A Cellular Sheaf Model for Aromaticity in Discrete Molecular Systems
- 1Perse School
Abstract
Aromaticity underpins molecular stability in fields ranging from pharmaceuticals to organic semiconductors, yet existing prediction methods are either too computationally costly for large-scale screening or too empirically restricted for broad applicability. This work introduces the molecular sheaf, a cellular sheaf model free of empirical parameters for chemical bonding that generalizes standard molecular graph theory. From this the frontier eigengap Δ_F is derived as a spectral approximation of the HOMO-LUMO gap requiring only molecular topology and electron count. Δ_F correctly classifies the aromaticity and antiaromaticity of the full annulene series, including benzene and cyclobutadiene, exactly recovering Hückel theory for regular hydrocarbon systems. At scale, it accounts for 62.5% of the variance in DFT HOMO-LUMO gaps across 17,523 structurally diverse polycyclic aromatic hydrocarbons and 21.7% across 52,000 heteroaromatic systems, with the reduction reflecting the deliberate cost of parameter freedom. This confirms that aromatic character can be approximated from molecular connectivity and electron count alone, suggesting that cellular sheaves offer a largely unexplored mathematical framework for the modeling of chemical bonding and structure. All calculations run at under 1 ms per molecule, over seven orders of magnitude faster than corresponding DFT calculations. The molecular sheaf thus also enables rapid, parameter-free pre-screening of aromatic character from structural data alone.
Related
- Quantifying antiaromatic destabilization: flashing aromaticity in cascade transformations of cycloheptatrienide systems
- Baird aromaticity as a molecular design principle for enhancing excited-state proton affinity
- Coupling Density Functional Theory and Discrete Element Method to Predict Volume Change in Batteries and Battery Systems
- MIRRA: Fast, High-Fidelity Molecular Generation with Chemistry-Informed Discrete Flow Matching
- Shape-Dependent Interactions of Gold Nanoparticles with Microalgae: Distinct Cellular and Molecular Responses.
BibTeX
@misc{han2026cellular,
title = {{A Cellular Sheaf Model for Aromaticity in Discrete Molecular Systems}},
author = {Roy Han},
howpublished = {ChemRxiv},
year = {2026},
month = oct,
doi = {10.26434/chemrxiv.15010344/v1},
url = {https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010344/v1},
note = {CC BY},
}
RIS
TY - UNPB
TI - A Cellular Sheaf Model for Aromaticity in Discrete Molecular Systems
AU - Roy Han
PY - 2026
DA - 2026/10/13
PB - ChemRxiv
DO - 10.26434/chemrxiv.15010344/v1
UR - https://chemrxiv.org/doi/full/10.26434/chemrxiv.15010344/v1
AB - Aromaticity underpins molecular stability in fields ranging from pharmaceuticals to organic semiconductors, yet existing prediction methods are either too computationally costly for large-scale screening or too empirically restricted for broad applicability. This work introduces the molecular sheaf, a cellular sheaf model free of empirical parameters for chemical bonding that generalizes standard molecular graph theory. From this the frontier eigengap Δ_F is derived as a spectral approximation of the HOMO-LUMO gap requiring only molecular topology and electron count. Δ_F correctly classifies the aromaticity and antiaromaticity of the full annulene series, including benzene and cyclobutadiene, exactly recovering Hückel theory for regular hydrocarbon systems. At scale, it accounts for 62.5% of the variance in DFT HOMO-LUMO gaps across 17,523 structurally diverse polycyclic aromatic hydrocarbons and 21.7% across 52,000 heteroaromatic systems, with the reduction reflecting the deliberate cost of parameter freedom. This confirms that aromatic character can be approximated from molecular connectivity and electron count alone, suggesting that cellular sheaves offer a largely unexplored mathematical framework for the modeling of chemical bonding and structure. All calculations run at under 1 ms per molecule, over seven orders of magnitude faster than corresponding DFT calculations. The molecular sheaf thus also enables rapid, parameter-free pre-screening of aromatic character from structural data alone.
ER -