For the sulphate ion, SO_4^2-, a) What is the total number of vibrational modes

Question

For the sulphate ion, SO_4^2-, a) What is the total number of vibrational modes expected? b) In which irreducible representations of the appropriate point group will vibrational modes be IR active in the free SO_4^2 ion? c) In which irreducible representations of the appropriate point group will vibrational modes be Roman active in the free SO_4^2- ion? d) What symmetry operation is necessary in a point group for there to be no common frequencies (mutual exclusion) between the IR and Raman spectrum of a species? Would the SO_4^2- ion shows this mutual exclusion? e) Give the symmetry point group of a SO_4^2- ion chelated through two O atoms to a metal ion. Should IR spectroscopy be able to distinguish a free SO_4^2- ion clearly from a SO_4^2 ligand coordinated to a metal? Explain.

Explanation / Answer

Part a) No of vibrational modes are given by the following formulae for nonlinear molecules

modes of vibration=3N-6 where N=no of atoms

modes of vibration=3*5(1S+4O)-6 = 9

Part b) SO4-2 is tetraedral sturture so its point roup is Td

there will be two IR active modes (2T2).

Part C) there will be four Raman active modes (A1, E, 2T2).

Part d) "Center of inversion" symmetry operation is necessary in point group for there to be no common frequencies.

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