How do molecules vibrate, and how can symmetry reveal what we observe in spectroscopy?

In this episode of The Chemistry Show, we explore vibrational spectroscopy through the lens of group theory and molecular symmetry, showing how mathematical tools are used to analyze and predict molecular motions. Rather than treating vibrations as isolated bond stretches, the episode frames them as collective motions that are constrained by molecular symmetry.

We introduce how character tables and transformation matrices are applied to track how individual atoms move under symmetry operations such as rotations and reflections. These methods allow chemists to construct reducible representations for molecular vibrations and systematically reduce them into irreducible representations, revealing the total number and symmetry types of vibrational modes.

Finally, the episode explains how symmetry directly determines IR and Raman activity, enabling scientists to predict which vibrational modes will be experimentally observable and what they reveal about chemical bonding and molecular geometry.

Powered by AI (Google NotebookLM), this episode is based on lecture material from the Structural Methods in Inorganic Chemistry course taught by Prof. Pedro Camargo at the University of Helsinki, and provides the conceptual bridge between abstract group theory and real spectroscopic data.