Point Groups Use of Point Groups Group Theory and Point Groups can help us understand and predict important properties of molecules. Three that are described here are: Optical Activity Dipole Moments IR and Raman Spectroscopy Optical Activity Optically active organic molecules (chiral molecules) contain at least one asymmetric carbon atom known as a chiral center. Many inorganic molecules have no chiral centers and yet are optically active. These molecules are called dissymmetric, because they do have some symmetry. Which molecules are expected to be optically active? Molecules with no improper axis of rotation are optically active. Note that S1 = σ and S2 = i. Which point groups have no mirror planes, centers of inversion or other improper rotations? C1, Cn, and Dn all fit this requirement. C1 is, of course, asymmetric. It has no symmetry and is the familiar situation from organic chemistry. L-(+)-Lactic acid (click for the image)(C3H6O3)is a chiral molecule. it is organic and small. Octahedral metal ion complexes can be optically active, particularly when they are chelated. For example, [Co(ethylenediamine)3]3- (click for the image) has two enantiomeric forms with D3 symmetry. If one of the ethylenediamine chelates is replaced with two chloride ions, the cis-dichlorobis(ethylenediamine)cobalt(III) ion (click for the image) has C2 symmetry and is optically active. Dipole Moments A molecule will have a dipole moment (that is, it will be polar) if the bond dipole moments do not cancel each other out. So a linear molecule like CO2 has two polar bonds facing in opposite directions with the result that the molecule itself is not polar. In fact, any molecule with a center of inversion, i, cannot be polar because the bond dipole moments will cancel each other. Likewise, a molecule with more than one Cn axis (n>1) cannot have a dipole moment. You can realize this logically because the dipole moment of the molecule cannot lie in more than one direction. PF5 is a good example where the bond dipole moments all cancel. Although it has one C3 axis, it also has 3 C2 axes. All molecules in D point groups all have multiple C axes and therefore cannot be polar. Also, molecules with a horizontal mirror plane cannot have a dipole moment. So, whats left? Polar molecules can be in one of these four point groups: C1, Cs, Cn, and Cnv. IR and Raman Spectroscopy One of the most practical uses of point groups and group theory for the inorganic chemist in is predicting the number of infrared and Raman bands that may be expected from a molecule. Alternatively, given the IR or Raman spectrum, the symmetry of a molecule may be inferred. In both IR and Raman spectroscopy the molecule is viewed as containing moving vectors. How these vectors are affected by symmetry will provide a means to determine how many bands would be expected in these spectra. IR spectroscopy Raman spectroscopy IR spectroscopy For IR spectroscopy, it is the vibrational motions of the atoms that are important. Actually, it is the change in the molecular dipole moment when the atoms vibrate that determines whether the vibration is or is not IR active. The question is: Does the dipole moment change in a way that corresponds with the x-, y-, or z-axis? The mathematically-rigorous way to answer this question is to draw the vectors and then see how these transform against the several symmetry operations in the molecules point group. The result is called the reducible representation. One can separate this into irreducible representations and compare these to the irreducible representations on a character table to determine the normal modes for the vibrations. If the normal modes correspond with the x-, y-, or z-axis then the vibration will be IR active. Alternatively, we can stick with pictures and use some logic to realize how many IR bands a molecule will have. Lets use water, H2O, as our example. Water has three vibrational modes: a symmetric stretch, a bending mode, and an asymmetrical stretch. Back to top Symmetrical stretch In this mode the dipole moment for the molecule does not change in direction, but it does change in magnitude. As the molecule stretches, the dipole moment increases. So the dipole moment changes and it does so along the z-axis. This vibration is IR active.
Posted on: Mon, 29 Sep 2014 01:48:14 +0000