Magnetic Properties, Spin-Vibration Couplings, and Temperature Effects in Phenalenyl and Triangulene

We introduce a computational methodology for evaluating and analyzing spin-vibration couplings in molecular systems, enabling insights into the interplay between electronic spins and molecular vibrations. By mapping ab initio electronic structure calculations onto molecular spin Hamiltonians, our approach captures those vibrational interactions potentially driving spin relaxation process. Spin-vibration couplings, derived from Holstein and Peierls terms, highlight the pivotal role of vibrational mode symmetry in spin decoherence and efficient energy dissipation. Additionally, second-order couplings provide a framework to explore the temperature dependence of spin properties via the thermal population of higher vibrational levels. Applied to phenalenyl and [3]triangulene, the results indicate that direct spin transitions dominate over Orbach relaxation in both systems. Hyperfine interactions primarily dictate spin-vibration couplings and thermal effects in phenalenyl, whereas zero-field splitting contributions are dominant in [3]triangulene. These findings advance the understanding of spin relaxation mechanisms in organic molecular systems.