ENERGY EXCHANGE IN PHOTOREACTIONS 11 



readily represented in terms of the three-dimensional contour map, one 

 cross section of which is shown in Fig. 1-5. However, the various situ- 

 ations can be investigated in a qualitative fashion in terms of the simpler 

 diagrams. 



2. INTERNAL CONVERSION OF ENERGY 



2-1. CONDITIONS FOR INTERSECTION 

 OF POTENTIAL-ENERGY SURFACES 



Internal conversion is defined as the exchange of energy between elec- 

 tronic and vibrational degrees of freedom within a single molecule (Teller, 

 1937 ; Franck and Livingston, 1941) . The essential distinction from other 

 energy-exchange processes is that it involves the crossing of potential- 

 energy surfaces for different electronic states, as shown in Fig. 1-3. 

 Molecular electronic states are either stable or unstable. If excitation 

 is to an unstable state C (Fig. 1-3, path 1), the molecule, in coming to 

 equihbrium in the new electric field of the electrons, undergoes a sepa- 

 ration of its parts, and the excess of energy above that required to form 

 the products appears in external degrees of freedom. A part of the excess 

 may pass through the vibrational degrees of freedom in so doing. When 

 the state is stable, several situations can occur, depending on the amount 

 and type of crossing possible from this state. If there is no crossing point 

 available except with high activation energy, as shown in Fig. 1-3, fluo- 

 rescence will occur with high probability via path 3. Increasing temper- 

 ature increases the rate of crossing the barrier with height Eq or E'o, so 

 that its effect will be one of quenching, i.e., diminution of fluorescence. 

 This is a common observation for most fluorescing substances. In Fig. 

 1-3 quenching returns the molecule to its ground electronic state A, with 

 energy greater than the dissociation value. Had the ground state been 

 represented by Fig. 1-5, B, no dissociation could result, and the electronic 

 excitation energy would be completely converted into vibrational energy 

 of the ground state, subsequently to be lost as heat. 



Internal conversion need not be to the ground state, but to any other 

 state of higher or lower energy whose surface crosses the surface repre- 

 senting the initially excited state. Rearrangement of energy by crossing 

 of surfaces is radiationless and hence subject to weaker restrictions than 

 apply to optical transitions. Crossing may occur between levels with 

 different multiplicity,^ as shown in Fig. 1-6. According to Lewis and 

 Kasha (1944), this is an explanation of phosphorescence; i.e., radiation is 



«The term "multiplicity" refers to the quantum number of the resultant spin 

 angular momentum for all the atoms of the molecule. If the over-all spin vector 

 has an associated quantum number S, the multiplicity is 2S + 1, and that is the 

 number of components of the spectral lines corresponding to the particular state. 

 It bears a direct relation to geometrical symmetry. Optical transitions between 

 states of different multiplicity are allowed only with very low probability. 



