Step 107

1. Does a molecule have a dipole moment?

Since the permanent electrical dipole moment of a molecule, which is resulting the bond moment, a stationary vector characteristic, which is invariant under all symmetry operations of the molecule, the dipole vector must be situated in each symmetry element of the molecule. Hence it follows that molecules with inversion center i (a vector cannot be situated in one point) or with not coaxial axes of rotation C (a vector can be situated not at the same time in several position-different axes) no dipole moment to have. All other molecules disgusting have a stationary dipole moment.

2. Is a molecule optically active?

Molecules are optically active, if their mirror image is not congruent to the original. Molecules are optically inactive, if their mirror image by suitable translation and rotation can be set with the original to the coincide. Since the mirror plane must be situated for the production of the mirror image not necessarily outside of the molecule, but e.g. with a mirror plane s of the molecule to coincide, is only a rotation can around an axis perpendicularly to s for the congruence necessary.
Since it can be shown that s _h and C_n commutate ( s _h C_n = C_n s _h ) and s _h C_n ise quivalent to a S_n - operation, all moleculs are optically inactive which have a axis of improper rotation S_n. Simple cases: n = l, S₁ = s ; n = 2, S₂ = i. Not simple: Molecules, which possess neither i nor s as item, but because of the presence of e.g. S₄ are nevertheless optically inactive. All molecules without rotational mirror axis S_n (n:1. 2, 3...) are optically active.

Before you begin with the processing of the following second section, repeat please again the summary 106 .
Begin with the next section training step 108 !