MICHAEL KASHA 49 



was discussed in the preceding section, and whose square is rehited 

 to the intensity of an electronic transition. 



The second integral involves the three conij)onents of the mag- 

 netic dipole operator, and again the total wavefunctions for the 

 ground and excited states. As stated in section Ill-C, the magnetic 

 dipole operator has the symmetry properties of a rotation, Rj., Ry, or 

 R,. These have not been tabulated in the character table, but are 

 given in standard sources (Appendix, 7) . 



The translations T^., Ty, and T. and the rotations R^, Ry, and R^ 

 transform in a complementary manner if there is a plane of symmetry 

 or a center of inversion in the molecule. In this case, since the rotatory 

 strength is a scalar product of the two (vector) integrals, and the two 

 integrals involving a given excited state wavefunction will not in- 

 volve the same coordinate component of the electric dipole and the 

 magnetic dipole operator simultaneously, the rotatory strength would 

 be zero. This is the tjuantum mechanical basis for the well-known rule 

 that to show optical activity, a molecule must possess neither a plane 

 of symmetry nor a center of symmetry (inversion). 



On the quantitative side, if a molecule does possess optical rotatory 

 power, the fact that two different integrals are involved, only one of 

 which is related to the intensity of a transition, leads to the possibility 

 that weak bands may in principle contribute more strongly to optical 

 rotatory power at a given wavelength, than strong bands contribute. 

 In particular, n -^ tt* bands, which as we shall see are inherently weak 

 even if formally allowed, usually contribute strongly to optical rota- 

 tory power. This confirms an empirical observation which occurs 

 frequently in the early literature on the importance of weak bands 

 in optical rotatory dispersion, although the spectral assignment of 

 the bands as w -> tt* transitions in heteromolecules in general is more 

 recent. 



V. Characteristics of n -^ tt* Transitions 



After the Mulliken-McMurry assignment (27, 22) of the carbonyl 

 absorption band was published, no immediate development of the 

 general topic ensued, partly because the abstract treatment was not 

 at once related to direct experimental proof, even though some of this 

 was already in the literature; and partly because in molecules with 

 higher ionization potentials for lone-pair electrons on heteroatoms, 

 the possibility of long wavelength /; -^ tt* transitions was not im- 

 mediately apparent. 



However, a lone-pair on a heteroatom carries immediate chemical 



