Symmetry-driven anisotropy and interpretable machine learning of molecular physisorption on carbonaceous lattices

The optimization of carbonaceous environmental sensors is currently limited by empirical statistical models that fail at quantum-mechanical boundaries. In this study, the standard Response Surface Methodology (RSM) diverges significantly in highly non-linear van der Waals regimes (MAE > 9.0 eV) and a hybrid Density Functional Theory (DFT-D3) and explainable AI framework to correct this limitation. By computing a deterministic 500-point 4D phase space (X,Y,Z,θ) for caffeine physisorption on nanobiochar, a Gaussian Process Regression surrogate (MAE = 0.0026 eV) was trained to efficiently isolate the global minimum. Symbolic Regression (PySR) was subsequently applied to derive a continuous analytical equation that explicitly couples vertical adsorbate displacement to the lateral periodic registry of the sp^2 lattice. Electronic structure analysis of the global minimum confirms an eclipsed π-π stacking architecture at an equilibrium distance of 3.4 Å. Out-of-plane p_z orbital hybridization induces localized donor-acceptor charge transfer, resulting in a 1.06 eV shift in the contact potential difference (increasing the local work function from 4.14 eV to 5.20 eV). The absolute magnitude of this intrinsic electronic binding enthalpy strictly exceeds the classical entropic penalty of surface confinement, ensuring macroscopic thermodynamic spontaneity (∆G_ads<0) at 298.15 K. This methodology provides a physically interpretable blueprint for predicting the selectivity and transduction mechanisms of molecular adsorbates on carbonaceous substrates.