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What makes a molecule a good initiator of collisionally induced ISC? $\ce{N2}$, $\ce{O2}$ and $\ce{CH4}$ have been mentioned as examples.

I imagine the most important factor is the ability to quench vibrational excitation so that the Franck-Condon factors for non-radiative decay are optimized.

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There are two factors that I recall that can enhance intersystem crossing (ISC, the conversion of an excited singlet state to an excited triplet state, or vice-versa; $\ce{S_1 <=> T_1}$). One is the presence of a "heavy atom" such as bromine or iodine in the colliding molecule (or the excited molecule itself). The other is the presence of a paramagnetic species.

Both types of molecules enhance ISC by relaxing the quantum rules which forbid singlet-triplet conversions. When a heavy atom or paramagnetic molecule collides with a molecule in its excited state it can facilitate the electron spin flip (e.g. converting paired electrons to unpaired electrons, or vice versa) through spin-orbit coupling. It is this spin-orbit coupling that relaxes the rules forbidding direct conversion between $\ce{S1}$ and $\ce{T1}$ states. In essence spin-orbit coupling leads to a mixing of the singlet and triplet wavefunctions, thereby allowing singlet-triplet conversion.

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