Knowledge Bank

Some recent $experiments1,2$ have shown that there is an increase in the measured phosphorescence lifetimes of certain organic molecules when hydrogen is replaced by deuterium In $benzene2$ the increase is by a factor of 1.6 while for $napthalene1,2$ it is by a factor of 8. Absolute quantum $yields3$ indicate the presence of a non radiative $T1\to S0$ process. The present paper discusses the mechanism of this process. It is shown that the rule constant for the radiationless transition is [ P;(sec^{-1})=\frac{4\pi^{2} V^{2} I^{2}}{\epsilon h} ] where $ϵ$; is the final state energy-spacing, V is the matrix element for the electronic perturbation interaction, and I is the vibrational overlap integral between initial and final states. No classical potential surface crossing is necessary for the radiationless process to occur. The longer lifetimes of benzene-$d6$, and napthalene-$d8$ compared with ordinary benzene and napthalene are explained in terms of the higher vibrational quantum number necessary to obtain near resonance between $T1$ and $S0$ states and the consequent smaller energy rational overlap integrals involved Similarly, smaller energy gaps are expected to lead to shorter lifetimes (and lower radiative quantum yields) in aromatic compounds; this is observed in the series $C6H6,C10H8$ and $C14H10$ (anthracene) whose lifetimes are 16 sec, 2.5 ser. and .l sec, respectively, and whose $T1-S0$ spacings are $29,400cm-1,21,300$ $cm-1$, and $14,700cm-1$ The theory is found to consistent with experimental lifetimes in all cases except those of coronene and triphenylene.