Modeling the Emission Spectra and Radiative Decay Rates in Polychlorinated Organic Radicals

Abstract

Owing to their unique combination of magnetic and optical properties, luminescent polychlorinated radicals are promising candidates for advanced applications in both optoelectronics and quantum technologies. In this study, we employ the lineshape formalism within a computational protocol based on time-dependent density functional theory (TD-DFT) to investigate the excited-state properties of six representative members of this family presenting different sizes and excited-state characters. We explore a wide range of density functionals, applying or not the Tamm–Dancoff approximation (TDA), combined with different vibronic models, namely, the vertical gradient (VG), vertical Hessian (VH), and adiabatic Hessian (AH), as well as dipole moment expansions using the Franck–Condon (FC) and Herzberg–Teller (HT) approximations. This systematic approach allows us to assess how these methodological choices influence the spectral shapes, excited-state energies, radiative and non-radiative decay rates, and emission yields. Our results show that although TDA effectively reduces spin contamination, it generally leads to poorer predictions of emission energies, radiative rates, and internal conversion rates. The VH model within the FC approximation emerged as the most balanced approach for reproducing both spectral profiles and radiative rates; the inclusion of HT contributions had a minor effect only. Internal conversion rates were found to be highly sensitive to the choice of the vibronic model and spectral broadening, which in turn strongly impacted the predicted fluorescence quantum yields, suggesting that incorporating higher-order expansions and anharmonic corrections could be crucial for more reliable estimates. Among the functionals tested, LC-$\omega$HPBE emerged as the most suited for consistently reproducing all key features, including emission shapes, energies, and decay trends. In short, this study demonstrates that despite the challenges posed by spin contamination and the open-shell character of these systems, TD-DFT remains a powerful and versatile framework for qualitatively capturing the emission properties of radical emitters even when the harmonic approximation is challenged.