ENERGY EXCHANGE IN PHOTOREACTION.S 



g 



molecules. An attempt has been made to unify most phases of energy 

 transfer in terms of a single type of potential-energy diagram. 



1-2. POTENTIAL ENERGY AND LIGHT ABSORPTION 



The potential energy of any collection of atoms can be diagramed in a 

 hyperspace with dimensionality equivalent to the number of independent 

 interatomic distances plus one additional coordinate for the values of the 

 energy. It is immaterial whether the assembly of atoms is stable or 

 unstable. In the simplest case of a 

 stable diatomic molecule, two di- 

 mensions are required: the inter- 

 atomic distance and the potential 

 energy. The relation of these two 

 variables is satisfactorily repre- 

 sented by a Morse function (Morse, 

 1929) 



M 





o 



Q. 



INTERNUCLEAR DISTANCE (rj 



Fig. 1-2. Franck curves of potential 

 energy for the ground and first electron- 

 ically excited states of a diatomic mole- 

 cule. The symbols include those of the 

 Morse function describing the ground 

 state. 



' (1-1) 



where the symbols have the mean- 

 ings shown in Fig. 1-2. In this fig- 

 ure there are two regions of stable 

 atomic configuration. One occurs 

 at infinite separation lying to the 

 right; the other, near the bottom 

 of the potential well at the equilib- 

 rium separation tq. The two situ- 

 ations are separated by the poten- 

 tial energy D, equal to D' minus 

 the zero-point energy }2hvo, where vo is the fundamental frequency of 



oscillation equal to — ^( - 



in which /j. is the reduced mass of the mole- 

 cule and / is the force constant existing between the atoms. Solutions of 

 the wave equation yield the allowed vibrational states, which are integral 

 multiples of the fundamental frequency. Each horizontal hue cuts the 

 potential well at the maximum and minimum interatomic distances through 

 which the atoms may pass in the steady oscillation allowed for the given 

 vibrational state. At these two points the energy is primarily potential, 

 and the atoms will move most slowly relative to each other in the region of 

 these points. According to the Franck-Condon principle (Franck, 1926a), 

 electronic transitions will occur most frequently in these regions, and 

 indeed so rapidly (IQ-^^ sec) that there is no appreciable change in the 

 mteratomic configuration, which can be altered only in the characteristic 

 time of 10-12-10-14 sec. Electronic transitions, under these conditions, 

 are said to be adiabatic. Accordingly paths 1 and 2 in the two-dimen- 



