44 LIGHT AND LIFE 



molecules under discussion will be described. Not all available orbi- 

 tals will be populated in the ground state of a molecule. For examj^le, 

 in the piaine molecule ten 77-electrons are available, so that in the 

 ground state the lowest 5 vr-orbitals will be filled, with two electrons 

 per orbital. 



One additional set of symmetry classifications can be derived by the 

 use of the character tables of Fig. 7. It is important to be able to 

 deduce how a vector, or arrow, pointing along each of the coordinate 

 axes, transforms in both the Co,, and the Cj,, point groups. These 

 vectors can be considered to be translations T,., Ty, T^, (or displace- 

 ments) along the coordinate axes. The symmetry species classification 

 is straightforward and is given in the left column of the two tables 

 of Fig. 7. The physical importance of these symmetry classifications 

 lies in the fact that the electric dipole moment induced in a molecule 

 by a light wave will have identical symmetry properties to the 

 translation vectors. 



Furthermore, it is of interest to classify the transformation proper- 

 ties of the magnetic dipole moment induced in a molecule by a light 

 wave. It turns out that these components transform analogously to 

 the rotations R,., R,,, R, about the coordinate axes. 



The above coordinate transformations are important in deducing 

 the intensity of electronic transitions (selection rules) and the optical 

 rotatory strength of electronic transitions, respectively, and ^vill be 

 discussed in the following section. 



The molecular orbitals of Fig. 3 for formaldehyde and Fig. 4 for 

 pyridine were presented in order to illustrate the use of symmetry 

 properties of electronic distribution functions (orbital wavefunc- 

 tions) . In addition, the contour diagrams for the molecular orbitals 

 serve to give a more explicit idea of the nature of the process of 

 electronic excitation, once the molecular state electronic configiua- 

 tions are described. However, the methods by which these orbitals 

 are derived, and the mathematical form of the wavefunctions, are 

 omitted from this presentation, partly because these arc more com- 

 plicated matters which require nuu h more involved analysis. 



I). Electronic Configuration, State, and Transitions 



The order of the molecular orl)itals, the number of available elec- 

 trons, and the Pauli princijile may next be used to designate the 

 electronic configination of a molecule in any desired electronic state. 

 In the molecules under consideration, all of the molecular orbitals 

 are single or of unicpie energy ("non-degenerate") , and therefore 

 can be occupied by only two electrons with opposed spins. 



