xyzgraph 1.0.9

Convert xyz molecule file to a graph.

xyzgraph: Molecular Graph Construction from Cartesian Coordinates

xyzgraph is a Python toolkit for building molecular graphs (bond connectivity, bond orders, formal charges, and partial charges) directly from 3D atomic coordinates in XYZ format. It provides both cheminformatics-based and quantum chemistry-based (xTB) workflows.

---

Table of Contents

1. Key Features
2. Installation
3. Quick Start
4. Methodology Overview
5. Workflow Comparison
6. CLI Reference
7. Python API
8. Visualization
9. Limitations & Future Work
10. Examples
11. References
12. Contributing & Contact

---

Key Features

• Distance-based initial bonding using consistent van der Waals radii across all elements from Charry and Tkatchenko [1]
• Two construction methods:
  • cheminf: Pure cheminformatics with bond order optimization
  • xtb: semi-empirical calculation of bond orders via xTB Wiberg bond orders with Mulliken charges [2]
• Cheminformatics modes:
  • --quick: Fast (crude) valence adjustment
  • Full optimization with valence and charge minimisation
    • --optimizer:
      beam: optimization across multiple paths (slightly slower, default)
      greedy: iterative valence adjustment
• Aromatic detection: Hückel 4n+2 rule for 6-membered rings
• Charge computation: Gasteiger (cheminf) or Mulliken (xTB) partial charges
• RDkit/xyz2mol comparison validation against RDKit bond perception [3], [4]
• ASCII 2D depiction with layout alignment for method comparison (see also [5])

---

Installation

From PyPI

pip install xyzgraph

From Source

git clone https://github.com/aligfellow/xyzgraph.git
cd xyzgraph
pip install .
# or simply
pip install git+https://github.com/aligfellow/xyzgraph.git

Dependencies

• Core: numpy, networkx, rdkit
• Optional: xTB binary (for --method xtb)

To install xTB (Linux/macOS) see here:

conda install -c conda-forge xtb # or download from GitHub releases

---

Quick Start

CLI Examples

Minimal usage (auto-displays ASCII depiction):

xyzgraph molecule.xyz

Specify charge and method:

xyzgraph molecule.xyz --method xtb --charge -1 --multiplicity 2

Detailed debug output:

xyzgraph molecule.xyz --debug

Compare with RDKit:

xyzgraph molecule.xyz --compare-rdkit

Python Example

Basic usage:

from xyzgraph import build_graph, graph_to_ascii, read_xyz_file

atoms = read_xyz_file("molecule.xyz") 
G = build_graph(atoms, charge=0)
# OR
G = build_graph("molecule.xyz", charge=0)

# Print ASCII structure
print(graph_to_ascii(G, scale=3.0, include_h=False))

---

Methodology Overview

Design Philosophy

xyzgraph offers two distinct pathways for molecular graph construction:

1. Cheminformatics Path (method='cheminf'):

   • Pure graph-based approach using chemical heuristics
   • No external quantum chemistry calls
   • Cached scoring, valence, edge and graph properties
   • Fast and suitable for both organic and inorganic molecules

2. Quantum Chemistry Path (method='xtb'):

   • Uses GFN2-xTB (extended tight-binding) calculations [2]
   • Reads in Wiberg bond orders and Mulliken charges from output
   • Potentially more accurate for unusual bonding situations
     • though, xTB may be less robust in these situations
   • Requires xTB binary installation

Cheminformatics Workflow (method='cheminf')

