MICHAEL KASHA 47 



the scjuaic ol a volunic iiilt\<;ral, over ilic entire space occupied by the 

 molecular electronic distribution. The integrand consists of three 

 parts: ^f,., the total wavefunction of the ground state of the molecule; 

 E,.,,,.;, which is an abbreviation for the sum of the electric dipole 

 operator components in the .v, )', and :, directions; and ^^^ the total 

 wavefunction of an excited state of the molecule. The total wavefunc- 

 tions for a state of a molecule are taken as those products, of the one- 

 electron orbital wavefunctions, which correspond to the electronic 

 configuration for the state of the molecule; thus, the symmetry species 

 for a state is readily determined from the symmetry species for the 

 orbitals involved, as shown in the previous section. Physically, one 

 can visualize the total electronic distribution of a molecule as a 

 superposition of each of the one-electron molecular orbital distribii- 



OO 



f>sj 



-oo 



oo 



~ 1 I ^n Ex.y.z ^E d^ H / ^G Mx,y,z ^e ^^ 



-66 -oo 



Fig. II. Ouanluni mechanical expressions relating to probability, P, of an electric 

 dipole transition, and optical rotatory strength, R, due to an electronic transition. 



tions which make up the configuration. As stated at the end of 

 section III C, the symmetry properties of the components of the 

 electric dipole operator are identical with the symmetry properties 

 of the vectors representing coordinate displacements, or translations. 

 The electric vector of the impinging light wave may be directed along 

 the X, y, or z axis of an oriented molecule, and may induce in it a 

 transitory electric dipole moment, which may lead to an excitation or 

 electronic transition, ^\^hether it does or does not depends on the 

 non-zero or zero vahie, respectively, of the square of the transition 

 moment integral, and the frequency of the hght wave. If the integrand 

 is antisymmetric with respect to any symmetry operation, then inte- 

 gration from minus infinity to plus infinity over the molecular co- 

 ordinates will give a zero value of the integral. If the integrand is 

 symmetric with respect to all symmetry operations, the integral over 

 all space of the molecule will not vanish, and the transition will be 



