Photoelectron Spectra of Hot Polyatomic Ions: A Statistical Treatment of Phenide

Many distinct vibrational states contribute to the congested photoelectron spectra of hot polyatomic anions. This often makes the complete Franck-Condon (FC) analysis both impractical and unnecessary. Although it is common to limit the FC calculations to a subset of the FC-active modes, such a limited approach is strictly applicable to the ground-state (cold) anions only. At high temperatures, all vibrational modes participate in thermal excitation, and the FC and thermal activities become intertwined. We report the photoelectron spectra of ∼700 K phenide (C₆H₅^-) obtained at 355 nm (3.49 eV), 532 nm (2.33 eV), and 611 nm (2.03 eV) and describe several practical models that help interpret and analyze the results. Among them are the active-modes model, the active modes + dark bath and the active modes + bright bath models, and, finally, the energy-conservation model. The models combine the results of limited (and, therefore, feasible) FC calculations with statistical analysis and provide efficient means of determining the ion temperature from the broad and congested photoelectron spectra. The described capability can be applied to hot plasmas, the collisional excitation or cooling of ions, and evaporative cooling in cluster ions.