222 RADIATION BIOLOGY 



of chemical processes. A summary of analyses of electronic spectra of 

 polyatomic molecules has been given by Sponer and Teller (1941). 



Again, as in the diatomic case, the potential function represents the 

 total energy of the molecule for a set of fixed values of the atomic posi- 

 tional coordinates, molecular vibration and rotation being constrained. 

 However, the potential surface which represents this potential function 

 geometrically is now a surface in {n + 1) -dimensional space, where n is 

 the number of independent coordinates necessary to specify the relative 

 positions of the atoms (3 for a triatomic molecule, 6 for a tetratomic mole- 

 cule, etc.). Thus even for a triatomic molecule the potential function is 

 a surface in four-dimensional space and cannot readily be visualized or 

 represented graphically. 



A polyatomic molecule in some definite vibrational level of an electronic 

 state has a quantum energy given by a cut through the potential surface 

 by the "plane" E = constant. As the various degrees of freedom 

 execute their vibrations, the point on the potential surface which repre- 

 sents the configuration of the molecule (henceforth called the "configu- 

 ration point") will move down from a point on the E = constant plane 

 through a region of lower potential energy and back toward E = constant 

 again. But this motion will not be constrained to two dimensions, as in 

 the diatomic case; rather, it wll execute an (n -h 1) -dimensional space 

 curve — a sort of generalized Lissajous figure. Thus there is a continual 

 energy exchange between various vibrational degrees of freedom — few, or 

 many, depending on the magnitude of the total vibrational excitation 

 energy and on the shape of the potential surface (the latter reflecting the 

 extent of " couphng" of various vibrations, or, in simpler terms, the degree 

 of "isolation" of the particular vibrating groups). One consequence of 

 this behavior is that any particular atomic configuration is reattained 

 infrequently compared to the corresponding time for the diatomic case, 

 namely, one vibration period or roughly 10~^* second. The time between 

 successive repetitions in the polyatomic case is usually very much longer 

 (and may be infinite if the molecule shows dissociation, predissociation, 

 or internal conversion; for the last-named see p. 226). 



It can be instructive in the triatomic case to consider a three-dimen- 

 sional section of the four-dimensional surface by supposing one of the 

 coordinates to be fixed, usually by considering only hnear configurations 

 of the molecule. Examination of such a surface, which can be repre- 

 sented graphically either by contour lines or in perspective, may lead to 

 insight into the behavior of the molecule. Such studies have only been 

 initiated in recent years. An example of this type of potential surface is 

 illustrated in Fig. 3-7. It represents the linear HgH2 molecule; this 

 molecule is not stable, but the properties of its potential surfaces for 

 excited states determine the course of the reaction between Hg* and Ho 



