BENT LEY GLASS 825 



sign reversed) with respect to the symmetry operations characteristic 

 of a molecule. Tliese are the reflections, rotations, and inversions 

 which lead to a molecule indistinguishable from the original one. 

 The classification of the orbitals is necessary for the evaluation of 

 the intensity of the absorption (i.e., probability of transition) as well 

 as the optical rotatory dispersion. The probability of a given transi- 

 tion is calculated from the transition moment integral, which, for 

 an electric dipole transition — the most important in chemistry and 

 biology — is 



/. 



+ 00 



where P is the probability of the transition, xpQ is the total wave func- 

 tion of the ground state of the molecule, -E.r,3/,s is the electric dipole 

 vector along x, y, and z axes chosen to define the plane of the mole- 

 cule, and ijje is the total wave function of the particular excited state 

 of the molecule. 



In the examples chosen, three different kinds of promotion, n -^ tt*, 

 n — > (T*, and tt -^ tt*, are considered for formaldehyde, two (n —> tt* 

 and 77- -» 77*) for pyridine, and two {n -^ 77* and tt -^ tt*) for 

 purine. 



To establish whether or not a particular transition is "allowed," 

 that is, has a reasonable probability of occurring, one needs only 

 to show that this integrand is of the totally symmetric species, since 

 in that case the integrand will always be positive and the whole in- 

 tegral cannot be zero. Translation of the molecule along the coordi- 

 nate axes is identical in symmetry properties to the electric dipole 

 moments induced by light waves having the same direction. The 

 magnetic dipole moments induced by light waves have the same 

 transformations as the rotations about the respective coordinate axes. 

 For example, if only a translation vector along the y axis causes the 

 integrand to transform totally symmetrically, then only light with 

 its electric vector oriented along the )' axis of the molecule will be 

 absorbed (Fig. 2) . Thus, in the case of formaldehyde, the n -^ tt* 

 transition is forbidden, the n — ^ cr* transition is allowed for light 

 polarized along the y axis, and the tt -^ tt* transition is allowed 

 for light polarized along the z axis. In general, transitions oi n -^ tt* 

 type are always polarized out of plane ( i.e., along the x axis) , if not 

 forbidden; whereas tt ^ tt* transitions are always polarized in plane, 

 if not forbidden. 