┌─────────────────────────────────────────────────────────────────┐
│ 1. Input Processing                                             │
│    • Parse XYZ file internally                                  │
│    • Load reference data (VDW radii, valences, electrons)       │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 2. Initial Bond Graph (Two-Step Construction)                   │
│                                                                 │
│    Step 1: Baseline Bonds (DEFAULT thresholds)                  │
│    • Uses DEFAULT threshold parameters (threshold=1.0)          │
│    • Builds reliable "core" connectivity                        │
│    • Bonds sorted by confidence: 1.0 (short) to 0.0 (at thresh) │
│    • High confidence (>0.4): added directly                     │
│    • Low confidence (≤0.4): geometric validation applied        │
│    • Result: stable molecular scaffold                          │
│    • Compute rings using NetworkX cycle_basis                   │
│                                                                 │
│    Step 2: Extended Bonds (if using CUSTOM thresholds)          │
│    • Sorted highest-confidence-first (most reliable first)      │
│    • Additional bonds require geometric validation:             │
│      - Acute angle check: 15° (metals) / 30° (non-metals)       │
│      - Collinearity check: trans vs spurious detection          │
│      - Existing ring diagonal rejection and 3-ring validation   │
│    • Allows sensible elongated bonds (e.g., TS structures)      │
│                                                                 │
│    • Create graph with single bonds (order = 1.0)               │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 3. Kekulé Initialization for Conjugated Rings                   │
│    • Find 5/6-membered planar rings with C/N/O/S/B/P/Se         │
│    • Initialize alternating bond orders (5-ring: 2-1-2-1-1,     │
│      6-ring: 2-1-2-1-2-1)                                       │
│    • Handle fused rings (naphthalene, anthracene):              │
│      - Detecting shared edges from previous rings               │
│      - Validated across extended ring system                    │
│    • Gives optimizer excellent starting point                   │
│    • Reduces iterations needed for conjugated systems           │
│    • Broader atom set than aromatic detection (P, Se included)  │
└────────────────────┬────────────────────────────────────────────┘
                     │
          ┌──────────┴─────────────┐
          │                        │
┌─────────▼────────────┐   ┌───────▼──────────────────────────────┐
│ 4a. Quick Mode       │   │ 4b. Full Optimization                │
│  • Lock metal bonds  │   │  • Lock metal bonds at 1.0           │
│  • 3 iterations      │   │  • Iterative BIDIRECTIONAL search:   │
│  • Promote bonds     │   │    - Test both +1 AND -1 changes     │
│    where both atoms  │   │    - Allows Kekulé structure swaps   │
│    need increased    │   │  • Score = f(valence_error,          │
│    valence           │   │             formal_charges,          │
│  • Distance check    │   │             electronegativity,       │
│                      │   │             conjugation_penalty)     │
│                      │   │  • Optimizer choice:                 │
│                      │   │    - Beam: parallel hypotheses       │
│                      │   │    - Greedy: single best change      │
│                      │   │  • Cache where possible for speed    │
│                      │   │  • Top-k edge candidate selection    │
└─────────┬────────────┘   └──────────┬───────────────────────────┘
          └───────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 5. Aromatic Detection (Hückel 4n+2)                             │
│    • Find 5/6-membered rings with C/N/O/S/B                     │
│    • Count π electrons (sp² carbons → 1e, N/O/S LP → 2e)        │
│    • Apply Hückel rule: 4n+2 π electrons                        │
│    • Set aromatic bonds to 1.5                                  │
│    • Other heteroatoms (e.g. P, Se) use Kekulé structures       │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 6. Formal Charge Assignment                                     │
│    • For each non-metal atom:                                   │
│      - B = 2 × Σ(bond_orders)                                   │
│      - L = max(0, target - B)  [target: 2 for H, 8 otherwise]   │
│      - formal = V_electrons - (L + B/2)                         │
│    • Balance total to match system charge                       │
│    • Metals forced to 0 (coordination not oxidation state)      │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 7. Gasteiger Partial Charges                                    │
│    • Convert bond orders to RDKit bond types                    │
│    • Compute Gasteiger charges                                  │
│    • Adjust for total charge conservation                       │
│    • Aggregate H charges onto heavy atoms                       │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 9. Output Graph                                                 │
│    Nodes: symbol, formal_charge, charges{}, agg_charge, valence │
│    Edges: bond_order, bond_type, metal_coord                    │
└─────────────────────────────────────────────────────────────────┘

xTB Workflow (method='xtb')

┌─────────────────────────────────────────────────────────────────┐
│ 1. Input Processing                                             |
│    • Parse XYZ file internally                                  │
│    • Write XYZ to temporary directory                           │
│    • Set up xTB calculation parameters                          │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 2. Run xTB Calculation                                          │
│    Command: xtb <file>.xyz --chrg <charge> --uhf <unpaired>     │
│    • GFN2-xTB Hamiltonian                                       │
│    • Single-point calculation                                   │
│    • Wiberg bond order analysis                                 │
│    • Mulliken population analysis                               │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 3. Parse xTB Output                                             │
│    • Read wbo file (Wiberg bond orders)                         │
│    • Read charges file (Mulliken atomic charges)                │
│    • Threshold: bond_order > 0.5 → create edge                  │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 4. Build Graph from xTB Data                                    │
│    • Create nodes with Mulliken charges                         │
│    • Create edges with Wiberg bond orders                       │
│    • No further optimization needed                             │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 5. Cleanup (optional)                                           │
│    • Remove temporary xTB files (unless --no-clean)             │
└────────────────────┬────────────────────────────────────────────┘
                     │
┌────────────────────▼────────────────────────────────────────────┐
│ 6. Output Graph                                                 │
│    Nodes: symbol, charges{'mulliken': ...}, agg_charge, valence │
│    Edges: bond_order (Wiberg), bond_type, metal_coord           │
└─────────────────────────────────────────────────────────────────┘

---

Workflow Comparison

Feature	cheminf (quick)	cheminf (full)	xtb
Speed	Very Fast	Fast	Moderate
Accuracy	Okay for simple molecules	Very good across various systems	Only limited by xTB performance (QM-based)
External deps	None	None	Requires xTB binary
Bond orders	Heuristic (integer-like)	Optimized formal charge and valency	Wiberg (fractional)
Charges	Gasteiger	Gasteiger	Mulliken
Metal complexes	Limited	Reasonable	Reasonable (limited by xTB metal performance)
Conjugated systems	Basic	Excellent	Excellent
Best for	Quick checks, where connectivity most important	Most cases	Awkward bonding, validation

