48 LIGHT AND LIFE 



allowed (for electric dipole radiation) . Thus, to establish Avhether 

 an electronic transition is allowed from one state of a molecule to 

 another, it is sufficient to show that the complete integrand belongs 

 to (or contains) the totally symmetric species. Thus, by taking the 

 direct product of the species of the ground state symmetry, the co- 

 ordinate translation symmetries, and the excited state symmetry, one 

 can establish the allowedness of an electronic transition. Further- 

 more, if only, e.g., a y translation vector causes the integrand to trans- 

 form totally symmetrically, then only light with its electric vector 

 oriented along the )'-axis of the molecide (for the chosen coordinate 

 scheme), will be absorbed. 



As an example, consider the ?? — > cr* promotion in formaldehyde. 

 Fig. 10. The ground state total wavefunction has symmetry A-^^. The 

 coordinate vectors x, y, z transform as B^, fio, A-^^ respectively (cf. 

 Fig. 7) , for the axis choice of Fig. 5. The excited state corresponding 

 to n —> cr* promotion transforms as Bo (third row of Fig. 10) . Thus 

 the direct products are: 



for the x-polarized transition y4i X -^i X -^2 = ^2 (forbidden) ; 

 for the )'-polarized transition A-^^ X -^2 X ^2 == ^1 (allowed) ; 

 for the z-polarized transition A-^ X ^1 X ^2 = ^2 (forbidden) . 



Thus, only if the electric vector of the impinging light wave is polar- 

 ized along the )'-axis of formaldehyde (i.e., according to Fig. 5, along 

 a line perpendicular to the C-O axis and in the plane of the H^CO 

 skeleton), will light be absorbed, even if of the right frequency or 

 wavelength. Column 4 of Fig. 10 tabulates the selection rules aiul 

 polarization directions for several molecules. 



It is especially to be noted that for singlet-singlet transitions, the 

 transitions of yi — » tt* type are always polarized out-of-plane (x-axis. 

 Fig. 5) , if not forbidden. Conversely, the transitions of tt -^ tt* type 

 are always polarized in-plane ()'-axis or z-axis. Fig. 5) , if not for- 

 bidden. 1 his characteristic jjolarization not only permits a qualita- 

 tive distinction to be made between these transitions, but also leads 

 to diilcicnccs in physical interactions between molecules, as will be 

 discussed later. 



B. Rotatory Strength 



The optical rotatory strength (contribution to optical rotatory 

 disj)ersion) of an electronic transition is given by a scalar product of 

 two different vector integrals (7) , as shown in the lower part of 

 Fig. 11. The first integral is the transition moment integral which 



