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ChemiGraph

A Python Library for Chemical Graph Theory

ChemiGraph turns a molecular structure into quantum-chemical insight using only graph theory and linear algebra. It is a fully automated implementation of the Valency Interaction Formula (VIF) theory — formulated by Oktay Sinanoğlu (Theoret. Chim. Acta 1985, 68, 251) — and its application to mass spectrometry by Berkay Sütay (JOTCSA 2017, 4(1), 179).

Give it nothing but a structure (a SMILES string or a PubChem name) and it will:

  • build the VIF graph of the molecule,
  • compute the Level Pattern Indices (LPI) = the exact count of bonding, nonbonding and antibonding molecular orbitals,
  • locate the soft bonds (the weakest linkages), and
  • predict the principal electron-impact (EI) mass-spectral fragments — a priori, in milliseconds, without any large-scale quantum-chemical computation.

Theoretical background

1. The molecule becomes a graph. Each atom is drawn as a set of vertices equal to the size of its valence shell — 1 for H/He, 4 (s + 3p) for the second- and third-row main-group elements, 9 for transition metals. The vertices of one atom form an intra-atomic clique (the hybrid-orbital interactions), and each chemical bond is an edge joining vertices of neighbouring atoms.

2. The graph is the Hamiltonian. This picture is exactly the matrix representation — the adjacency matrix — of the one-electron molecular Hamiltonian in a non-orthonormal valence-orbital basis. Nothing is approximated away; the graph encodes the same connectivity the operator does.

3. Reduction = congruence = invariant signature. Sinanoğlu showed that the pictorial reduction rules of VIF are congruence transformations (A → SᵀAS) of this matrix under the general linear group. By Sylvester's law of inertia (1852), a congruence transformation cannot change the signature — the number of positive, zero and negative eigenvalues. That invariant is the LPI:

LPI = (n+, n0, n-)
      n+  = # positive eigenvalues = bonding molecular orbitals
      n0  = # zero eigenvalues     = nonbonding molecular orbitals
      n-  = # negative eigenvalues = antibonding molecular orbitals

So the electronic level pattern of a molecule can be read off its structural formula alone — no basis-set SCF cycle required.

4. Soft bonds and mass spectra. Sütay's insight (2017) is that the interactions which cancel during reduction — the soft bonds — are the chemically weakest linkages, and are precisely the bonds that break first under 70 eV electron impact. Each soft-bond cleavage is a fragment peak in the mass spectrum.

What ChemiGraph adds

It reduces Sinanoğlu's hand-drawn calculus directly to numerical linear algebra:

LPI(G) = signature of the adjacency matrix of G,  via numpy.linalg.eigvalsh   (O(n³))

Soft-bond detection is a rank-2 perturbation test: if deleting bond (i, j) leaves the LPI unchanged, that bond would already have vanished during reduction — so it is soft. A chemically motivated α-cleavage rule suppresses unphysical fragments (e.g. a bare carbonyl oxygen would never leave as atomic O), and every m/z is reported on the nominal-mass (most-abundant-isotope) scale, the mass-spectrometric convention.

The implementation reproduces the reference LPI values of Sinanoğlu (1985) and the mass-spectral predictions of Sütay (2017) — including the chlorine- substituted cyclohexanone-oxime of the 2017 paper, for which it returns the experimental peaks at m/z = 35 (Cl), 17 (OH) and 218 (M − OH) exactly.

Worked example — nitrobenzene

chemigraph nitrobenzene

Nitrobenzene VIF graph    Nitrobenzene predicted MS

Left — the VIF graph. Every atom is a coloured clique of valence-orbital vertices; solid black edges are ordinary bonds; red dashed edges are soft bonds. The single soft bond linking the benzene ring to the nitro group is the C–N bond — LPI = {18, 0, 23}.

Right — the predicted mass spectrum. Because the C–N bond is soft, the nitro group is lost, giving the phenyl cation C₆H₅⁺ at m/z = 77 — the dominant fragment observed experimentally — alongside the molecular ion M⁺ at 123. This matches Figure 6 of Sütay (2017).

Bar heights are schematic: VIF predicts which fragments form, not their intensities.

Installation

ChemiGraph is distributed as a pre-compiled package — one pip command installs it and its five scientific dependencies (numpy, networkx, matplotlib, rdkit, mendeleev). Python 3.9+ is required.

pip install chemigraph

pip automatically downloads the pre-built binary matching your operating system (Linux, Windows, macOS) and Python version. Alternatively, grab the wheel for your platform from the Releases page and install it directly:

pip install chemigraph-1.0.0-<your-platform>.whl

Windows users: install Python from https://www.python.org/downloads/ (tick “Add Python to PATH” during setup), then open the Command Prompt (Win + R → cmd → Enter) and run pip install chemigraph. A virtual environment (python -m venv venv && source venv/bin/activate) is recommended on every platform.

Usage

From the terminal

After installation a chemigraph command is available everywhere:

chemigraph aspirin                 # a molecule name → fetched from PubChem
chemigraph "Clc1ccccc1"            # a raw SMILES string
chemigraph caffeine nitrobenzene   # several molecules in one run
chemigraph                         # no argument → the substituted-halogen demo

Each molecule prints its LPI and predicted fragment list, and opens two windows: the VIF graph and the predicted mass spectrum.

As a Python library

import chemigraph as cg

# Full analysis from a SMILES string
result = cg.VIF("Clc1ccccc1")           # chlorobenzene
lpi = result["lpi"]
print(lpi["n+"], lpi["n0"], lpi["n-"])  # 15 0 18   (bonding / nonbonding / antibonding)
print(result["mol_mass"])               # 112       (nominal M+)

# Fetch a molecule by name from PubChem
cg.VIF_from_pubchem("nitrobenzene")

# Silent analysis (no plots), inspect the fragments
r = cg.VIF("CC(=O)Oc1ccccc1C(=O)O", draw=False, show_spectrum=False, verbose=False)
for f in r["fragments"]:
    if f["split"]:
        print(f["bond"], "->", [(x[0], x[2]) for x in f["fragments"]])

Interpreting the output

Field Meaning
lpi {n+, n0, n-} — counts of bonding / nonbonding / antibonding MOs
mol_mass nominal mass of the molecular ion M⁺ (m/z)
soft_bonds the weak interactions detected by the perturbation test
fragments predicted EI fragments; each split gives two (formula, m/z) pairs

References

  1. O. Sinanoğlu, Theoret. Chim. Acta 1985, 68, 251.
  2. O. Sinanoğlu, Chem. Phys. Lett. 1984, 103, 315.
  3. B. Sütay, J. Turk. Chem. Soc. A 2017, 4(1), 179.

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Credits

Author: Sinan Gökmen

License

MIT

Requires

Python >=3.9

Tags

chemical-graph-theory mass-spectrometry valency-interaction-formula quantum-chemistry cheminformatics

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