When to Use Each Method

Use --method cheminf (default):

• Most use cases
• No xTB installation available
• Batch processing structures

Use --method cheminf --quick:

• Extremely large molecules
• Initial rapid screening
• When approximate bond orders suffice

Use --method xtb:

• Validation of cheminf results
• Unusual electronic structures
• Low confidence in bonding structure

Optimizer Algorithms (cheminf full mode only)

Beam Search Optimizer (--optimizer beam default, --beam-width 3 default):

• Explores multiple optimization paths in parallel
• Maintains top-k hypotheses at each iteration (of top candidates)
• Bidirectional: tests both +1 and -1 bond orders for each hypothesis
• More robust against local minima
• Slower, but better convergence
• Best for robust bonding assignment across periodic table

Greedy Optimizer (--optimizer greedy):

• Tests all top candidate edges, picks single best change per iteration
• Bidirectional: tests both +1 and -1 bond order changes
• Fast and effective for most molecules
• Can get stuck in local minima (e.g. alpha, beta unsaturated systems)

---

CLI Reference

Command Syntax

> xyzgraph -h
usage: xyzgraph [-h] [--method {cheminf,xtb}] [-q] [--max-iter MAX_ITER] [--edge-per-iter EDGE_PER_ITER] [-o {greedy,beam}] [-bw BEAM_WIDTH] [--bond BOND]
                [--unbond UNBOND] [-c CHARGE] [-m MULTIPLICITY] [-b] [-d] [-a] [-as ASCII_SCALE] [-H] [--compare-rdkit] [--no-clean]
                xyz

Build molecular graph from XYZ.

positional arguments:
  xyz                   Input XYZ file

options:
  -h, --help            show this help message and exit
  --method {cheminf,xtb}
                        Graph construction method (default: cheminf) (xtb requires xTB binary installed and available in PATH)
  -q, --quick           Quick mode: fast heuristics, less accuracy (NOT recommended)
  --max-iter MAX_ITER   Maximum iterations for bond order optimization (default: 50, cheminf only)
  -t THRESHOLD, --threshold THRESHOLD
                        vdW Scaling factor for bond detection thresholds (default: 1.0)
  --edge-per-iter EDGE_PER_ITER
                        Number of edges to adjust per iteration (default: 10, cheminf only)
  -o {greedy,beam}, --optimizer {greedy,beam}
                        Optimization algorithm (default: beam, cheminf , BEAM recommended)
  -bw BEAM_WIDTH, --beam-width BEAM_WIDTH
                        Beam width for beam search (default: 5). i.e. number of candidate graphs to retain per iteration
  --bond BOND           Specify atoms that must be bonded in the graph construction. Example: --bond 0,1 2,3
  --unbond UNBOND       Specify that two atoms indices are NOT bonded in the graph construction. Example: --unbond 0,1 1,2
  -c CHARGE, --charge CHARGE
                        Total molecular charge (default: 0)
  -m MULTIPLICITY, --multiplicity MULTIPLICITY
                        Spin multiplicity (auto-detected if not specified)
  -b, --bohr            XYZ file provided in units bohr (default is Angstrom)
  -d, --debug           Enable debug output (construction details + graph report)
  -a, --ascii           Show 2D ASCII depiction (auto-enabled if no other output)
  -as ASCII_SCALE, --ascii-scale ASCII_SCALE
                        ASCII scaling factor (default: 3.0)
  -H, --show-h          Include hydrogens in visualizations (hidden by default)
  --show-h-idx SHOW_H_IDX
                        Show specific hydrogen atoms by index (comma-separated, e.g., '3,7,12')
  --compare-rdkit       Compare with xyz2mol output (uses rdkit implementation)
  --no-clean            Keep temporary xTB files (only for --method xtb)
  --threshold-h-nonmetal THRESHOLD_H_NONMETAL
                        ADVANCED: vdW threshold for H-nonmetal bonds (default: 0.42)
  --threshold-h-metal THRESHOLD_H_METAL
                        ADVANCED: vdW threshold for H-metal bonds (default: 0.5)
  --threshold-metal-ligand THRESHOLD_METAL_LIGAND
                        ADVANCED: vdW threshold for metal-ligand bonds (default: 0.65)
  --threshold-nonmetal THRESHOLD_NONMETAL
                        ADVANCED: vdW threshold for nonmetal-nonmetal bonds (default: 0.55)

Method comparison:

xyzgraph molecule.xyz --debug > cheminf.txt
xyzgraph molecule.xyz --method xtb --debug > xtb.txt
diff cheminf.txt xtb.txt

