8 



RADIATION BIOLOGY 



typical of such plots for stable molecules. Increasing numbers of atoms 

 in a molecule require multidimensional plots in which there is a valley of 

 relatively low potential energy corresponding to great extension in each 

 bond direction. A minimum, two valleys, and a plateau are seen to exist 

 in Fig. 1-4. One of the valleys represents N2 + O; another, NO + N. 

 Both lie off the figure out along the two axes shown. The least stable 

 situation is the plateau at the upper right, and it represents complete 

 separation into the atoms. The region of particular interest is near the 

 origin. A vertical cross section parallel to either axis through the center 

 of this region would look like the lower curve of Fig. 1-2, as seen to the 

 right of Fig. 1-4. Excited states would lie above the one shown in Fig. 

 1-4. All potential surfaces can be approximately calculated by the 

 "semiempirical" method of Eyring and Folanyi.* For a number of 

 small molecules, very accurate potential relations have been calculated 

 (for ground states) by detailed analysis of infrared spectra in much the 

 same way that the dissociation energies for Morse functions are deter- 

 mined (Herzberg, 1945). Few excited states have been studied in this 

 way, and only a very few molecules containing more than four atoms 

 have been thus studied. The details of excited surfaces in the neighbor- 

 hood of their potential minima have been calculated from spectra for 

 only a limited number of molecules. 



The semiempirical method is quantitatively unsatisfactory in most 

 cases; yet it remains the only way to secure potential-energy information 

 about complex molecules and for the calculation of absolute reaction 

 velocities. It should be mentioned that energy transfer in and among 

 molecules or atoms will be understood in terms of qualitative theories 

 for many years to come. The trouble is the same that has beset all 

 precise quantum-mechanical calculations, namely, mathematical com- 

 plexity. Qualitative or, at best, semiquantitative information has, how- 

 ever, been remarkably satisfactory in advancing our knowledge of physi- 

 cal and chemical processes. 



Consider a generalized triatomic molecule as pictured here: 



'' Detailed treatments of the "semiempirical" method, potential surfaces, and the 

 N2O system, in particular, are given by Glasstone et al. (1941, p. 337). 



