82 RADIATION BIOLOGY 



or triplet. A superscript zero is placed at the right when a state is " odd,"^ 

 that is, when the product of orbital types, even or odd, for all electrons 

 is odd. Only even-odd transitions are allowed. The " even " and " odd " 

 notation is, of course, valid and useful only when a molecule has a center 

 of symmetry. The Mulliken notation (1939; Mulliken and Rieke, 1941) 

 for polyene states is also indicated in Table 2-1 for comparison. 



Strictly, the transition frequencies predicted by the free-electron model, 

 as just given and as shown in Figs. 2-1, 2, and 6, were computed neglect- 

 ing electron interaction, and so they represent only the energy jump 

 between shells, or the "center of gravity" of a configuration. It was 

 therefore slightly misleading in the figures to compare the first pre- 

 dicted frecjuency with the first strong absorption frequency, which is 

 undoubtedly ^A~^B°. What we should have done was to locate the 

 other transition to the first excited configuration ^A-^B°, which lies at 

 lower frequencies (by the Hund rule, which says that, in a given con- 

 figuration, states of higher spin generally lie lower). The average of these 

 two frequencies could then be compared with the predicted frequency. 



However, the singlet-triplet intensity is weaker than the singlet-singlet 

 by a factor of about 10^ in hydrocarbons. For this reason and probably 

 for other reasons discussed later under Photoisomerism, excited triplets 

 seem never to have been found in polyenes, so that the exact location of 

 the centers of gravity of excited configurations is not feasible. We may 

 nevertheless use the theory for qualitative understanding or for com- 

 paring the singlet-singlet transitions of similar molecules. For these 

 purposes our ignorance of the triplets is not so serious. 



In the upper part of Fig. 2-6 the length of the horizontal lines indi- 

 cates the logarithm of the molar extinction of the transition from the 

 ground state, since this is a useful indication of the character of an 

 excited state. For completeness the unknown triplets are indicated 

 schematically for /3-carotene. Such an energy-level diagram is a simple 

 way of summing up the information on electronic excitation obtained 

 from an absorption spectrum. It omits the vibrational structure shown 

 by the exact contour of the spectrum, which in large molecules is not 

 essential to an understanding of the electronic excitation. 



The "free-electron" line in the top half of Fig. 2-6 shows the predicted 

 position of the center of gravity of the first excited configuration by the 

 free-electron model. It is seen that a symmetrical cyanine fits this curve 

 much better than the corresponding polyene because of the alternating 

 Kuhn potential in the latter. 



EMISSION OF LIGHT 



The emission of light by an excited molecule is a process the reverse 

 of the absorption process. It seems to be controlled, as the absorption 

 is not, by time-constant considerations. An energy-level diagram of a 



