THE IMPORTANCE OF THE VIBRATIONAL OVERLAP INTEGRAL WITH RESPECT TO RADIATIONLESS TRANSITIONS DENSE MEDIA
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Date
1961
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Ohio State University
Abstract
Some recent $experiments^{1,2}$ have shown that there is an increase in the measured phosphorescence lifetimes of certain organic molecules when hydrogen is replaced by deuterium In $benzene^{2}$ the increase is by a factor of 1.6 while for $napthalene^{1,2}$ it is by a factor of 8. Absolute quantum $yields^{3}$ indicate the presence of a non radiative $T_{1}\to S_{0}$ 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 $\epsilon$; 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-$d_{6}$, and napthalene-$d_{8}$ compared with ordinary benzene and napthalene are explained in terms of the higher vibrational quantum number necessary to obtain near resonance between $T_{1}$ and $S_{0}$ 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 $C_{6}H_{6}, C_{10}H_{8}$ and $C_{14}H_{10}$ (anthracene) whose lifetimes are 16 sec, 2.5 ser. and $<$.l sec, respectively, and whose $T_{1}-S_{0}$ spacings are $29,400 cm^{-1}, 21,300$ $cm^{-1}$, and $14,700 cm^{-1}$ The theory is found to consistent with experimental lifetimes in all cases except those of coronene and triphenylene.
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$^{1}$C. A. Hutchison and B. W Mangum, J. Chem. Phys. 32, 1261 (1960). $^{2}$M. R. Wright, R. P. Frosch, and G. W. Robinson, J. Chem Phys. 33, 934 (1960); also unpublished work. $^{3}$E.H Gilmore, G. E. Gibson, and D S. McClure J Chem. Phys. 20, 829 (1952); and correction to this is paper, J. Chem. Phys. 23, 399 (1955) $^{*}$D. P. Craig and I. G. Ross, J. Chem Soc. (LONDON) 1589 (1954).
Author Institution: Division of Chemistry and Chemical Engineering, California Institute of Technology
Author Institution: Division of Chemistry and Chemical Engineering, California Institute of Technology