User:Mtt.cucchi

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(rISC) is a radiationless process involving a transition between two electronic states with different spin spin multiplicity: specifically, it refers to the transition of an electron from a triplet state to a singlet state, as opposed to the intersystem crossing.

Singlet and Triplet states

See the page about intersystem crossing or about Jablonski diagram.

rISC rate in organic molecules

Triplets are more stable than singlets. The energy difference between the two states Δ_ST is given, in organic molecules and metal-organic compounds, by the double of the exchange integral J. J can be calculated as the superposition of the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular orbital (LUMO) of a given compound, as follows:

$\Delta _{ST}=2J=2\int d^{3}r_{1}\int d^{3}r_{2}\rho (r_{1}){\frac {e^{2}}{4\pi \epsilon _{0}|r_{1}-r_{2}|}}\rho (r_{2})$.

As the HOMO and LUMO energies are affected by the dielectric environment, K can show a strong dependence depending on the materials the compounds are immersed in. Such dependence is particularly strong in case of charge-transfer states i.e. electronic excited states in which the hole and and the electron reside on different moyeties of the molecule.

The rate with which a triplet exciton can undergo a spin-flip and become a singlet is the reverse intersystem crossing rate (K_risc). It is, as a first approximation, a thermally activated process:

$K_{risc}=K_{isc}\exp({-{\frac {\Delta E}{KT}}})$

where KT is the thermal energy and K_isc is the rate of the intersystem crossing.

Molecules can be designed in such a way to minimize the intgral K, and hence maximize the rISC: in this regards, a photophysical process called thermally-activated delayed fluorescence is of commercial interested in the display industries, where it is employed to enhance the efficiency of organic fluoropheres for OLED displays.

In case heavy atoms are present in the molecular structure, the spin-orbit coupling can become predominant and speed up the rISC. This is the case of many phospsorescent molecules.