8.2 Infrared spectroscopy and vibrational spectra

Infrared Spectroscopy Principles

Infrared spectroscopy reveals molecular vibrations by analyzing how molecules absorb specific infrared frequencies. This technique is one of the most practical tools for identifying functional groups and molecular structures, since different chemical bonds absorb at predictable, characteristic frequencies.

Fundamentals of Infrared Spectroscopy

Molecules absorb specific frequencies of infrared radiation that match their natural vibrational modes. When IR light at the right frequency hits a molecule, energy transfers into the bond vibration, producing a characteristic absorption band in the spectrum.

The frequency of each vibrational mode depends on two things: the strength of the chemical bond and the masses of the atoms involved. This relationship is quantified by the harmonic oscillator model (covered below), and it's the reason IR spectroscopy can distinguish between different functional groups so reliably.

Common applications include structural elucidation, functional group identification, and quantitative analysis across fields like pharmaceuticals, polymer science, and environmental monitoring.

Regions of the IR Spectrum

The IR spectrum is divided into three regions:

The near-IR region picks up weaker overtone and combination bands (useful for quantitative work), while the far-IR region captures heavy-atom vibrations and crystal lattice modes.

Vibrational Spectra Analysis

Characteristic Absorption Bands of Functional Groups

Different functional groups absorb in predictable frequency ranges, making IR spectroscopy a powerful diagnostic tool. Here are the most important ones to know:

• Carbonyl (C=O) stretch: Strong, narrow band at 1700–1800 $\text{cm}^{-1}$. The exact position shifts depending on the type of carbonyl compound. Esters and carboxylic acids absorb toward the higher end, while ketones and amides absorb lower.
• Hydroxyl (O–H) stretch: Broad, intense band at 3200–3600 $\text{cm}^{-1}$. The broadness comes from hydrogen bonding. A free (non-hydrogen-bonded) O–H appears as a sharper peak near the high-frequency end.
• Amine (N–H) stretch: Medium-to-strong band at 3300–3500 $\text{cm}^{-1}$. Primary amines ($\text{–NH}_2$) show two bands (symmetric and asymmetric stretch), while secondary amines ($\text{–NH–}$) show only one.
• Alkyl (C–H) stretch: Medium-to-weak bands at 2850–3000 $\text{cm}^{-1}$. The exact position tells you about hybridization: $sp^3$ C–H absorbs below 3000 $\text{cm}^{-1}$, while $sp^2$ and $sp$ C–H absorb above 3000 $\text{cm}^{-1}$.

Fingerprint Region and Molecular Identification

The fingerprint region (1500–400 $\text{cm}^{-1}$) contains a dense, complex pattern of absorption bands that is unique to each molecule. Think of it as a molecular barcode.

This region includes bending, wagging, and twisting vibrations of various groups, plus skeletal vibrations of the molecular backbone. These modes are highly sensitive to the overall molecular structure, so even molecules with the same functional groups will have different fingerprint patterns.

Identification works by comparing the fingerprint region of an unknown spectrum against reference spectra. Spectral libraries and databases (like the SDBS or NIST databases) contain thousands of reference spectra, making this comparison practical for routine analysis.

Selection Rules for Vibrations

Dipole Moment Change and IR Activity

Not every vibration produces an IR absorption band. The fundamental selection rule for IR spectroscopy is:

This is why homonuclear diatomic molecules like $\text{N}_2$ and $\text{O}_2$ are IR-inactive. Their symmetric stretch doesn't change the dipole moment (which is zero throughout), so there's no mechanism for IR light to couple with the vibration.

Asymmetric stretching and bending vibrations are usually IR-active because they do produce a changing dipole moment. For the quantum mechanical selection rule, the allowed fundamental transitions are $\Delta v = \pm 1$ in the harmonic approximation.

The intensity of an absorption band is proportional to the square of the change in dipole moment during the vibration: $I \propto \left(\frac{\partial \mu}{\partial Q}\right)^2$, where $Q$ is the normal coordinate. Larger dipole moment changes mean stronger absorptions.

Overtone and Combination Bands

Real molecules aren't perfect harmonic oscillators. Anharmonicity allows transitions beyond $\Delta v = \pm 1$, giving rise to overtone and combination bands.

• Overtones occur when a mode is excited by more than one quantum at once ($v = 0 \to 2$, $v = 0 \to 3$, etc.). The first overtone appears at roughly twice the fundamental frequency, the second at roughly three times, and so on.
• Combination bands result from the simultaneous excitation of two or more different vibrational modes. Their frequency is approximately the sum of the contributing fundamentals.

Both types are generally much weaker than fundamental transitions because they rely on anharmonic contributions. They typically appear in the near-IR region and can provide additional structural information or serve as the basis for quantitative near-IR analysis methods.

Molecular Structure and Vibrational Bands

Factors Influencing Vibrational Frequencies

The vibrational frequency of a bond is described by the harmonic oscillator (Hooke's law) model:

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

where $k$ is the force constant of the bond (in N/m) and $\mu$ is the reduced mass of the two atoms:

$\mu = \frac{m_1 \cdot m_2}{m_1 + m_2}$

Two trends follow directly from this equation:

1. Stronger bonds (higher $k$) vibrate at higher frequencies. Bond order matters: $\text{C≡N}$ > $\text{C=N}$ > $\text{C–N}$, and $\text{C=O}$ > $\text{C–O}$.
2. Lighter atoms (lower $\mu$) vibrate at higher frequencies. For the same bond type, C–F absorbs at a higher frequency than C–Cl, which absorbs higher than C–Br.

This is why O–H and C–H stretches appear at the high-frequency end of the mid-IR (above 2500 $\text{cm}^{-1}$), while bonds involving heavier atoms like C–Cl appear at much lower frequencies.

Factors Influencing Band Intensities

Band intensity depends on both molecular properties and experimental conditions:

• Dipole moment change: Polar functional groups (C=O, O–H, N–H) produce stronger bands than non-polar ones (C–H, C=C) because the dipole moment changes more during vibration.
• Concentration and path length: The Beer-Lambert law governs this quantitatively: $A = \varepsilon b c$, where $A$ is absorbance, $\varepsilon$ is the molar absorptivity, $b$ is the path length, and $c$ is the concentration.
• Hydrogen bonding broadens and shifts O–H and N–H bands. A hydrogen-bonded O–H stretch is broad and shifted to lower frequency compared to a free O–H.
• Conjugation and resonance lower the effective force constant of a bond by delocalizing electron density. For example, a conjugated C=O absorbs at a lower frequency than an isolated C=O because resonance gives the bond partial single-bond character.