ENERGY EXCHANGE IN PHOTOREACTIONS 9 



The species ahc has three valence electrons, which can be considered 

 to interact in pairs. In terms of the formalism of modern quantum 

 mechanics, the interactions are of two types: (1) coiilombic, due to elec- 

 trical interaction of the charged bodies, nuclei, and electrons involved, 

 and (2) exchange, due to the indistinguishability of electrons. Energies 

 resulting from the latter (a, /3, 7) have no classical analogy but provide 

 most of the stabilizing energy of the molecule. In fact, the coulombic 

 energies A, B, C can usually be approximated as a small fixed fraction of 

 their respective exchange energies (about 14 per cent) . The total energy 

 of the system of three atoms is given bj^ a formula of London (1929a,b) : 



E = A^B^C~ {Hiia - 0r + (/3 - 7)'^ + (t - ay]]^^ (1-8) 



Each total interaction, i.e., A + a, etc., can be approximated by a Morse 

 function, with constants for the pair of atoms determined from spectra. 

 If the approximation with regard to coulombic energy is made, it is then 

 relatively easy, though tedious, to evaluate the total potential energy for 

 every separation of the atoms. Further complications arise in excited 

 states because of the additional information needed for the new Morse 

 functions, but when this is known, the excited-state potential-energy 

 surfaces can be calculated in the same manner. In this way any desired 

 potential-energy plot can be obtained in approximate form. 



A linear triatomic molecule like N2O can be graphed in three dimen- 

 sions if the bending vibrations are neglected. The general case treated 

 above requires more, 3n — 6 + 1, for the general nonlinear molecule and 

 one more for linear molecules. 



It is now possible to consider the various processes which result from 

 photoexcitation or which produce radiation from chemical energy. 

 Potential-energy surfaces play a central role in such a discussion for the 

 following reason: A random choice of coordinates to represent the geo- 

 metrical situation that exists for a molecule at any instant will usually 

 lead to a complicated expression for potential and kinetic energies in 

 terms of these coordinates. It is possible, however, by taking suitable 

 combinations of any such random set of coordinates to form another set 

 containing the same number of independent coordinates, but one in which 

 the energy expressions reduce to sums of terms in the single coordinates. 

 That is, cross terms in two or more variables are eliminated so that 

 motions in these "normal" coordinates, which may be extremely compli- 

 cated visually, can be treated as independent of all other motions in other 

 normal coordinates. In linear triatomic molecules, representation of the 

 normal coordinates can be achieved by a simple method involving only 

 the change in angle formed by the axes and the relative magnitude of 

 units on the two axes. Normalization in Fig. 1-4 was obtained by cast- 

 ing the axes at an angle less than 90°. A useful property of potential- 

 energy surfaces is the fact that after normalization the frictionless move- 



