 Solution

ID: 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/solution

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.

 New to topics? Read the docs here!