Validate against RDKit:

xyzgraph molecule.xyz --compare-xyz2mol

---

Python API

Direct graph construction:

from xyzgraph import build_graph, graph_debug_report

# Cheminf full optimization
G_full = build_graph(
      atoms='molecule.xyz',
      charge=0,
      max_iter=50,              # maximum iterations (normally converged <20)
      edge_per_iter=6,          # default 10
      bond=[(0,1)],             # ensure a bond between 0 and 1
      debug=True
   )

---

Visualization

ASCII Depiction

xyzgraph includes a built-in ASCII renderer for 2D molecular structures. This is heavily inspired by work elsewhere, e.g. [5] by Andrew White.

from xyzgraph import graph_to_ascii

# Basic rendering
ascii_art = graph_to_ascii(G, scale=3.0, include_h=False)
print(ascii_art)

Output example (acyl isothiouronium):

                                       C
                                        \
                                        \
                                         C-------C
                                      ///
        ---C-               /C-------C
    C---     ---          //          \           /C----
   /            -C------N\            \          /      ---C
  C             /        \\           /C-------C/           \\
   \\          /          \\        //          \             C
     \\    ---C-          -C\-----N/            \           //
       C---     ----   ---         \             C---     //
                    -S-             \                ----C
                                    /C===
                                  // =======O
                                C\       ====
                                 \\
                                  \\
                                  /C\
                                //
                              C/

Features:

• Single bonds: -, |, /, \
• Double bonds: =, ‖ (parallel lines)
• Triple bonds: #
• Aromatic: 1.5 bond orders shown as single
• Special edges: * (TS), . (NCI) if G.edges[i,j]['TS']=True

Layout Alignment

Compare methods by aligning their ASCII depictions:

from xyzgraph import build_graph, graph_to_ascii

# Build with both methods
G_cheminf = build_graph(atoms, method='cheminf')
G_xtb = build_graph(atoms, method='xtb')

# Generate aligned depictions
ascii_ref, layout = graph_to_ascii(G_cheminf)
ascii_xtb = graph_to_ascii(G_xtb, reference_layout=layout)

print("Cheminf:\n", ascii_ref)
print("\nxTB:\n", ascii_xtb)

Debug Report

Tabular listing of all atoms and bonds:

from xyzgraph import graph_debug_report

report = graph_debug_report(G, include_h=False)
print(report)

Full example:

> xyzgraph benzene_NH4-cation-pi.xyz -c 1 -a -d

============================================================
BUILDING GRAPH (CHEMINF, FULL MODE)
Atoms: 17, Charge: 1, Multiplicity: 1
============================================================

  Added 17 atoms
  Initial bonds: 16
  Found 1 rings
  Initial bonds: 16
  Pruning distorted rings (sizes: [3, 4])
  Initialized 1 6-membered carbon rings with Kekulé pattern
============================================================
  
BEAM SEARCH OPTIMIZATION (width=3)
============================================================
  Initial score: 15.50
  
Iteration 1:
      No improvements found in any beam, stopping
  
Applying best solution to graph...
------------------------------------------------------------
  Explored 13 states across 1 iterations
  Found 0 improvements
  Score: 15.50 → 15.50
------------------------------------------------------------

============================================================
AROMATIC RING DETECTION (Hückel 4n+2)
============================================================
  
Ring 1 (6-membered): ['C0', 'C1', 'C2', 'C3', 'C4', 'C5']
    π electrons: 6 (C0:1, C1:1, C2:1, C3:1, C4:1, C5:1)
    ✓ AROMATIC (4n+2 rule: n=1)

------------------------------------------------------------
  SUMMARY: 1 aromatic rings, 6 bonds set to 1.5
------------------------------------------------------------

    Gasteiger charge calculation failed: Explicit valence for atom # 12 N, 4, is greater than permitted

============================================================
GRAPH CONSTRUCTION COMPLETE
============================================================

# Molecular Graph: 17 atoms, 16 bonds
# total_charge=1  multiplicity=1  sum(gasteiger)=+1.000  sum(gasteiger_raw)=+0.000
# (C–H hydrogens hidden; heteroatom-bound hydrogens shown; valences still include all H)
# [idx] Sym  val=.. chg=.. agg=.. | neighbors: idx(order / aromatic flag)
[  0]  C  val=4.00  formal=+0  chg=+0.059  agg=+0.118 | 1(1.50*) 5(1.50*)
[  1]  C  val=4.00  formal=+0  chg=+0.059  agg=+0.118 | 0(1.50*) 2(1.50*)
[  2]  C  val=4.00  formal=+0  chg=+0.059  agg=+0.118 | 1(1.50*) 3(1.50*)
[  3]  C  val=4.00  formal=+0  chg=+0.059  agg=+0.118 | 2(1.50*) 4(1.50*)
[  4]  C  val=4.00  formal=+0  chg=+0.059  agg=+0.118 | 3(1.50*) 5(1.50*)
[  5]  C  val=4.00  formal=+0  chg=+0.059  agg=+0.118 | 0(1.50*) 4(1.50*)
[ 12]  N  val=4.00  formal=+1  chg=+0.059  agg=+0.294 | 13(1.00) 14(1.00) 15(1.00) 16(1.00)
[ 13]  H  val=1.00  formal=+0  chg=+0.059  agg=+0.059 | 12(1.00)
[ 14]  H  val=1.00  formal=+0  chg=+0.059  agg=+0.059 | 12(1.00)
[ 15]  H  val=1.00  formal=+0  chg=+0.059  agg=+0.059 | 12(1.00)
[ 16]  H  val=1.00  formal=+0  chg=+0.059  agg=+0.059 | 12(1.00)

