---
title: "Reducible Representations and Predicting Infrared and Raman Activity"
description: "Take the motions of a molecule as a basis, work out the characters of that basis under each symmetry operation, and reduce it into irreducible labels. The labels say directly which vibrations absorb i"
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source: https://lightmysky.com/learn/science/reducible-representations-and-predicting-infrared-and-raman-activity-mt_DP4JfkS6c0.md
retrieved: 2026-09-12
---

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# Reducible Representations and Predicting Infrared and Raman Activity

Take the motions of a molecule as a basis, work out the characters of that basis under each symmetry operation, and reduce it into irreducible labels. The labels say directly which vibrations absorb infrared light and which scatter it.

Subject: Science · Area: Chemistry · Ages 22 to 23
Page: https://lightmysky.com/learn/science/reducible-representations-and-predicting-infrared-and-raman-activity-mt_DP4JfkS6c0

## Ready when they can

- Builds the reducible representation for a chosen basis by counting unshifted contributions
- Applies the reduction formula and subtracts translation and rotation to leave the vibrations
- Assigns each remaining label as infrared active, Raman active, both or neither
- Uses the predicted band count to choose between two candidate geometries

## Lesson: From symmetry to band count

Shape comes first: electron domains push apart, two in a line, three in a plane, four toward tetrahedron corners. The point group is the full set of symmetry moves the resting shape obeys: rotation axes, mirror planes, and centers. Assign that group before anything else, because every later count hangs on it.

Next, build the reducible picture of the motions. Run through each class of symmetry move and count the contributions that stay unshifted. Those counts, class by class, are the raw material for everything after.

**Example.** Feed the counts into the reduction formula, which splits them into whole-number shares of each irreducible label. Subtract the labels of translation and rotation, and the survivors are the vibrations. The character table has already flagged each label: matching x, y, or z means infrared active through a changing dipole, matching a quadratic function means Raman active through changing polarizability, and matching neither means silent.

**Tip.** Use the band count to judge shapes. Each candidate geometry predicts its own count, so compare the spectrum against each prediction and let it vote. Water, ammonia, and methane land in different groups, which is why their spectra read so differently.

**Recap.** Group first, count unshifted moves, reduce, strip translations and rotations, and read each surviving label as infrared, Raman, or silent.

## Practice

8 questions on this page, each with its working shown.

## Needs first

- [NMR After Assignment: Relaxation, Distance and Exchange](https://lightmysky.com/learn/science/nmr-after-assignment-relaxation-distance-and-exchange-mt_dCV2EbNlF2)
- [Character Tables and What Symmetry Predicts](https://lightmysky.com/learn/science/character-tables-and-what-symmetry-predicts-mt_L8cTQjeKwf)
- [Selection Rules and Why Some Transitions Never Appear](https://lightmysky.com/learn/science/selection-rules-and-why-some-transitions-never-appear-mt_oJDr81W4fW)

## Opens up

- [Choosing Between Vibrational Methods: Infrared, Raman and Resonance Raman](https://lightmysky.com/learn/science/choosing-between-vibrational-methods-infrared-raman-and-resonance-raman-mt_YxLAvBIBAR)