IR Spectroscopy¶

Creates conformational changes in molecules with varying polarity

Is useful for identification of molecular structure, however is limited to identification of functional groups and “fingerprinting”
Is highly limited by its likelihood of being interfered with

Typical Spectrum¶

Measured as transmittance (peaks going down from 100%) instead of absorbance
Wavelength measured in \(\bar{\nu}=\frac{1}{\lambda (cm)}\)

Types of IR¶

Near-IR - Photometry/spectrophotometry similar to UV-VIS - quantification of organo-macromolecules
Mid-IR - Surface analysis, reflectance/diffuse reflectance/photoacoustic
Far-IR - Quantification of functional groups containing C, H, O rather than compound identification

FTIR¶

measures an interferogram and uses FT to convert it to a spectra
IR radiation is primarily thermal energy and induces stronger molecular vibrations within bonds
- Bonds act as springs, even with their own spring constant (see later)

Types of molecular interactions¶

Rotational¶

Rotational transitions occur in the far-IR range (lower energy) at \(<100\:cm^{−1}\)
There are far more rotational transitions than vibrational transitions and only small amounts of energy are required to trigger them *This however means that they only are really observed in gasses

Vibrational¶

Vibrational modes are higher in energy and come in bond length and atom rotational forms.
Each mode is given a Greek letter to denote it’s behaviour

¶

Radial¶

Symmetrical Stretching - \(\nu_s\)	Asymmetrical Stretching - \(\nu_{as}\)

Latitudinal¶

Scissoring - \(\sigma\)	Rocking - \(\rho\)

Longitudinal¶

Wagging - \(\omega\)	Twisting - \(\tau\)

Peak height¶

Peaks can be (depending on their height):
- Weak (w) - <30%
- Medium (m) - 30−60%
- Strong (s) - >60%
This is dependent on the polarity of the bond in question. The more polar the bond, the higher the absorbance at that peak.

Peak width¶

Peaks can also be:
- Broad - wide and smooth * Typically seen in O-H bonds (water!)
- Narrow - thin and pointy
This is caused by resolution limitations causing multiple absorbance peaks to blend into the one curve
- This is dependent on the amount of excitation states for the particular bond

Polarity¶

Only polar bonds will be active, as they need to be able to change their dipole when they rotate or vibrate
- The movement of atoms causes a shift in the electron density and thus a shift in the bond’s dipole
As a result pure covalent bonds will not show up, such as \(\ce{O2, N2, H2}\) etc.
- \(\ce{CO2}\) and \(\ce{H2O}\) are still envirnmental interferants however.

Symmetric bonds¶

If a bond has polarity but the molecule is symmetric, the resulting dipole will not move either, causing there to be no identifiable change
- Strong * Strongly Polar bonds
- Medium * Medium polarity bonds * Asymmetric bonds
- Weak * Weakly polar bonds * Symmetric bonds

Symmetric molecules will also show a more simple spectra, as the bonds will be duplicated, since they’ll be in the same environment and will overlap in their absorbance.

Coupling¶

If vibrations occur around a central atom, the effect of their shift may not cause a net change in the dipole
This is likely when:
- The have a common atom in stretching modes
- They have a common bond in bending modes
- They have a common bond in bending and stretching modes
- They have similar vibrational frequencies
This is unlikely when
- The atoms are separated by two or more bonds
- The symmetry is inappropriate

Electron density¶

When an EDG contributes more density to a bond, it gets stronger and as a result will take more energy to excite the group
The opposite is true for EWGs
E.g. \(\ce{C-O}\) bond in:
- Methanol - \(1034\:cm^{−1}\)
- Ethanol - \(1053\:cm^{−1}\)
- Butanol - \(1105\:cm^{−1}\)

Anharmonic oscillation¶

The vibrational modes of bonds is dependent on the amount of energy put in. The process follows the Morse Potential pattern

Too much energy and the bond will break
The bond will get significantly longer rather than compressing significantly
This is due to a Coulombic effect as well harmonic oscillation

Diatomic formula¶

calculates where peaks appear¶

Where:

\(m_1\) and \(m_2=\) the masses of the atoms
\(k=\) the sprinc constant (Hooke’s law)
\(\mu=\text{reduced mass}=\frac{m_1m_2}{m_1+m_2}\)

\[ \bar{\nu}=\frac{1}{2\pi c}\big(\frac{k}{\mu}\big)^{\frac{1}{2}}=130.3\big(\frac{k}{\mu}\big)^{\frac{1}{2}} \]

\(k\) can be obtained from the following table

\(\ce{O\bond{-}H}\)	\(\ce{C\bond{-}H (sp^3)}\)	\(\ce{C\bond{-}H (sp^2)}\)	\(\ce{C\bond{=}O}\)	\(\ce{C\bond{#}C}\)	\(\ce{C\bond{=}C}\)	\(\ce{C\bond{-}C}\)	\(\ce{C\bond{-}O}\)
780	480	510	1210	690	760	540	450

Peak count¶

To determine the amount of peaks we’d expect to see, we can use the following formula, which utilises the degrees of freedom for a molecule to determine what is possible
Where \(N=\) number of atoms:

\[ \text{Linear molecule - }3N−5 \]

\[ \text{Non-linear molecule - }3N−6 \]

Each vibration is called a normal mode and has a characteristic frequency
This will give the maximum number of fundamental peaks

Fewer peaks¶

Fewer peaks may be observed due to:

Symmetry of the molecule causing cancellations
Similar bonds sharing energy
Low absorption intensity
Energy of peak being out of the range of the spectrophotometer

More peaks¶

Harmonics of the fundamental frequency can cause overtones at multiples of the fundamental frequncy
- uncommon but possible
- occurs when an excitation happens from ground state to the second excited state (\(\ce{v=0 -> v=2}\))
When multiple vibrational modes are excited by a single photon, either the sum of the two modes or the difference can be seen as a result

Example - \(\ce{CO2}\)¶

Has \(3N−5=4\) vibrational modes
Actual peaks:
- Symmetric stretching will result in no net change of the dipole
- Asymmetric stretching will result in a net change and thus a peak
- The two bending modes will have the same energy and thus will show up as a single peak
Thus only two peaks are observed, not the expected four