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

¶

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