ENERGY EXCHANGE IN PHOTOREACTIONS 



41 



the potential-energy surfaces for Hg*'"- + Hg^*^^ and Hg^''^ + Hg*-"^ 

 will be completely superimposed, so that crossing points exist at infinite 

 separation of the atoms. The crossing efficiency is limited by the rapid 

 decrease in interaction potential with internuclear or intermolecular dis- 

 tance but may be appreciable over very large distances if the potential 

 surfaces are closely congruent. The formula of Landau and Zener, Eq. 

 (1-9), is clearly not applicable, since e and \si — Sj\ both go to zero as the 

 surfaces achieve close superposition. A different theoretical approach, 

 initiated in quantum-mechanical form by Kallmann and London (1929), 

 is necessary when the energy discrepancy between initial and final exci- 

 tation energies becomes small. The observed resonance dependency of 

 transfer efficiency appears in the theories and explains the observations 

 of resonance in thallium fluorescence sensitized by mercury. As perfect 

 resonance is approached, gateways 

 develop at larger internuclear dis- 

 tances and hence at lower potential 

 energies. Similarly the transmis- 

 sion coefficient approaches 3^2) ^i^d 

 the rotational partition function in- 

 creases. All these factors increase 

 the rate of energy transfer, and it 

 can be seen that the dependence of 

 the rate on energy discrepancy can 

 be something like a resonance rela- 

 tion.^ The relation, approximately 

 as calculated by Kallmann and 

 London (1929), is shown in Fig. 1-14. 

 As Figs. l-13a and b are drawn, 

 the transfer on Fig. l-13a will be 

 more efficient than that on h because 



-3-2-101234 

 RELATIVE ENERGY DISCREPANCY 



Fig. 1-14. A calculated resonance rela- 

 tion between the rate of energy transfer 

 and the energy discrepancy existing 

 between the excitation energy available 

 in a particular degree of freedom of the 

 primary molecule and the energy that 

 can be taken up by a degree of freedom 

 of a quenching molecule. (After Kall- 

 mann and London, 1929.) 



the collision energy is negative. 



It might be expected, by analogy with the former figure, that some 

 quenching processes will demonstrate the unusual phenomenon of nega- 

 tive temperature coefficients. A temperature study of the mercury-thal- 

 lium quenching reaction could, perhaps, distinguish whether Fig. l-13a or 

 b is appropriate. 



Fluorescence from the lower electronic levels of thallium, which do not 

 match in their transitions the excitation energy of mercury, may be 

 explained by the occurrence of collisions of the second kind which thallium 

 atoms undergo following their initial excitation to the highest possible 

 level. Little electronic energy need be converted in this way into trans- 



^ That the resonance relation is actually predicted by theory is a matter of consid- 

 erable complexity. The reader is referred to Mott and Massey (1949), Chaps. 8 

 and 12, and to Stueckelberg (1932). 