# Bonds (i-j: order) (filtered)
[ 0- 1]: 1.50
[ 0- 5]: 1.50
[ 1- 2]: 1.50
[ 2- 3]: 1.50
[ 3- 4]: 1.50
[ 4- 5]: 1.50
[12-13]: 1.00
[12-14]: 1.00
[12-15]: 1.00
[12-16]: 1.00

============================================================
# ASCII Depiction
============================================================
         -C-------------------C-
      ---                       ----
  ----                              ----
C-                                      -C
  \\                                 ///
    \\\                            //
       \\                       ///
         \C-------------------C/


                    H
                    |
                    |
                    |
H-------------------N--------------------H
                    |
                    |
                    |
                    H

---

Limitations & Future Work

Current Limitations

1. Metal Complexes

   • Bond orders locked at 1.0 (no d-orbital chemistry)
   • Metal-metal bonds partially supported (single bond allowed)
   • Can deal with both ionic and neutral ligands

2. Radicals & Open-Shell Systems

   • Unlikely to appropriately solve a valence structure
   • Not explicity dealt with currently
   • May behave, may be unreliable

3. Zwitterions

   • Formal charge and valence analysis does identify -[N+](=O)(-[O-]) bonding and formal charge pattern
   • This is performed without pattern matching
   • May not always be fully robust

4. Large Conjugated Systems

   • May need many iterations for convergence (kekule initialised rings)

5. Charged Aromatics

   • Hückel electron counting is simplistic
   • Should still solve with valence/charge optimisation

---

Built-in Comparison

xyzgraph can directly compare its output to rdkit/xyz2mol:

xyzgraph molecule.xyz --compare-rdkit --debug

Output includes:

• Layout-aligned ASCII depictions
• Edge differences (bonds only in one method)
• Bond order differences (Δ ≥ 0.25)

Example:

# Bond differences: only_in_native=1   only_in_rdkit=0   bond_order_diffs=2
#   only_in_native: 4-7
#   bond_order_diffs (Δ≥0.25):
#     1-2   native=1.50   rdkit=1.00   Δ=+0.50
#     2-3   native=2.00   rdkit=1.50   Δ=+0.50

---

Examples

This section demonstrates xyzgraph's capabilities on real molecular systems, showcasing Kekulé initialization, aromatic detection, metal coordination analysis, and formal charge assignment.

Example 1: Metal Complex (Ferrocene-Manganese Hydride)

This example demonstrates xyzgraph's handling of organometallic complexes with multiple ligand types.

System: [(η⁵-Cp)₂Fe][Mn(H)(CO)₂(PNN)] - Ferrocene cation with manganese hydride complex
File: examples/mnh.xyz (77 atoms)

Command:

xyzgraph examples/mnh.xyz --ascii --debug

Key Features:

• Detection of Cp⁻ (cyclopentadienyl) rings coordinated to Fe
• Metal coordination summary (Fe²⁺, Mn¹⁺) with ligand classification
• Hydride ligand (H⁻) recognition
• Carbonyl (CO) ligands with triple-bonded oxygen
• Aromatic Cp rings with charge contribution to π system

Output (truncated):

KEKULE INITIALIZATION FOR AROMATIC RINGS
    
Ring 1 (5-membered): ['C7', 'C13', 'C11', 'C9', 'C8']
      ✓ Detected Cp-like ring (all 5 C bonded to Fe0)
      π electrons estimate: 6
    
Ring 2 (6-membered): ['C37', 'C39', 'C41', 'C43', 'C45', 'C36']
      π electrons estimate: 6
    
Ring 3 (6-membered): ['C34', 'C32', 'C30', 'C28', 'C26', 'C25']
      π electrons estimate: 6
    
Ring 4 (6-membered): ['C55', 'C53', 'N6', 'C52', 'C58', 'C57']
      π electrons estimate: 6
    
Ring 5 (5-membered): ['C15', 'C17', 'C19', 'C21', 'C23']
      ✓ Detected Cp-like ring (all 5 C bonded to Fe0)
      π electrons estimate: 6
  
------------------------------------------------------------
  SUMMARY: Initialized 5 ring(s) with Kekulé pattern
------------------------------------------------------------

BEAM SEARCH OPTIMIZATION (width=5)
  Locked 16 metal bonds
  Initial score: 456.70
  
