ENERGY EXCHANGE IN PHOTOREACTIONS 



21 



Et and after collision is E't, n is the vibrational quantum number, and 

 V is the vibrational frequency, the energy-conservation expression for 

 conversion of one vibrational quantum is 



E; - £, = (n + y2)hv - {n~\ + y^hv, 



neglecting rotation, as we generally will for purposes of simplified expo- 

 sition. If now the potential-energy surface for approach along the line 

 of centers, i.e., along the best direction for such a collision, is constructed 

 as in Fig. 1-5. the dotted line, which is the change of configuration with 

 time, represents the collision process. In Fig. 1-10 an enlarged section 

 of a typical collision path is shown. Since vibrational energies must 



DISTANCE ALONG COLLISION COORDINATE 



Fig. 1-10. Enlarged drawing of collision trajectory for interconversion of vibrational 

 and translational energy (of. Fig. 1-5). 



change by integral numbers of quanta, the best classical picture is to 

 suppose that all such trajectories of configurations which differ in vibra- 

 tional energy from the quantized values by small fixed amounts are 

 allowed and that all other trajectories are unsuccessful. The successful 

 trajectories per unit time can then be counted using statistical mechani- 

 cal expressions in a way analogous to the calculation of reaction rates. 

 The present problem of determining efficiency in energy transfer is some- 

 what more difficult in that more restrictions are required than in reaction- 

 rate theory. It is therefore necessary to examine several conditions on 

 which the simpler theory rests and extend them to collision processes. 

 We shall not be especially concerned with rotational degrees of freedom, 

 since these may be treated in a complete theory as a special application 

 of what will be said about vibration. 



Speaking classically, certain phases of the 'rotational motion, such as 

 linear collision of molecule and atom or side-by-side approach of t^^o 

 molecules, will be more effective for energy transfer than others. It is 

 generally assumed that the potential surface is calculated only for such 



