80 RADIATION BIOLOGY 



remove the alternation and see a shift to lower frequencies. Kuhn 

 (1949b) showed how we can do this, in effect, in the symmetrical cyanine 

 dyes, where an even number of electrons are confined to an odd-membered 

 chain. It is then the atoms and not the bonds which are at alternate 

 maxima and minima of electron density. The bonds are all approxi- 

 mately equivalent. These features have their counterparts in the classi- 

 cal valence structures for these molecules, where the excess charge is 

 localized on alternate atoms and where every bond is alike, a one-and- 

 one-half bond, single in one valence structure and double in another, 

 equivalent structure. There is then no alternation of bond lengths. The 

 alternation of charges on the atoms does produce a periodic potential, 

 but a much smaller one than when adjacent atoms are drawn together. 

 Therefore, as seen in Fig. 2-2 and in the top part of Fig. 2-6, these com- 

 pounds should, and do, absorb at almost exactly the frequencies predicted 

 by the square-well approximation. 



With unsymmetrical cyanines, some alternation appears again and may 

 increase in magnitude up to its value in the polyenes. The spectra show 

 corresponding shifts to higher frequencies with greater asymmetry, as was 

 shown by Brooker and Sprague (1941) and Kuhn (1949b). 



Possibly the difference between the symmetrical cyanines and the 

 polyenes will be less marked for exceedingly long chains, longer than 

 any observed in the laboratory, because the alternation in the polyenes 

 should eventually approach zero with increasing length. 



Nomenclature. The molecular orbital energies shown in Fig. 2-3 and 

 at the bottom of Fig. 2-6 were obtained by letting a single electron travel 

 in a potential trough. Each of these orbitals or energies then represents 

 a shell, in which electrons may be located, like the X-ray shells of an 

 atom. The total energy of the molecule is approximately the sum of 

 these one-electron energies for all the electrons. The resonance energy 

 may be computed simply by carrying out the summation and comparing it 

 with the energy if the molecule were separated into isolated double bonds. 



The total energy of the molecule in its lowest energy state, or with 

 various types of excitation of an electron from a filled shell to an unfilled 

 shell, is shown in the energy-level diagram or state diagram at the top of 

 Fig. 2-6. The distinction between shells and states is essential and must 

 be remembered. 



It is convenient to adopt the following simple uniform nomenclature 

 for all conjugated systems: Let the highest filled shell be /, the next 

 highest, e, etc.; the lowest unfilled, g, the next lowest, h, etc. The first 

 transition will then be J-g, the next, e-g, etc. 



The configuration of the whole molecule specifies how many electrons 

 are in ea(;h shell. The lowest energy configuration is then . . . d-e-p; 

 the next lowest, . . . d~e-fg; the next, . . . d^epg; etc., where the super- 

 scripts give the number of electrons of each kind. 



