4. (a) The 12 normal vibrations of trans- C2H2Cl2 are shown below. Carry out a normal mode analysis to find the symmetries and then assign them to the normal vibrations. Indicate the IR and/or Raman allowedness of each vibration. In the case of Raman, also indicate if the band is polarized. Note that +, indicate motion of the atoms out and in with respect to the plane of the molecule. * Indicates frequencies measured from combination bands. (b) Carry out a stretch mode analysis of trans- C2H2Cl2 to separate these modes from the other types of vibrations. What assumptions are made to justify this type of analysis? (c) The frequencies of v7 and v12 were measured from weak transitions that appeared in the IR and Raman spectra in