pasted 0.3.0

Pointless Atom STructure with Entropy Diagnostics — structure fuzzer for QC/ML-potential codes

PASTED

Pointless Atom STructure with Entropy Diagnostics

PASTED is a structure fuzzer for quantum chemistry (QC) and machine-learning potential (MLP) codes. It generates intentionally random, physically meaningless atomic structures and quantifies their disorder through a suite of 13 structural metrics. Useful for stress-testing structure optimizers, generating worst-case inputs for QC codes, or exploring what "maximum chaos" looks like in structural space.

Features

• Four placement modes — random gas (gas), chain-growth (chain), coordination-complex-like (shell), and maximum-entropy (maxent)
• 13 disorder metrics computed per structure, all usable as output filters
• Element pool specified by atomic number (Z = 1–106); composition sampled randomly per structure
• Guaranteed atom count — post-placement L-BFGS repulsion relaxation ensures --n-atoms atoms are always delivered regardless of initial density
• Auto-scaled --cutoff — defaults to cov_scale × 1.5 × median(r_i + r_j) over the element pool; all graph, Steinhardt, ring, and charge metrics share this single cutoff
• Structure optimizer — StructureOptimizer runs simulated annealing or basin-hopping on an existing structure to maximize a user-defined disorder objective
• Charge/multiplicity parity validation, reproducible via --seed, incremental output via stream()

Requirements

Python >= 3.10
numpy
scipy

A C++17 compiler is required to build the optional acceleration extensions (~25x speedup for compute_all_metrics at N=1000). If no compiler is available, the package falls back to pure Python/NumPy transparently.

Installation

pip install pasted

or from source:

git clone https://github.com/ss0832/pasted.git
cd pasted
pip install -e .
# or run directly without installing:
python pasted.py --help

Verify that the C++ extensions compiled successfully:

from pasted._ext import HAS_RELAX, HAS_MAXENT, HAS_STEINHARDT, HAS_GRAPH
print(HAS_RELAX, HAS_MAXENT, HAS_STEINHARDT, HAS_GRAPH)
# True True True True  ->  all acceleration active

Quick Start

# 10 atoms drawn from H-Zn, placed randomly in a sphere
pasted --n-atoms 10 --elements 1-30 --charge 0 --mult 1 \
    --mode gas --region sphere:8

# Chain structure (C/N/O), 20 samples, filter by disorder
pasted --n-atoms 15 --elements 6,7,8 --charge 0 --mult 1 \
    --mode chain --branch-prob 0.4 --n-samples 20 \
    --filter "H_total:2.0:-" -o organic_junk.xyz

# Coordination-complex-like structure with Fe center
pasted --n-atoms 12 --elements 6,7,8,26 --charge 0 --mult 1 \
    --mode shell --center-z 26 --coord-range 4:6 --n-samples 10

# Stop as soon as 10 disordered structures are found
pasted --n-atoms 15 --elements 1-30 --charge 0 --mult 1 \
    --mode gas --region sphere:8 \
    --filter "H_total:2.0:-" --n-success 10 --n-samples 500 \
    -o disordered.xyz

# Select spatially random electronegativity arrangements (Moran's I near 0)
pasted --n-atoms 50 --elements 1-30 --charge 0 --mult 1 \
    --mode gas --region sphere:12 --n-samples 200 \
    --filter "moran_I_chi:-0.1:0.1" -o random_en.xyz

Placement Modes

gas (default)

Atoms placed uniformly at random inside a sphere or box. No clash checking at placement time — repulsion relaxation resolves all violations afterward.

--region sphere:R       sphere of radius R Angstrom
--region box:L          cube of side L Angstrom
--region box:LX,LY,LZ   orthorhombic box

chain

Atoms grow one by one from a seed via a random walk with directional persistence. Produces elongated, tree-like structures.

--branch-prob FLOAT     branching probability (default: 0.3)
--chain-persist FLOAT   directional persistence 0.0-1.0 (default: 0.5)
--chain-bias FLOAT      global axis drift; higher -> more rod-like (default: 0.0)
--bond-range LO:HI      bond length range Angstrom (default: 1.2:1.6)

shell

One center atom surrounded by a coordination shell, plus tail atoms grown from shell members. Resembles coordination complexes.

--center-z Z            atomic number of center atom (default: random)
--coord-range MIN:MAX   coordination number range (default: 4:8)
--shell-radius LO:HI    shell radius range Angstrom (default: 1.8:2.5)
--bond-range LO:HI      tail bond length range Angstrom (default: 1.2:1.6)

maxent

Atoms start from a random gas placement and are repositioned by gradient descent on an angular repulsion potential, spreading neighbor directions as uniformly over the sphere as the distance constraints allow.

