97 



place. 



The potential energy surface which one generates from the parameters given 

 above is an elliptical paraboloid: on a horizontal cross section, ellipses are 

 obtained which represent the Lissajou interaction of the two normal vibrations; 

 in a vertical cross section, parabolas are obtained representing the potential 

 energy of a harmonic oscillator (in this approximation, i.e. , dissociation is om- 

 mitted). 



A succession of electronic states requires a series of such parabaloids in 

 three-dimensional space in the present case, the minimum of each parabaloid 

 corresponding to the zero-point electronic energy (roughly) of each successively 

 higher electronic state. 



Only two points remain to complete the picture. One is, if the essential 

 bonds in the molecule are not broken, so the geometrical structure remains 

 similar in various excited states (so that the same set of normal vibrations can 

 represent the molecular vibrations), then there is a mutual rotation of the ellip- 

 tical parabaloids in space about the common energy axis. 



The result of the above effect is the production of an extraordinary region of 

 interaction of two successive potential surfaces, representing two adjacent elec- 

 tronic states. This, I should say, is the main reason for the extraordinary 

 probability of internal conversion in complex molecules. 



Let me re-emphasize this, because the physicist familiar only with nuclear, 

 atomic, and diatomic phenomena would not realize the existence and efficiency 

 of this process of internal conversion in molecules. No case is known in which 

 a pentatomic or larger molecule can emit from any but its lowest allowed excited 

 electronic state. The internal conversions are thus usually about 100% efficient 

 as far as re-emission from higher levels is concerned. 



Another point worth mentioning, and again one which would perhaps surprise 

 the nuclear-atomic-diatomic physicist, is the limited number of low-lying elec- 

 tronic states in relatively complex molecules. For example, in benzene, there 

 are only three excited singlet and three excited triplet states below the Rydberg 

 states, which latter lie in the vacuum U. V. region. 



Combined with what I have said previously in this conference about relative 

 probability of normal internal conversions and intercombinational (e.g. singlet- 

 triplet) internal conversions (it will be noted that both of these are radiationless, 

 the electronic energy disappearing as heat), the conclusion one can draw is that 

 frequently all of the electronic excitation energy can end up in the lowest metas- 

 table electronic (e. g. triplet) state. 



Thus, most molecules are not fluorescent, but most organic molecules are 

 phosphorescent (of course, when studied under appropriate conditions), with a 

 quantum efficiency which is complementary to the fluorescence quantum efficien- 

 cy (if both are observed). 



LINSCHITZ: This would mean that all the estimates of the singlet lifetime 

 must be off by a factor of ten. 



KASHA: Yes, that is very possible. In fact, the lowest singlet and the low- 

 est triplet, if they radiate at all, are the only radiation levels in the molecule, 

 and if the triplet does radiate then the intrinsic (natural), singlet lifetime is 

 longer by a factor which corresponds to the quantum efficiency. 



