Singlet and triplet to doublet energy transfer: improving organic light-emitting diodes with radicals

Organic light-emitting diodes (OLEDs) must be engineered to circumvent the efficiency limit imposed by the 3:1 ratio of triplet to singlet exciton formation following electron-hole capture. Here we show the spin nature of luminescent radicals such as TTM-3PCz allows direct energy harvesting from both singlet and triplet excitons through energy transfer, with subsequent rapid and efficient light emission from the doublet excitons. This is demonstrated with a model Thermally-Activated Delayed Fluorescence (TADF) organic semiconductor, 4CzIPN, where reverse intersystem crossing from triplets is characteristically slow (50% emission by 1 µs). The radical:TADF combination shows much faster emission via the doublet channel (80% emission by 100 ns) than the comparable TADF-only system, and sustains higher electroluminescent efficiency with increasing current density than a radical-only device. By unlocking energy transfer channels between singlet, triplet and doublet excitons, further technology opportunities are enabled for optoelectronics using organic radicals.


Theoretical considerations of energy transfer by FRET and Dexter mechanisms
Here we consider the electronic structure algebra of the following energy transfer and emission processes: Eq. 1a S 1 + D 0 → S 0 + D 1 → S 0 + D 0 + ℎ . Eq. 1b In this section we demonstrate that both these processes are fully quantum mechanically spin-allowed (without requiring spin-orbit coupling) as they can conserve both total spin and spin projection .

The energy transfer system
We consider a minimal four (spatial) orbital, five-electron model that comprises: the HOMO of the radical energy acceptor, A (orbital 1); the SOMO of A (orbital 3); the HOMO of the energy donor, D (orbital 2); and the LUMO of D (orbital 4).
The electronic states considered are: where no bar indicates electron-spin 'up' and bar indicates electron-spin 'down'.
We wish to identify these determinants in the basis of the S 0 , S 1 and T 1 electronic states of D, and the D 0 and D 1 states of A. This is already set out Eq. 2a, Eq. 2b and Eq. 2e. This can be achieved from Eq. 2c and Eq. 2d by taking linear combinations: Eq. 4 For states of non-zero spin (doublets and triplets) we have added a subscript index of the projection spin quantum number, MS.
The quartet is uniquely defined as: and the two doublet states can be chosen to be: Note that |D(S 1 )A(D 0,+1/2 )⟩ is an eigenstate of 2 whereas |D(T 1,0 )A(D 0,+1/2 )⟩ and |D(T 1,+1 )A(D 0,−1/2 )⟩ are not. Although different linear combinations of the doublet eigenstates can be taken, it is possible to verify that the triplet-doublet determinants cannot be eigenstates of 2 .

Electronic interaction
We aim to find the interaction between the spin eigenstates |Q⟩, |D( )⟩, |D( )⟩ and the /2 )⟩. We find: where we have integrated out the spin contributions and written the integrals in chemists' notation (Szabo A, Ostlund NS. Modern quantum chemistry: introduction to advanced electronic structure theory, 2012).
where 2 ( 1 ) corresponds to the value of the wavefunction of orbital 2 at position 1 .