(1) Show with the aid of diagrams the action of each of thefollowing symmetry operations on a point located at (x, y, z). C4S4 {2 marks}

(2) With reference to a set of character tables, determine theorder of each of the following point groups. D2d Oh {2 marks}

(3) Determine the total degeneracy of each of the followingirreducible representations ().  = 3Ag + B1u + 2B2u  = A1g +3Eg + 2T1g + T2u {2 marks}

(4) For each of the following species, sketch the molecule orion and determine its point group using the flow chart available onBlackboard. In order to secure full marks, you are required to showyour answers to each of the questions in the flow chart for eachmolecule or ion. IF4 + ClF2 + AsF5 N2O4 O3 CS2 trans-[PCl4F2] {7 ×1mark}

(5) IF5 is square pyramidal (point group C4v). By constructing asuitable basis, corresponding to the I-F stretching vibrationsonly:

(i) Determine the reducible representation (I-F) for the I-Fbond stretching vibrations in IF5. {3 marks}

(ii) Using the reduction formula together with the charactertable for Td available on blackboard, reduce this representation toits irreducible form. {3 marks} Question continues on next page

(iii) By reference to the character table for Td, determinewhich of these vibrations are (a) infrared active (b) Raman active.Give reasons for your answer.