The Förster triplet-triplet (T-T) transition is forbidden primarily due to the Wigner spin conservation rule, which is based on the conservation of spin angular momentum during electronic transitions. Here's a detailed explanation:

1. Understanding Spin States Singlet State (S): Total spin quantum number S=0S = 0S=0. The spins of the electrons are paired (opposite), leading to a net spin of zero. Triplet State (T): Total spin quantum number S=1S = 1S=1. The spins of the electrons are parallel, resulting in a net spin of one.

2. Wigner’s Spin Conservation Rule The Wigner spin conservation rule states that electronic transitions must conserve the total spin quantum number (S).Allowed transitions: S=0→S=0 or S=1→S=1. Forbidden transitions: S=0→S=1 or S=1→S=0.

3. Why T-T Transition is Forbidden Förster resonance energy transfer (FRET) typically involves dipole-dipole coupling. Dipole operators (electric or magnetic) cannot change the spin quantum number of the system. Since triplet states (T) have S=1, transitions involving the absorption or emission of energy between triplet-triplet pairs via dipole interactions cannot occur because it would violate spin conservation.

4. Implications for T-T Transition Förster resonance energy transfer can efficiently mediate singlet-singlet transitions (S-S) but not triplet-triplet transitions (T-T) due to this spin-forbidden nature. For triplet-triplet interactions, higher-order processes like Dexter energy transfer (which involves electron exchange) are required. Dexter transfer can mediate T-T transitions because it doesn't rely on dipole-dipole coupling but instead on short-range orbital overlap.

5. Alternative Mechanisms for T-T Transfer Dexter Energy Transfer: This process allows spin-allowed transitions by exchanging electrons between donor and acceptor molecules, preserving total spin. Spin-Orbit Coupling: In some cases, weak spin-orbit coupling can mix singlet and triplet states, partially relaxing the spin-forbidden rule. However, such transitions are weak compared to dipole-allowed ones.

Summary The triplet-triplet Förster transfer is forbidden because the transition must preserve spin quantum numbers, and dipole-dipole interactions cannot change spin states. Alternative mechanisms like Dexter transfer and spin-orbit coupling are required to facilitate T-T transitions, albeit with lower efficiency.