7.5 Infrared and UV-Vis Spectroscopy

7.5 Infrared and UV-Vis Spectroscopy

Spectroscopy measures the interaction of electromagnetic radiation with matter. As photon energy spans the infrared, visible, ultraviolet, and radiofrequency spectra, distinct molecular transitions are excited: nuclear spins, electronic energy levels, and vibrational bond coordinates.

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Infrared (IR) Spectroscopy: Principles, Dipole Requirements & Diagnostic Absorptions

Infrared radiation ($4000-400\text{ cm}^{-1}$, where wavenumber $\tilde{\nu} = 1/\lambda$) possesses energy corresponding to quantized vibrational transitions (stretching and bending) of covalent bonds.

Hooke's Law and Bond Vibrations

A vibrating covalent bond behaves approximately as a classical harmonic oscillator governed by Hooke's law:

$$\tilde{\nu} = \frac{1}{2\pi c} \sqrt{\frac{k}{\mu}}$$

where $k$ is the bond force constant (bond strength) and $\mu$ is the reduced mass of the bonded atom pair ($\mu = \frac{m_1 m_2}{m_1 + m_2}$):

• Bond Strength ($k$): Stronger bonds possess higher spring constants and vibrate at higher wavenumbers: triple bonds ($\text{C}\equiv\text{C}$, $\approx 2200\text{ cm}^{-1}$) vibrate at higher frequencies than double bonds ($\text{C}=\text{C}$, $\approx 1650\text{ cm}^{-1}$), which in turn vibrate higher than single bonds ($\text{C}-\text{C}$, $\approx 1000\text{ cm}^{-1}$).
• Reduced Mass ($\mu$): Lighter atoms vibrate at higher wavenumbers. Bonds involving light hydrogen atoms ($\text{C}-\text{H}$, $\text{O}-\text{H}$, $\text{N}-\text{H}$) have small reduced masses and absorb in the highest-energy region ($2800-3600\text{ cm}^{-1}$).

The Dipole Moment Selection Rule

For a molecular vibration to absorb an infrared photon, the vibration must cause a change in the molecule's net electric dipole moment:

$$\left( \frac{d\mu_{\text{dipole}}}{dx} \right) \neq 0$$

• Polar bonds (such as $\text{C}=\text{O}$ and $\text{O}-\text{H}$) undergo massive dipole oscillations during stretching and produce exceptionally intense absorption bands.
• Symmetrical nonpolar bonds—such as the internal triple bond of 2-butyne ($\text{CH}_3-\text{C}\equiv\text{C}-\text{CH}_3$), the double bond of trans-3-hexene, or homonuclear diatomics ($\text{O}_2$, $\text{N}_2$)—experience zero net change in dipole moment during symmetric stretching and are completely IR-inactive (silent on the spectrum).

The Two Spectral Domains

1. Diagnostic Region ($4000-1400\text{ cm}^{-1}$): Contains distinct stretching vibrations characteristic of specific functional groups. This is the primary region tested on the MCAT.
2. Fingerprint Region ($1400-600\text{ cm}^{-1}$): Contains complex bending vibrations and single-bond skeleton movements unique to an individual compound, functioning as an unforgeable molecular fingerprint.

Key Diagnostic IR Stretching Frequencies

Dissecting the Carbonyl Region ($1650-1750\text{ cm}^{-1}$)

The exact position of the carbonyl band reflects electronic resonance and inductive effects:

