QUESTION ONE [20 MARKS] (a) Determine the molecular point group for each of the following species; (i) XeO4 (ii) CC13+ (iii) NOF (iv) I3 (6 marks) (b) (i) Generate a matrix representation of the C2h point group using a set of x, y, and z coordinates as your basis. (2 marks) (ii) Show that the matrix representation satisfy the requirements of a mathematical group (2 marks) (c) Consider the C3 point group to which the NH3 molecule belongs: (i) Construct the multiplication table for the C3 point group (ii) Tabulate the non-trivial sub-groups of the C3 point group (iii) Determine the classes of the C3v point group (5 marks) (2 marks) (3 marks)