--region SPEC           same as gas mode (required)
--maxent-steps N        gradient-descent iterations (default: 300)
--maxent-lr LR          learning rate (default: 0.05)
--maxent-cutoff-scale S neighbour cutoff scale factor (default: 2.5)

Element Pool

--elements SPEC

Syntax	Meaning
1-30	Z = 1 through 30 (H to Zn)
6,7,8	Z = 6, 7, 8 (C, N, O)
1-10,26,28	Z = 1-10 plus Fe(26) and Ni(28)
(omitted)	all Z = 1-106

If H (Z = 1) is in the pool and the sampled composition contains no hydrogen, a random number of H atoms is automatically appended. Disable with --no-add-hydrogen.

Interatomic Distance Control

PASTED enforces a minimum interatomic distance using Pyykkoe single-bond covalent radii (Pyykkoe & Atsumi, Chem. Eur. J. 15, 186-197, 2009):

d_min(i, j) = cov_scale x (r_i + r_j)

Default --cov-scale 1.0. Post-placement relaxation uses L-BFGS to minimize a harmonic penalty energy until all violations are resolved (or --relax-cycles is exhausted).

Disorder Metrics

All 13 metrics are computed for every structure and embedded in the XYZ comment line. All are usable in --filter.

Metric	Description	Range
H_atom	Shannon entropy of element composition	>= 0
H_spatial	Shannon entropy of pairwise-distance histogram	>= 0
H_total	w_atom * H_atom + w_spatial * H_spatial	>= 0
RDF_dev	RMS deviation of empirical g(r) from ideal-gas baseline	>= 0
shape_aniso	Relative shape anisotropy from gyration tensor	[0, 1]
Q4, Q6, Q8	Steinhardt bond-order parameters	[0, 1]
graph_lcc	Largest connected-component fraction at cutoff	[0, 1]
graph_cc	Mean clustering coefficient at cutoff	[0, 1]
ring_fraction	Fraction of atoms in at least one cycle in the cutoff-adjacency graph	[0, 1]
charge_frustration	Variance of	delta-chi
moran_I_chi	Moran's I spatial autocorrelation for Pauling electronegativity	unbounded

Unified cutoff

Five metrics share a single adjacency definition: a pair (i, j) is "adjacent" when d_ij <= cutoff. These are graph_lcc, graph_cc, ring_fraction, charge_frustration, and moran_I_chi. Using a unified cutoff prevents the zero-value pathology that occurs when a covalent-radius threshold is used for bond detection in relaxed structures (relax_positions guarantees d_ij >= cov_scale * (r_i + r_j)).

The auto cutoff is printed to stderr:

[cutoff] 2.130 Ang (auto: cov_scale=1.0 x 1.5 x median(r_i+r_j)=1.420 Ang)

Override with --cutoff FLOAT when needed.

Moran's I interpretation

moran_I_chi measures how randomly Pauling electronegativity is distributed in space:

Value	Meaning
I near 0	Random spatial arrangement — the target for disordered structures
I > 0	Atoms of similar electronegativity cluster spatially (phase separation)
I < 0	Alternating high/low electronegativity (NaCl-like ionic order)

Note: Moran's I is not bounded to [-1, 1] for sparse weight matrices.

ring_fraction and charge_frustration

ring_fraction counts the fraction of atoms that belong to at least one cycle in the cutoff-adjacency graph (detected via Union-Find spanning tree). charge_frustration measures the variance of |delta-chi| across all adjacent pairs — high values indicate strongly heterogeneous electrostatic environments.

Filtering

--filter METRIC:MIN:MAX

Use - for an open bound. Multiple flags are ANDed together.

--filter "H_total:2.0:-"          # H_total >= 2.0
--filter "Q6:-:0.3"               # Q6 <= 0.3
--filter "shape_aniso:0.5:-"      # rod-like structures
--filter "graph_lcc:0.8:-"        # well-connected graph
--filter "moran_I_chi:-0.1:0.1"   # spatially random electronegativity

Output Format

12
sample=3 mode=chain charge=+0 mult=1 comp=[C:4,N:5,O:3]  H_atom=1.0986 ... moran_I_chi=-0.0312
C       1.234567    -0.987654     2.345678
N      -1.456789     3.210987    -0.123456
...

pasted ... -o out.xyz          # XYZ to file, progress to terminal
pasted ... 2>/dev/null | tool  # pipe XYZ, discard progress
pasted ... -o /dev/null        # progress only (check filter hit rate)

Python API

Functional API

from pasted import generate

structures = generate(
    n_atoms=12, charge=0, mult=1,
    mode="gas", region="sphere:9",
    elements="1-30", n_samples=50, seed=42,
    filters=["H_total:2.0:-"],
)
for s in structures:
    print(s)           # Structure(n=14, comp='C2H8N2O2', mode='gas', H_total=2.341)
    print(s.to_xyz())

