Describing static mechanism of vibronic luminescence in lanthanides from first principles

Identification of molecular vibrations which are most strongly coupled to lanthanide emission is important for applications of the optical lanthanide spectroscopy. Extracting the information about the interaction between the electronic degrees of freedom and vibrations from the emission spectra is challenging due to complexity of vibronic structures of these spectra. To overcome this challenge, we developed a fully ab initio methodology that predicts contribution of individual vibrational modes to the overall vibronic structure by calculating the mode-specific electron-vibrational couplings. We derive the analytical expression for the energy gradients of the emitting and ground spin-orbit states, which are the key quantity required for calculating the electron-vibrational couplings. To illustrate this methodology, we calculate the ⁴S_3/2→⁴I_15/2 emission spectrum of the erbium trensal complex and provide the full decomposition of the vibronic structure of the spectrum.