• Esters ($\approx 1735-1750\text{ cm}^{-1}$): The electronegative alkoxy oxygen exerts an inductive electron-withdrawing effect that strengthens the $\text{C}=\text{O}$ $\sigma$-bond, shifting the frequency upward.
• Aldehydes ($\approx 1725\text{ cm}^{-1}$) and Ketones ($\approx 1715\text{ cm}^{-1}$): Standard baseline carbonyl frequencies.
• Carboxylic Acids ($\approx 1710\text{ cm}^{-1}$): Sightly lower due to hydrogen-bonded dimer formation.
• Conjugation Effect ($\Delta\tilde{\nu} \approx -20\text{ to }-40\text{ cm}^{-1}$): When a carbonyl is conjugated with a $\text{C}=\text{C}$ double bond or an aromatic ring, delocalization of $\pi$-electrons into the carbonyl weakens double-bond character (increasing single-bond character), shifting the absorption downward to $1680-1690\text{ cm}^{-1}$.
• Amides ($\approx 1650-1680\text{ cm}^{-1}$): Heavy resonance donation from the nitrogen lone pair ($40\%$ double-bond character in $\text{C}-\text{N}$) severely weakens the $\text{C}=\text{O}$ double bond, shifting the stretching band down to $\approx 1650\text{ cm}^{-1}$.

Ultraviolet-Visible (UV-Vis) Spectroscopy & Electronic Conjugation

UV-Vis spectroscopy ($200-800\text{ nm}$) measures the absorption of light that promotes valence electrons from a lower-energy bonding or non-bonding orbital to a higher-energy antibonding molecular orbital.

Electronic Transitions and Molecular Orbitals

• $\pi \to \pi^*$ Transitions: Occur in compounds containing $\pi$-bonds (alkenes, alkynes, carbonyls, aromatics).
• $n \to \pi^*$ Transitions: Occur when an atom with non-bonding lone pairs ($\text{O}$, $\text{N}$, $\text{S}$) is adjacent to a $\pi$-system (e.g., carbonyl compounds).
• HOMO to LUMO: Light absorption promotes an electron from the Highest Occupied Molecular Orbital (HOMO) to the Lowest Unoccupied Molecular Orbital (LUMO). The absorbed wavelength is governed by Planck's relation:

$$\Delta E = \frac{hc}{\lambda_{\text{max}}}$$

Conjugation and the Bathochromic Shift

As the number of alternating single and double bonds (conjugated $\pi$-system) increases:

1. Orbital mixing creates an expanded set of delocalized molecular orbitals.
2. The energy gap between the HOMO and LUMO ($\Delta E$) progressively narrows.
3. Because wavelength is inversely proportional to energy ($\lambda = hc/\Delta E$), narrowing the gap causes $\lambda_{\text{max}}$ to shift to longer wavelengths.

Directional Spectral Shifts:

• Bathochromic Shift (Red Shift): Shift of $\lambda_{\text{max}}$ to a longer wavelength (lower energy), caused by increased conjugation or polar solvent interactions.
• Hypsochromic Shift (Blue Shift): Shift of $\lambda_{\text{max}}$ to a shorter wavelength (higher energy).
• Hyperchromic Effect: An increase in molar absorptivity (peak intensity $\varepsilon$).
• Hypochromic Effect: A decrease in molar absorptivity (peak intensity $\varepsilon$).

Biological Chromophores

• Conjugation Leading to Visible Color: Isolated double bonds absorb in the deep UV (ethene absorbs at $171\text{ nm}$). Butadiene absorbs at $217\text{ nm}$. When conjugation extends to $\approx 8-11$ conjugated double bonds (as in $\beta$-carotene, with 11 conjugated double bonds), $\Delta E$ drops into the visible range: $\beta$-carotene absorbs strongly in the blue region ($\lambda_{\text{max}} \approx 450\text{ nm}$) and reflects the complementary wavelengths, appearing brilliant orange.
• Protein Concentration (Beer-Lambert Law): The aromatic amino acids tryptophan and tyrosine possess conjugated indole and phenol rings that absorb UV light at $280\text{ nm}$. Spectrophotometers exploit this absorption to determine protein concentration using the Beer-Lambert Law:

$$A = \varepsilon \cdot b \cdot c$$

where $A$ is absorbance, $\varepsilon$ is molar absorptivity ($\text{M}^{-1}\text{cm}^{-1}$), $b$ is cuvette path length ($1\text{ cm}$), and $c$ is molar concentration.