42 



LIGHT AND LIFE 



flies symbol is reserved for molecular states (see below). Similarly, 

 the highest /^orbital of formaldehyde is said to "transform as sym- 

 metry species b.J' Both of these classifications depend on the axis 

 choice as given in Figs. 5 and 7. 



Using the Co^, character table of Fig. 7, together with the coordinate 

 choices shown in Fig. 5, the reader should be able to classify all of 

 the molecular orbitals shown in Fig. 3 for the formaldehyde molecule, 

 and Fig. 4 for the pyridine molecule. The results are tabulated in 

 Fig. 8. 



Formaldehyds (Coy) Pyridine (C2v ) Pyrimidine {C2v) Purine (C,h) 



IT 



n 



TT 



cr 



at 



TT, 



'^ b| 



TTa 



^3 



7T- 



TT, 



b, 

 b, 



b2 

 Qi 

 b, 



C2 



b, 



< • 



r\j a 



n,, Hg 



I 



TT. 



Fig. 8. Symmetry species classification of niolcculai oibilals 

 (cf. Figs. 3, 4, 5, 7, and 9). 



For pyrimidine, and the other diazines, a unicjue problem appears 

 in relation to the symmetry classification of the n-orbitals. Referring 

 to the coordinate axis choice of Fig. 5, it is evident that neither lone- 

 pair orbital n,^ nor u,, for pyrimidine (Fig. 9) has proper symmetry 

 properties by itself. For example, if r?„ is subjected to the Co or 

 or/ (xz) operation, it fails to go into n^ or (— ) n^; instead it goes 

 into 77,, under these operations, and vice versa. Thus, neither the 

 orbital 77^ nor 77^ woidd satisfy the symmetry eigenvalue equation of 

 Fig. 6 (top). However, if one considers the linear combinations of n^^ 

 and Ui^ as shown in the lower part of Fig. 9, then it is found that the 

 resultant orbitals 77+ and 77- do transform either symmetrically or 

 antisynnnetrically luider all four operations of the C2„ point group, 

 to which pyrimitiine belongs. These classifications are entered into 

 the third column of Fig. 8. The interaction between the orbitals 1%^ 

 and 77^ is exaggerated somewhat in the schematic drawing of Fig. 9. 

 However, the interaction is physically significant (26) and \\'ill be 

 discussed further, below. 



