R Valiev
The harmonic approximation is commonly used to describe internal conversion in large organic molecules. Here, local X-H vibrations are represented by Morse oscillators, while cubic and quartic force constants explicitly couple the X-H subsystem to the remaining vibrational bath. Dynamic programming retains complete final product states, and each state-specific spreading width, Γfn, is correlated with the energy mismatch and first-order intensity of that same state. For the representative 240-mode azatrioxa[8]circulene system, the cubic force field is dominated by terms containing X-H coordinates, whereas the strongest quartic contributions are concentrated in the low-frequency bath. At Eif = 22 000 cm-1, the calculation gives 〈Γfn〉 = 589.1 cm-1 and a state-correlated internal-conversion rate of (2.45 ± 0.05) × 105 s-1. Resonance-network Hamiltonians built from H3 and H4 were further assessed through spectral statistics and exact product-state survival. For the complete H3 + H4 Hamiltonian, the distinct spectra give 〈r〉 = 0.426 ± 0.022 and a mean Brody parameter of 0.173. No Gaussian orthogonal ensemble (GOE) background or quantum-scar signature is found. Nevertheless, robust X-H-localized breather-like families persist from 10 000 to 35 000 cm-1, demonstrating incomplete delocalization of high overtones carried predominantly by one X-H bond. The anharmonic interactions therefore generate extended resonance networks and structured nonergodic mixing without a fully ergodic GOE regime.