My research area is computational study of Thermally activated delayed fluorescence (TADF) Materials and their use in Organic light emitting diodes (OLEDs). I want to know What is the exact relation between HOMO-LUMO overlap and Singlet-Triplet energy difference (ΔEST =ES1-ET1)
Normally, smaller the overlap, smaller the energy difference and better will be the TADF Properties, but my designed systems show reverse effect, i mean they show larger overlap but smaller energy difference. i don't know why. can anyone tell me what maybe the reason? Thanks.
At the zeroth-order approximation, the singlet-triplet energy gap is equal to the static correlation between the HOMO and LUMO; if the orbitals are orthogonal, it will be zero (as in the case of pyridine n->π* transitions). At higher levels of computation, the spin-occupancy of each orbital will perturb that of all other orbitals with which it has overlap, and of course there is also the dynamic correlation of the orbitals.
I am not particularly familiar with TADF, but I could imagine a case where, even if the HOMO-LUMO overlap was vanishingly small, there might be significant overlap between the HOMO and lower-energy orbital X and between lower-energy orbital X and the LUMO, or some longer chain of association. In a strictly symmetric system, this would probably be forbidden by symmetry, but since most systems are only approximately symmetric or not symmetric at all, most orbitals will have a non-zero overlap with most other orbitals, and perhaps there is a chain of perturbation. It seems to me also that if this were the case, it would be of significant theoretical interest and definitely worth your time to track down. I would only caution that you make sure your computational methods are good enough to be worth believing, as you might otherwise be chasing phantoms.
I think that Singlet-Triplet energy difference resulting from two solutions ( Exited state (T) and solution of ground state (S) Individually, it mean energy of T from 1st solution - energy of S from 2nd solution.( SOMO T - HOMO S )
If I understood your last comment correctly, what you are describing is not what is usually meant by the singlet-triplet energy difference; rather, what is usually meant is the difference in energy between the singlet and triplet versions of the first excited state. In a pure, simple, zeroth-order system where all electronic transitions are from a single canonical occupied orbital to a single canonical unoccupied orbital, the singlet and triplet states in question differ only in whether the electrons in the SOMO (which would be the LUMO in the ground state) and the SOMO-1 (which would be the HOMO in the ground state) have the same spin (or, more accurately, are spin coupled). If there is no overlap between the GS HOMO and the GS LUMO, the relative spins of the SOMO and SOMO-1 do not affect their mutual repulsion and therefore do not affect the energy. It is true that in such a simple, zeroth-order case, the HOMO of the T1 state – the HOMO of the S0 state is equal to the HOMO-LUMO gap in the GS, but that doesn't tell you anything about the static correlation energy which is responsible for triplets in general being lower in energy than singlets. Also, such systems are pretty rare; they generally have to be highly symmetric, contain only light atoms, and even those requirements are not in and of themselves sufficient.
I might be able to give more specific information if I knew more about your system; on the other hand, since I have never dealt with TADF, I might just not know enough about what you are attempting.
