Q RADIATION BIOLOGY 



abscissa is any nuclear separation under discussion. Excited states for 

 polyatomic molecules, represented on the same plot, will only infre- 

 quently have the same degree of freedom involved in any reaction proc- 

 ess as does the ground state. To avoid complexity in presentation, 

 we must generally ignore the latter fact. It is unavoidable that any 

 visualizable simplification for the very complicated potential-energy situ- 

 ations that occur when there are more than two atomic separations is 

 unsatisfactory. It will be found that these surfaces, represented as 

 curves in two dimensions or contour maps of three dimensions, are inade- 

 quate for certain discussions. Unfortunately no more satisfactory alter- 

 native method for exposition is available. 



The potential surfaces for diatomic molecules are widely separated 

 along the energy coordinate. There will be, consequently, but a few 

 excited states, if any, in the limit of photoenergies under consideration 

 (2000-10,000 A; 1 X 10^-5 X 10^ cm-^; 28-142 kcal/einstein; 1.2-6.2 ev). 

 Triatomic species have more closely spaced electronic levels, and gener- 

 ally the number of levels increases and their spacing decreases as the 

 molecules increase in size and complexity. Any saturated organic mole- 

 cule of more than three atoms will have a very dense distribution of 

 electronic levels. If there are n bonding electrons in the molecule, there 

 will be 2" eigenf unctions corresponding to the lowest states of the sepa- 

 rated atoms. When the atoms are combined, this number is preserved, 

 though not all the functions will correspond to different energies. The 

 number of different surfaces is n!/(n!/2!)- « n-''^2". For most organic 

 molecules this is a large number, yet states due to excited electrons have 

 not been considered. The total fraction of states lying within 150 kcal, 

 or 6.5 ev, of the ground state, though small, is still a large number, so 

 that there is practically a continuum of states. The density of crossing 

 points, i.e., points of intersection of surfaces, will be high, and it becomes 

 apparent that precise treatment of the structure of energy-transfer proc- 

 esses for these molecules is very complicated. A quantum-mechanical 

 treatment of a small protein molecule (molecular weight 50,000), for 

 example, one composed entirely of leucine, according to present simplified 

 methods would require consideration of something like 



17,200-^^ X 2i"oi = 10^1" 



independent states— impossible complexity from a detailed point of view. 

 For a triatomic molecule such as N2O, there are eight valence electrons. 

 A three-dimensional contour map of the type shown in Fig. 1-4 can be 

 used to display each potential-energy surface. Two internuclear sepa- 

 rations are reciuired to describe the potential energy (plotted along the 

 axis normal to the surface of the page) if the bending vibration is neg- 

 lected, as it may be for convenience. Inclusion of this bending vibration 

 would require an additional coordinate. The contour map of Fig. 1-4 is 



