accepted within each family group. The former inferred forms such as sqq show 512 and sqq color 512 blue are not accepted.

Unlike show, sqq color accepts exactly one family per command. Colors accept a case-insensitive VMD color name, an in-range ColorID, or default. Cage and guest overrides are independent and persist across frame/selection changes until sqq clear, re-sourcing, or an explicit default reset. Cross-family layers always render as phase -> cluster -> domain -> cage -> guest, so guests remain last and visible regardless of show order. This family order is separate from the fixed cage-topology priority used for coincident cage edges and multi-cage guests. Cage networks use DynamicBonds with a 3.5 angstrom cutoff; guests use CPK and include the full molecule. A single cage layer uses a 0.125 angstrom cylinder radius (0.250 angstrom diameter); multi-type layers remain bounded from 0.125 to 0.130 angstrom.

The renderer manages representations by VMD's stable representation names, so show, color, and frame changes remove only SQQ-created representations and preserve representations added by the user. Rapid frame notifications are coalesced into one pending redraw. Fully unknown cage, cage-ID, guest-selection, cluster-ID, and domain-ID targets are rejected against the complete loaded trajectory; recognized phase names remain valid even when the current frame has no matching membership. Re-sourcing a generated script resets its selection/color state.

Cage, cluster, and domain identifiers are deterministic frame-local classifications in 0.4.1; the renderer does not claim cross-frame cage identity. Category selections (phase, cluster, or domain) and recognized phase labels simply report no membership when cluster analysis was not run; an explicit cage/type/cluster/domain target that never occurs anywhere in the loaded trajectory is rejected.

When cage or guest objects are shown, the generated VMD script uses the following stable cage-type colors; guest defaults follow the cage type that selected them. The visible shades follow the active VMD ColorID palette.

Ordinary per-frame GRO files are opt-in through YAML output.type. cluster-gro is separately opt-in and requires cluster search; no documented engine preset includes either category by default. With output.type: [none], only sqq_config_resolved.yaml remains.

With YAML run.strict: false, standalone serial/process/thread read failures become failed summary rows and analysis continues where the reader remains usable. Failed inputs appear in summary.xlsx/failures and <summary_csv_dir>/failures.csv when their respective main-summary output types are enabled, and always in the mandatory sqq_config_resolved.yaml run.failures list. With run.strict: true, SQQ re-raises the error after updating sqq_config_resolved.yaml to status: failed.

GRO structure folders, filenames, and title lines use portable ASCII structure labels since version 0.2.4, for example 5^126^2 and qc_5r_5^36^2_56566. Markdown and main-summary scientific labels retain their readable superscript notation. This avoids Windows GBK/legacy-reader failures caused by Unicode superscript or subscript characters in generated GRO paths and titles.

Each *_info.md report starts with SQQ version, SQQ engine: sqq-py or SQQ engine: sqq-cpp, date/time, source, input format, topology when applicable, resolved sampling metadata for trajectory-like input, half/quasi search state, frame/time, requested-to-effective graph mode, effective bond mode, ring sizes, status, and molecule counts. It never formats the backend as py (sqq-py). LAMMPS reports also record units, timestep, atom style, and type-map source.

When quasi-cage or cage isomers are present, the same report adds description tables:

• Quasi Cage Isomer Description explains each observed layered quasi-cage isomer by base ring and L1/L2/L3 ring sequence.
• Cage Isomer Description explains each observed closed-cage isomer by face composition and 6-ring face adjacency pattern.

Cage Occupancy remains a separate table because it describes guest assignment rather than cage topology. It expands exact guest compositions across dynamic columns in source guest order.

summary-xlsx and summary-csv use one shared main-table builder. SQQ-Py main output contains summary, optional failures, the effective connection table, ring, half_cage, compact composition-level quasi_cage, cage, optional hydrate_cluster, order_parameter, ice, and detail_index when detail files exist. SQQ-CPP emits the applicable subset: summary, optional failures, cage, order_parameter, and optional detail_index. XLSX stores these as sheets; CSV stores one UTF-8-SIG file per table under output.summary_csv_dir (default summary/). summary-detail-csv writes cage_occupancy.csv and cage_isomer.csv for both engines, plus quasi_cage_isomer.csv for SQQ-Py. cluster-detail adds hydrate_domain.csv and hydrate_cluster_detail.csv. Main, detail, and cluster-detail CSV files share the same summary/ directory; they have disjoint filenames and can be selected together. The first summary table is the compact dashboard, failures has one failed input/frame per row, and detail_index lists generated detail files. cage_isomer.csv defaults to observed nonzero isomer rows plus per-frame totals; YAML output.cage_isomer_row: all restores the zero-filled matrix. order_parameter contains only the selected F3, F4, Q_l, MCG, and DHOP columns; --order-parameter none omits it.

Summary construction records rows, columns, cells, bytes, CSV/XLSX write time, formatting time, and final-save time in sqq_config_resolved.yaml -> run.summary_write; the terminal prints its total seconds. The mandatory output-root sqq_config_resolved.yaml records final SQQ version, requested engine, effective SQQ engine, requested and effective graph modes, requested and resolved workers, normalized output types, input metadata, status/failures, and summary timing. Main CSV, XLSX, detail CSV, and sqq_config_resolved.yaml are written to same-directory temporary files and atomically replaced on success or failure. XLSX sheets above 200,000 cells or 128 columns keep header styling, filter, freeze pane, and fixed column widths but skip costly body-cell formatting; scientific values and table schemas are unchanged.

The hydrate_cluster main-summary table reports the mutually exclusive classified_cage_count, boundary_cage_count, ambiguous_cage_count, and unclassified_cage_count. Optional cluster-detail CSV records add the corresponding cage-id groups and boundary_composition; hydrate-domain CSV records expose only external boundary contacts through external_boundary_contact_count and external_boundary_contact_ids.

Output ownership is:

cage > quasi_cage > half_cage > ring

SQQ-Py cage files include cage waters, CNT center pseudoatoms, and assigned guests. SQQ-CPP cage files omit the synthetic CNT center pseudoatom. Exact guest-composition files are generated from the guest names present in the frame, such as CH4, CH4x2, or CH4+CO2.

See docs/design.md for algorithm details and docs/update.md for release changes.