Modeling the emission spectra of polycyclic aromatic hydrocarbons by recurrent fluorescence

Recurrent fluorescence (RF) is an important relaxation mechanism in polycyclic aromatic hydrocarbons (PAHs), which could stabilize them and contribute to the production of aromatic infrared bands that are observed in the infrared spectra of the interstellar medium (ISM). In this theoretical work, a statistical model of relaxation by recurrent fluorescence is formally developed, including Herzberg-Teller and Duschinsky rotation effects as well as a full account of vibrational progressions. Using canonical and harmonic approximations, the RF rate constants can be determined from the transition dipole moment time autocorrelation functions. Application to the naphthalene, anthracene, and pyrene cations is presented based on quantum chemical inputs obtained from time-dependent density-functional theory. For these highly symmetric molecules, the low-lying, symmetry-forbidden electronic transitions are predicted to contribute possibly even more than higher energy, non-forbidden transitions. Such an unexpected contribution could increase the cooling efficiency of PAHs and, in turn, stabilize them further under the highly ionized environments of the ISM.