Iteration 1:
      Generated 2 candidates, keeping top 2
      ✓ New best: O3-C64      Δtotal =  81.00  score =   375.70
  
Iteration 2:
      Generated 4 candidates, keeping top 4
      ✓ New best: O4-C65      Δtotal =  81.00  score =   294.70
  
Iteration 3:
      Generated 6 candidates, keeping top 5
      ✓ New best: O3-C64      Δtotal =  20.00  score =   274.70
  
Iteration 4:
      Generated 5 candidates, keeping top 5
      ✓ New best: O4-C65      Δtotal =  20.00  score =   254.70
  
Iteration 5:
      No improvements found in any beam, stopping
  
------------------------------------------------------------
  Explored 181 states across 5 iterations
  Found 4 improvements
  Score: 456.70 → 254.70
------------------------------------------------------------

FORMAL CHARGE CALCULATION
    
Initial formal charges:
        Sum: -3 (target: +0)
      
  Metal coordination summary:
        
[  0] Fe  oxidation_state=+2  coordination=10
          • 5-ring (-1)  [donor: C13]
          • 5-ring (-1)  [donor: C19]
        
[  1] Mn  oxidation_state=+1  coordination=6
          •      H (-1)  [donor: H67]
          •     CO ( 0)  [donor: C64]
          •     CO ( 0)  [donor: C65]
          •      N ( 0)  [donor: N6]
          •      P ( 0)  [donor: P2]
          •      N ( 0)  [donor: N5]
    
Metal complex detected: 
        Residual: +3 (represents metal oxidation states)

AROMATIC RING DETECTION (Hückel 4n+2)
  
Ring 1 (5-membered): ['C7', 'C13', 'C11', 'C9', 'C8']
    π electrons: 6 (C7:1, C13:1, C11:1, C9:1, C8:1+1(charge))
    ✓ AROMATIC (4n+2 rule: n=1)
  
Ring 5 (5-membered): ['C15', 'C17', 'C19', 'C21', 'C23']
    π electrons: 6 (C15:1, C17:1, C19:1, C21:1, C23:1+1(charge))
    ✓ AROMATIC (4n+2 rule: n=1)

------------------------------------------------------------
  SUMMARY: 5 aromatic rings, 28 bonds set to 1.5
------------------------------------------------------------

# Selected atoms from molecular graph:
[  0] Fe  val=10.00  metal=0.00  formal=0   | 7(1.00) 8(1.00) 9(1.00) 11(1.00) 13(1.00) ...
[  1] Mn  val=6.00  metal=0.00  formal=0   | 2(1.00) 5(1.00) 6(1.00) 64(1.00) 65(1.00) 67(1.00)
[  3]  O  val=3.00  metal=0.00  formal=+1  | 64(3.00)
[  4]  O  val=3.00  metal=0.00  formal=+1  | 65(3.00)
[  8]  C  val=4.00  metal=1.00  formal=-1  | 0(1.00) 7(1.50*) 9(1.50*) 47(1.00)
[ 23]  C  val=4.00  metal=1.00  formal=-1  | 0(1.00) 15(1.50*) 21(1.50*)
[ 64]  C  val=3.00  metal=1.00  formal=-1  | 1(1.00) 3(3.00)
[ 65]  C  val=3.00  metal=1.00  formal=-1  | 1(1.00) 4(3.00)
[ 67]  H  val=0.00  metal=1.00  formal=-1  | 1(1.00)

ASCII Depiction:

[!TIP] Don't look at this in too much detail, not good for complex molecular visualisation...

            C---------C
           /           \
           /            \               C--
          /              \            //   ----
         /                \         //         --C
         /                 C      //             |
        C                 /      C                |
         \               /       |                |
          \             /         |               |
           \            /         |   O            |
            \          /          |  #             C
             C--------C            |#            //
                       \          #C--         //
                        \        //   ----   //
                         \\    /C       H --C     C---------C                  C
      C----                \ // \      /         /           \                /
     / \   -----C         --P    \    /   C#####/             \              /
  C----\---    /\     ----   \\   \   / //     /####O         \             /
  |\\\  \  --//----C--         \\ \  ///      /                \           /
 /|   \  \  /  ---\|             \\ //   ----N                  C---------N
C----- \\\ /---   |                Mn----     \                /           \
 |    ----Fe---   |                |           \              /            \
 |  ---- /|\\  ----C               |           \             /              \
 C--    /|   \\---|                |             \           /                \
  \\  // |---- \\|                |              C---------C                 \
   \\/---|     --C\               |             /                             C
    C-\\|  ----    \\\          --N-          //
        C--           \\    ----  | ---      /
                        \C--      |    ---  /
                         |        |       -C
                         |        |
                        |         |
                        |         H
                        |
                        C

Analysis:

• Ferrocene fragment: Fe(II) coordinated to two Cp⁻ ligands (η⁵ coordination)
• Cp rings: Detected as aromatic with 6 π electrons (includes -1 charge contribution from each ring)
• Manganese center: Mn(I) with octahedral-like coordination
  • Hydride (H⁻) ligand correctly identified (formal charge -1)
  • Two CO ligands with C≡O triple bonds (formal charges: C: -1, O: +1), net neutral ligand
  • Phosphine (P) and amine (N) dative bond donors
• Charge balance: System is neutral (Fe(II) + Mn(I) - 2×Cp⁻ - H⁻ = 0)

---

Example 2: Organic Cation (Acyl Isothiouronium)

This example shows aromatic detection, formal charge assignment, and handling of heteroaromatic systems.

