Computational Feasibility of a Rectangular Chrysene Network: Comparison with a Dibenzochrysene Kagome Benchmark

Abstract

This Supplemental Information provides the calculation and reproducibility framework supporting the conditional feasibility analysis of a 3,6,9,12-connected rectangular chrysene network. A provenance system distinguishes analytically defined, prospectively fixed, computed, measured, and literature-sourced quantities. Tridiagonal determinant recurrences and transfer matrices describe bridge-mediated electronic coupling for N- and N+2-segment directions. A homogeneous reduction gives closed-form Chebyshev expressions for propagating, band-edge, and off-resonant coupling regimes and defines the admissible set of bridge orders satisfying the minimum two-direction coupling threshold. Primitive-cell accounting separates geometric density from density per unit mass and establishes the effects of bridge length, metals, counterions, and retained species on mass-normalized optical and hydrogen-evolution rates. Deterministic intervals, simultaneous confidence bounds, covariance-aware logarithmic propagation, and joint resampling procedures are developed for the hydrogen-rate lower bound. Metal ions are represented through an energy-dependent Schur-complement self-energy that permits calculation of energetic shifts, directional-coupling perturbations, induced broadening, and the competition between productive charge separation and excited-state quenching. A prospective calculation sequence specifies candidate locking, numerical verification, uncertainty calibration, controlled measurement, and archival requirements. These results define reproducible conditions for selecting and testing candidate networks; they do not establish candidate-specific hydrogen production, catalyst-free proton reduction, water oxidation, or overall water splitting.