1 Derive The Irreducible Representations For The Four Cl Sigma And Pi Orbitals O

1) Derive the irreducible representations for the four Cl sigma and pi orbitals of tetrahedral [TiCl4]- using only the 3p orbitals (one p sigma and two p pi orbitals per Cl site).
2)  Generate and place the proper number of electrons in a  schematic mo diagram for the Ti(III) complex [TiCl4]- assuming tetrahedral symmetry and using the Ti 3d,4s, 4p and Cl 3p as valence orbitals.( The 3Cl 3p orbitals are used to give one sigma and two pi donor orbitals per Cl center.)
3)  What are the ground and first excited electronic states for [TiCl4]- ? 
4) Is the pure electronic (d to d) transition from the ground to the first excited electronic state spin and or orbitally allowed as an electric dipole transition ?
5)  Generate the irreducible representations for the coordinates and the vibrational normal modes of [TiCl4]- .
6)  Which of the fundamental vibrational transitions are infrared and or Raman active?
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