System: Acyl isothiouronium cation (quaternary nitrogen)
File: examples/isothio.xyz (52 atoms, +1 charge)

Command:

xyzgraph examples/isothio.xyz --charge 1 --ascii --debug

Key Features:

• Benzene ring aromatic detection
• 5-membered heterocycle evaluation (thiazole-like ring)
• Formal charge on quaternary nitrogen (N⁺)
• Beam search optimization of carbonyl bond order

Output (truncated):

> xyzgraph examples/isothio.xyz -a -d -as 2 --charge 1

============================================================
KEKULE INITIALIZATION FOR AROMATIC RINGS
============================================================
    
Ring 1 (6-membered): ['C24', 'C23', 'C22', 'C21', 'C26', 'C25']
      π electrons estimate: 6
       
Ring 4 (6-membered): ['C8', 'C9', 'C10', 'C11', 'C12', 'C7']
      π electrons estimate: 6
  
------------------------------------------------------------
  SUMMARY: Initialized 2 ring(s) with Kekulé pattern
------------------------------------------------------------

============================================================
BEAM SEARCH OPTIMIZATION (width=5)
============================================================
  Initial score: 657.00
  
Iteration 1:
      Generated 3 candidates, keeping top 3
      ✓ New best: C1-C2       Δtotal =  72.00  score =   585.00
  
Iteration 2:
      Generated 5 candidates, keeping top 5
      ✓ New best: N18-C19     Δtotal = 116.50  score =   468.50
  
Iteration 3:
      Generated 4 candidates, keeping top 4
      ✓ New best: O0-C1       Δtotal =  71.00  score =   397.50
  
Iteration 4:
      No improvements found in any beam, stopping
  
Applying best solution to graph...
------------------------------------------------------------
  Explored 148 states across 4 iterations
  Found 3 improvements
  Score: 657.00 → 397.50
------------------------------------------------------------

============================================================
FORMAL CHARGE CALCULATION
============================================================
    
Initial formal charges:
        Sum: +1 (target: +1)
        Charged atoms:
            N18: +1
    
No residual charge distribution needed (sum matches target)

============================================================
AROMATIC RING DETECTION (Hückel 4n+2)
============================================================
  
Ring 1 (6-membered): ['C24', 'C23', 'C22', 'C21', 'C26', 'C25']
    π electrons: 6 (C24:1, C23:1, C22:1, C21:1, C26:1, C25:1)
    ✓ AROMATIC (4n+2 rule: n=1)
  
Ring 2 (5-membered): ['N18', 'C19', 'S20', 'C21', 'C26']
    π electrons: 7 (N18:2(LP), C19:1, S20:2(LP), C21:1, C26:1)
    ✗ Not aromatic (4n+2 rule violated)
  
Ring 3 (6-membered): ['N18', 'C17', 'C13', 'C6', 'N5', 'C19']
    ✗ Not planar, skipping aromaticity check
  
Ring 4 (6-membered): ['C8', 'C9', 'C10', 'C11', 'C12', 'C7']
    π electrons: 6 (C8:1, C9:1, C10:1, C11:1, C12:1, C7:1)
    ✓ AROMATIC (4n+2 rule: n=1)

------------------------------------------------------------
  SUMMARY: 2 aromatic rings, 12 bonds set to 1.5
------------------------------------------------------------

    Gasteiger charge calculation failed: Explicit valence for atom # 18 N, 4, is greater than permitted

============================================================
GRAPH CONSTRUCTION COMPLETE
============================================================

# Molecular Graph: 52 atoms, 55 bonds
# total_charge=1  multiplicity=1  sum(gasteiger)=+1.000  sum(gasteiger_raw)=+0.000
# (C–H hydrogens hidden; heteroatom-bound hydrogens shown; valences still include all H)
# [idx] Sym  val=.. metal=.. formal=.. chg=.. agg=.. | neighbors: idx(order / aromatic flag)
# (val = organic valence excluding metal bonds; metal = metal coordination bonds)
[  0]  O  val=2.00  metal=0.00  formal=0   chg=+0.019  agg=+0.019 | 1(2.00)
[  1]  C  val=4.00  metal=0.00  formal=0   chg=+0.019  agg=+0.019 | 0(2.00) 2(1.00) 5(1.00)
[  5]  N  val=3.00  metal=0.00  formal=0   chg=+0.019  agg=+0.019 | 1(1.00) 6(1.00) 19(1.00)
[ 18]  N  val=4.00  metal=0.00  formal=+1  chg=+0.019  agg=+0.019 | 17(1.00) 19(2.00) 26(1.00)
[ 19]  C  val=4.00  metal=0.00  formal=0   chg=+0.019  agg=+0.019 | 5(1.00) 18(2.00) 20(1.00)
[ 20]  S  val=2.00  metal=0.00  formal=0   chg=+0.019  agg=+0.019 | 19(1.00) 21(1.00)

