Raman Spectroscopy Applications & Symmetry

Vocabulary-style flashcards covering Raman spectroscopy applications, symmetry operations, the 'Recipe for Success' for vibrational analysis, and specific case studies for water and ammonia.

$$C_{2v}$$

The point group to which 1,1-dichloroethene and water ($H_2O$) belong.

Mutual Exclusion Rule

A rule that does not apply to 1,1-dichloroethene because it lacks a center of inversion ($i$), allowing many modes to appear in both IR and Raman spectra.

$$3N$$

The calculation for the total degrees of freedom of a molecule, resulting in $9$ for water and $12$ for ammonia.

Water Total Representation ($\Gamma_{3N}$)

$$3A_1 + A_2 + 2B_1 + 3B_2$$

Water Vibrational Modes ($\Gamma_{vib}$)

$2A_1 + B_2$, consisting of the Symmetric stretch, Symmetric bend, and Asymmetric stretch.

Symmetry "Recipe for Success"

A 6-step procedure used to determine the symmetry of all molecular motions, including identifying point groups and decomposing representations.

Trace of the Matrix ($E$)

A value of $3$ used for the Identity operation in vibrational analysis.

Trace of the Matrix ($\sigma$)

A value of $1$ used for the Reflection operation in vibrational analysis.

Trace of the Matrix ($C_2$)

A value of $-1$ used for the $C_2$ Rotation operation in vibrational analysis.

Trace of the Matrix ($i$)

A value of $-3$ used for the Inversion operation in vibrational analysis.

$$C_{3v}$$

The point group associated with Ammonia ($NH_3$).

Ammonia Total Representation ($\Gamma_{3N}$)

$$3A_1 + A_2 + 4E$$

Ammonia Vibrational Modes ($\Gamma_{vib}$)

$2A_1 + 2E$, which results in 4 distinct peaks in both IR and Raman spectra.

Doubly Degenerate

A property of the "E" modes in ammonia, where two vibrations share the same energy.