Past exam of the chemistry course of the year 3 of the natural sciences course of the University of Cambridge / 2021 / Paper 2A / Section B / 21 / a / ii

An infrared fundamental must transform like a component of the electric dipole moment; a Raman spectroscopy fundamental must transform like a component of the symmetric polarizability tensor. For this centrosymmetric D4h molecular point group, the resulting classification is:

Symmetry	Number of modes of this symmetry	Infrared	Raman	$A_{1 g}$	1	No	Yes: $x^{2} + y^{2}, z^{2}$	$B_{1 g}$	1	No	Yes: $x^{2} - y^{2}$	$B_{2 g}$	1	No	Yes: $x y$	$A_{2 u}$	1	Parallel, $z$	No	$B_{2 u}$	1	No	No	$E_{u}$	2, each doubly degenerate	Perpendicular, $(x, y)$	No

Here parallel and perpendicular refer to the principal fourfold axis. The table obeys infrared and Raman mutual exclusion.

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