ASCII Depiction:

                            C
                           /
                         //
                        C\
                         \\
                         \\
                         /C\
                        /
               O======C/
               ========\
   /C------C           \           /S-
  /         \           N---     //   ---     --C\
C/          \         //    ---C\        -C---    \\
\           \        /          \\       /          \C
 \          /C------C           \\       /          /
  \        /         \           N\-----C           /
  C------C/          \         //        \\         /
                      C---    /            \    ---C
                    //    ---C              C---
           C---    /
               ---C
                   \
                   \
                    C

Analysis:

• Benzene rings: Two rings correctly identified as aromatic (bond order 1.5)
• 5-membered heterocycle: N-C-S-C-C ring retains Kekulé structure with N=C double bond
• Quaternary nitrogen: N16 assigned +1 formal charge (4 bonds, no lone pairs)
• a,b-unsaturated: O=C and C=C double bonds correctly optimized

---

Bond Detection Thresholds

xyzgraph uses distance-based bond detection with thresholds derived from van der Waals (vdW) radii by Charry and Tkatchenko [1]. By default, these thresholds are calibrated for different atom pair types:

Atom Pair Type	Default Threshold	Parameter Name
H-H	0.38 × (r₁ + r₂)	threshold_h_h
H-nonmetal	0.42 × (r₁ + r₂)	threshold_h_nonmetal
H-metal	0.48 × (r₁ + r₂)	threshold_h_metal
Metal-ligand	0.6 × (r₁ + r₂)	threshold_metal_ligand
Nonmetal-nonmetal	0.55 × (r₁ + r₂)	threshold_nonmetal_nonmetal

Where r₁ and r₂ are the VDW radii of the two atoms.

Detecting Elongated Bonds (Transition States)

The two-step construction allows detection of elongated bonds in transition state structures by adjusting the global threshold:

# Detect elongated bonds in TS structures
xyzgraph ts_structure.xyz --threshold 1.2 --debug

# For more dense connectivity, one can use relaxed mode (more permissive geometric validation)
xyzgraph structure.xyz --threshold 1.2 --relaxed --debug

Recommended threshold ranges:

• 1.0 (default): Ground-state structures
• 1.1-1.2: Slightly elongated bonds
• 1.2-1.3: Transition states with stretched geometries
• ≥1.35: Unstable - spurious bonding likely

The two-step construction with geometric validation helps reject spurious diagonals even at higher thresholds. The --relaxed flag can be used for more permissive angle and diagonal thresholds (but note: this is likely to produce spurious structures).

Example workflow: See vib_analysis for a complete workflow analyzing transition state vibrational modes using xyzgraph connectivity.

Advanced Threshold Modification (Not Recommended)

Global Scaling:

• The --threshold (or threshold in Python) parameter provides a simple way to globally scale all thresholds.
• This is safer than modifying individual thresholds.
• e.g. --threshold 1.1
  • threshold_h_nonmetal × (r₁ + r₂) × 1.1

Individual Scaling:

These parameters are exposed for users who need to:

• Handle unusual bonding situations not covered by defaults
• Specifically wish to obtain dense connectivity
• Fine-tune bond detection for specific molecular systems
• Debug or validate bond detection behavior

Can be performed using the cli e.g. --threshold_h_nonmetal 0.5 or directly in python within build_graph(threshold_h_nonmetal=0.5)

[!WARNING]
Modifying these thresholds is not recommended unless you have a specific reason and understand the implications
Changing values can produce chemically invalid structures

---

References

1. van der Waals Radii: Jorge Charry and Alexandre Tkatchenko, J. Chem. Theory Comput., 2024, 20, 7469–7478. DOI.

2. xTB (Extended Tight Binding): Christoph Bannwarth, Sebastian Ehlert, and Stefan Grimme, J. Chem. Theory Comput. 2019, 15, 1652–1671. DOI. Repo.

3. xyz2mol: Jan Jensen et al., xyz2mol. Now integrated into RDKit as Chem.rdDetermineBonds.DetermineBonds(). See also Y. Kim, W. Y. Kim, Bull. Korean Chem. Soc., 2015, 36, 1769–1777.

4. RDKit: RDKit: Open-source cheminformatics. https://www.rdkit.org. Repo.

5. moltext: A. White, moltext. Repo

---

Contributing & Contact

Contributions welcome! Please open an issue or pull request and get in touch with any questions here.