# Advanced Inorganic Chemistry/Stretching frequencies and structure determination (3.3)
## Stretching vibrations and structure determination (3.3)
#### 1. Stretching Modes of Vibration

Stretching modes in molecules can be represented by the individuals bonds in a molecule. To determine the activity of stretch frequencies, only those bonds of the same type are considered together. As an example, Mn(CO)$_4$NO has two types of bonds, 4 CO bonds, and 1 NO bond. To determine the stretching frequencies, each must be considered separately. To determine the stretching vibrations of the CO molecules (ν$_{CO}$), use the Mn-CO bonds as a basis and transform them according to the character table to determine the reducible representation. After performing the symmetry elements to the molecule, any bond that moves contributes 0, any bond that is inverted contributes -1, and any bond that remains stationary contributes 1. Since the bonds being used are sigma bonds, they have no directionality and thus will only contribute 1 or 0.
| C$_{4v}$ | E | 2C$_{4v}$ | C$_2$ | 2σ$_v$ | 2σ$_d$ |
| A$_1$ | 1 | 1 | 1 | 1 | 1 |
| A$_2$ | 1 | 1 | 1 | -1 | -1 |
| B$_1$ | 1 | -1 | 1 | 1 | -1 |
| B$_2$ | 1 | -1 | 1 | -1 | 1 |
| E | 2 | 0 | -2 | 0 | 0 |
| Γν$_{CO}$ | 4 | 0 | 0 | 2 | 0 |
After generating the reducible representation, it can be reduced to Γν$_{CO}$=A$_1$+B$_1$+E. Using the character table, A$_1$ and E are identified as IR active and A$_1$, B$_1$, and E as Raman active.

#### 2. Structure Determination using Stretching and Vibrational Frequencies

Spectroscopy can also be used to determine the structure of an unknown molecule. Using the stretching frequencies present, the molecular geometry can be determined by finding the symmetry necessary to generate them. Rather than using a molecule's symmetry to determine its vibrations, the vibrations can be used to discover the molecule's symmetry, and thus structure. For example, a molecule with the structure MX$_3$Y$_3$ could be facial or meridional. To determine which would be correct, the representation for all normal modes of vibration must be found, reduced, and examined.
| C$_{2v}$ | E | C$_2$ | σ$_v$(xz) | σ$_v$(yz) |
| A$_1$ | 1 | 1 | 1 | 1 |
| A$_2$ | 1 | 1 | -1 | -1 |
| B$_1$ | 1 | -1 | 1 | -1 |
| B$_2$ | 1 | 1 | -1 | -1 |
| Γ$_{MX}$ | 3 | 1 | 3 | 1 |
| C$_{3v}$ | E | 2C$_3$ | 2σ$_v$ |
| A$_1$ | 1 | 1 | 1 |
| A$_2$ | 1 | 1 | -1 |
| E | 2 | -1 | 0 |
| Γ$_{MX}$ | 3 | 0 | 1 |
For the meridional case the representation would reduce to Γ$_{mer}$ = 2A$_1$+E and the facial case Γ$_{fac}$ = A$_1$+E. The full character tables indicate that all of the reducible representations are IR active, so the meridional case has 3 IR active frequencies, and the facial case only 2. By knowing the number of IR and Raman active frequencies in an unknown molecule, group theory can be utilized to propose a structure. A useful rule to remember for structure determination is that in centrosymmetric molecules (those that contain an inversion center), the IR and Raman active frequencies are mutually exclusive. This can be useful in deciding if a structure is either square planar or tetrahedral.

## References

* ↑ Pfennig, Brian (2015). Principles of Inorganic Chemistry. Hoboken, New Jersey: John Wiley & Sons, Inc. pp. 233–242. ISBN 978-1-118-85910-0.