When do tripdoublet states fluoresce? A theoretical study of copper(II) porphyrin.

Open-shell molecules rarely fluoresce, due to their typically faster non-radiative relaxation rates compared to closed-shell ones. Even rarer is the fluorescence from states that have two more unpaired electrons than the open-shell ground state, since they involve excitations from closed-shell orbitals to vacant-shell orbitals, which are typically higher in energy compared to excitations from or out of open-shell orbitals. States that are dominated by the former type of excitations are known as tripdoublet states when they can be described as a triplet excitation antiferromagnetically coupled to a doublet state, and their description by unrestricted single-reference methods (e.g., U-TDDFT) is notoriously inaccurate due to large spin contamination. In this work, we applied our spin-adapted TDDFT method, X-TDDFT, and the efficient and accurate static-dynamic-static second order perturbation theory (SDSPT2), to the study of the excited states as well as their relaxation pathways of copper(II) porphyrin; previous experimental works suggested that the photoluminescence of some substituted copper(II) porphyrins originate from a tripdoublet state, formed by a triplet ligand