Coulomb 2D-Snapshot Model for Polycyclic Aromatic Hydrocarbons: A Simple Predictor of Electronic Properties

Abstract

We extend the Coulomb Snapshot model from one-dimensional conjugated chains to two-dimensional polycyclic aromatic hydrocarbons (PAHs). The original 1D formulation, which quantifies π-electron delocalization through electron–nuclear Coulombic interactions, showed strong logarithmic correlations (R2 = 0.98) with experimental absorption wavelengths and combustion enthalpies in linear oligoenes and oligoynes. The 2D extension introduces geometry-specific interaction factors for rectangular, linear, and hexagonal (regular and irregular) PAH topologies. Statistical validation on 20 structurally diverse PAHs (C12–C54) yields R2 = 0.656 for ionization energy (MAE = 0.221 eV) and R2 = 0.672 for the fundamental gap (MAE = 0.441 eV) across the complete dataset; after z-score outlier removal (|z| > 1.5σ), these improve to mean relative errors of 2.25% for ionization energy (MAE = 0.154 eV, R2 = 0.857) and 5.29% for the fundamental gap (MAE = 0.298 eV, R2 = 0.843). Three outliers (acenaphthylene, fluoranthene, dibenzo[bc,kl]coronene) show systematic deviations attributable to five-membered-ring fusion and extended irregular hexagonal geometries not fully captured by the simplified geometric factors. Error analysis—normally distributed residuals, a narrow 95% prediction band (±0.38 eV for IE, ±0.75 eV for the fundamental gap), and consistent performance across molecular sizes—supports predictive reliability while maintaining physical interpretability and minimal computational cost. Although developed and evaluated on a relatively small dataset, the 2D-Snapshot model thus offers a fast, physically interpretable estimate of the electronic properties of benzenoid PAHs and represents a promising framework for rapid screening in organic materials design that warrants validation on larger, more structurally diverse sets.