Class API with n_success

from pasted import StructureGenerator

gen = StructureGenerator(
    n_atoms=15, charge=0, mult=1,
    mode="gas", region="sphere:8",
    elements="1-30",
    n_success=10,   # stop when 10 structures pass
    n_samples=500,  # give up after 500 attempts
    filters=["H_total:2.0:-"],
    seed=42,
)
structures = gen.generate()

Streaming output

for s in gen.stream():
    s.write_xyz("out.xyz")   # written immediately on each PASS

Structure attributes

s = structures[0]
s.atoms        # ['C', 'N', 'H', ...]
s.positions    # [(x, y, z), ...]
s.metrics      # {'H_atom': 1.09, 'moran_I_chi': -0.03, ...}
s.charge       # 0
s.mult         # 1
s.mode         # 'gas'
s.sample_index # 1
len(s)         # 12

Structure optimizer

from pasted import StructureOptimizer

opt = StructureOptimizer(
    n_atoms=50, charge=0, mult=1,
    objective={"H_total": 1.0, "Q6": -2.0},
    elements="24,25,26,27,28",   # Cantor alloy
    method="annealing",
    max_steps=5000,
    lcc_threshold=0.8,
    seed=42,
)
best = opt.run()

Accessing metrics

s = structures[0]
print(s.metrics["H_total"])
print(s.metrics["moran_I_chi"])   # new in v0.1.12
print(s.metrics["ring_fraction"]) # non-zero in v0.1.13+

Full Option Reference

required:
  --n-atoms N           number of atoms per structure
  --charge INT          total system charge
  --mult INT            spin multiplicity 2S+1

placement mode:
  --mode {gas,chain,shell,maxent}
  --region SPEC         [gas/maxent] sphere:R | box:L | box:LX,LY,LZ
  --branch-prob FLOAT   [chain] branching probability (default: 0.3)
  --chain-persist FLOAT [chain] directional persistence 0.0-1.0 (default: 0.5)
  --chain-bias FLOAT    [chain] global axis drift (default: 0.0)
  --bond-range LO:HI    [chain/shell] bond length range Ang (default: 1.2:1.6)
  --center-z Z          [shell] fix center atom by atomic number
  --coord-range MIN:MAX [shell] coordination number range (default: 4:8)
  --shell-radius LO:HI  [shell] shell radius range Ang (default: 1.8:2.5)
  --maxent-steps N      [maxent] gradient-descent iterations (default: 300)
  --maxent-lr LR        [maxent] learning rate (default: 0.05)
  --maxent-cutoff-scale S [maxent] neighbour cutoff scale (default: 2.5)

elements:
  --elements SPEC       atomic-number spec (default: all Z=1-106)

physical constraints:
  --cov-scale FLOAT     d_min = cov_scale x (r_i + r_j) (default: 1.0)
  --relax-cycles INT    max L-BFGS iterations for repulsion relaxation (default: 1500)
  --no-add-hydrogen     disable automatic H augmentation

sampling:
  --n-samples INT       number of structures to attempt (default: 1)
  --n-success INT       stop after this many passing structures
  --seed INT            random seed

metrics:
  --n-bins INT          histogram bins for H_spatial and RDF_dev (default: 20)
  --w-atom FLOAT        H_atom weight in H_total (default: 0.5)
  --w-spatial FLOAT     H_spatial weight in H_total (default: 0.5)
  --cutoff FLOAT        unified adjacency cutoff Ang for all five cutoff-based
                        metrics (default: auto = cov_scale x 1.5 x median(r_i+r_j))

filtering:
  --filter METRIC:MIN:MAX   repeatable; use - for open bound

output:
  --validate            check charge/mult against one random composition, then exit
  -o / --output FILE    XYZ output file (default: stdout)
  --verbose             print per-sample metrics to stderr

Notes and Limitations

• Repulsion relaxation uses L-BFGS (harmonic penalty energy, convergence criterion E < 1e-12). If [warn] relax_positions did not converge appears, the structure may contain marginal distance violations. Increase --relax-cycles.
• Unified cutoff: the five cutoff-based metrics all use the same cutoff parameter. Ring detection and charge frustration are computed on the cutoff-adjacency graph, not the covalent-radius bond graph, so they yield informative non-zero values in relaxed structures.
• Moran's I range: not bounded to [-1, 1] for sparse weight matrices. Use it as a relative indicator.
• Pyykkoe radii: for Z > 86 (Fr through Sg), same-group proxies are used.
• Noble gas EN: He/Ne/Ar/Rn = 4.0; Kr = 3.0; Xe = 2.6 (literature estimates from Allen/Allred-Rochow scale).

License

MIT License. See LICENSE.