Abstract
In this work, we present a general method for predicting phosphorescence rates and spectra for molecules using time-dependent density functional theory (TD-DFT) and a path integral approach for the dynamics that relies on the harmonic oscillator approximation for the nuclear movement. We first discuss the theory involved in including spin–orbit coupling (SOC) among singlet and triplet excited states and then how to compute the corrected transition dipole moments and phosphorescence rates. We investigate the dependence of these rates on some TD-DFT parameters, such as the nature of the functional, the number of roots, and the Tamm–Dancoff approximation. After that, we evaluate the effect of different SOC integral schemes and show that our best method is applicable to a large number of systems with different excited state characters.
Highlights
Phosphorescent materials have been a major focus of research during the past few years, with applications in organic lightemitting diodes (OLEDs),[1−6] light-emitting electrochemical cells,[7,8] photovoltaic cells,[9,10] chemical sensors,[11−14] and bioimaging.[15−19] Because most molecular materials presenting this kind of long-lived emission contain heavy metals to increase spin−orbit coupling (SOC), the interest in purely organic molecules presenting triplet emission has grown recently,[20,21] for economical and ecological reasons
We suggest using Quasi-Degenerate Perturbation Theory (QDPT)[31] to calculate the mixing between singlets and triplets obtained from time-dependent density functional theory (TD-DFT),[32,33] with or without the Tamm−Dancoff approximation (TDA),[34] to get a more complete picture of the SOC mixing
We have provided a derivation of the spin−orbit coupling between TD-DFT ground and excited states and the application of the corrected transition dipole moment matrix elements for the computation of phosphorescence rates and spectra
Summary
Phosphorescent materials have been a major focus of research during the past few years, with applications in organic lightemitting diodes (OLEDs),[1−6] light-emitting electrochemical cells,[7,8] photovoltaic cells,[9,10] chemical sensors,[11−14] and bioimaging.[15−19] Because most molecular materials presenting this kind of long-lived emission contain heavy metals to increase spin−orbit coupling (SOC), the interest in purely organic molecules presenting triplet emission has grown recently,[20,21] for economical and ecological reasons. Where ΔE12 is the energy difference between states 1 and 2 with the three sublevels labeled from 1 to 3 and k1, k2, and k3 correspond to the individual rate from each level This simple approach works in some cases for molecules with heavy atoms, where the SOC is large enough to induce a strong mixing and a large transition dipole moment,[4,29,30] but it fails when these matrix elements are small and vibronic coupling must be accounted for.[28] the use of eq 2 neglects the mixture of excited triplets with the ground singlet and the effects of triplet−triplet coupling. DFT and the SOC integrals on a small subset of molecules and show that this method can be applied to a larger number of molecules with different excited state characters, including solvent effects
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
