Infrared Spectroscopy

How IR works

Molecules vibrate. The atoms in a chemical bond aren't rigidly bolted together — they oscillate around an equilibrium distance like masses on a spring. Quantum mechanics quantises these oscillations into discrete energy levels, and the gaps between levels happen to coincide with the energy of infrared photons. Shine an IR beam at a sample and a photon whose energy matches a vibrational gap gets absorbed; everything else passes through. Plot transmittance or absorbance against wavenumber and you have an IR spectrum.

The frequency of the absorbed photon depends on two things: the stiffness of the bond (force constant k) and the masses of the atoms it joins (reduced mass µ). Hooke's-law oscillator model:

ν̃ = (1 / 2πc) √(k / µ)
µ = (m₁ × m₂) / (m₁ + m₂)

The math predicts the gross trends. Triple bonds are stiffer than double bonds are stiffer than single bonds, so C≡C (~2200 cm⁻¹) > C=C (~1650 cm⁻¹) > C–C (~1100 cm⁻¹). Light atoms vibrate faster than heavy ones, so C–H (~3000 cm⁻¹) > C–D (~2200 cm⁻¹) > C–C. Memorise those two scaling laws and you've got an intuition for half the IR table.

Not every vibration absorbs. The IR selection rule is: a vibration must change the molecular dipole moment to be IR-active. The symmetric stretch of N₂ doesn't change the dipole (zero throughout), so N₂ has zero IR absorption — atmospheric nitrogen is invisible to IR, which is why IR can probe the rest of the air. Asymmetric stretches and polar bonds are bright; symmetric stretches in homonuclear diatomics are dark.

The diagnostic-band cheat sheet

The working chemist's brain runs on this table:

Functional group	Wavenumber (cm⁻¹)	Intensity	Notes
O–H, alcohol	3200 – 3550	Strong, broad	Hydrogen bonded; sharp at 3650 if free.
O–H, carboxylic acid	2500 – 3300	Very broad	Distinctive boulder-shaped band.
N–H, primary amine	3300 – 3500	Medium, two bands	Symmetric and asymmetric stretches.
N–H, secondary amine	3300 – 3400	Medium, single band	Only one N–H to stretch.
C–H, sp³ alkyl	2850 – 2960	Medium	Below 3000.
C–H, sp² vinyl/aromatic	3000 – 3100	Medium	Above 3000 — classic split.
C–H, aldehyde	2700 – 2850	Medium, two bands	Diagnostic doublet plus C=O.
C≡C, alkyne	2100 – 2260	Weak (terminal stronger)	Often weak; symmetric internal alkynes invisible.
C≡N, nitrile	2200 – 2260	Medium, sharp	Distinctive narrow peak in dead window.
C=O, carbonyl	1670 – 1820	Very strong	The most diagnostic band in IR.
C=C, alkene	1620 – 1680	Variable	Stronger if polar (cis vs trans).
C=C, aromatic	1450 – 1600	Variable	Multiple bands; ring breathing.
C–O, ether/ester	1000 – 1300	Strong	Broad; sits in fingerprint region.
N–O, nitro	1300 – 1550	Strong, two bands	Asymmetric and symmetric NO₂ stretches.

The carbonyl zoo: one band, six diagnoses

The C=O stretch is the most useful diagnostic in IR because its position pins down the carbonyl class to ~20 cm⁻¹.

• Acid anhydride: two bands, ~1820 and ~1750 cm⁻¹. Two coupled C=O stretches.
• Acid chloride: ~1800 cm⁻¹. Cl is electron-withdrawing, raises C=O bond order.
• Ester: ~1735 cm⁻¹ saturated, lower for conjugated. Plus strong C–O at 1170–1280 cm⁻¹.
• Aldehyde: ~1725 cm⁻¹ (1700 if conjugated). Confirm with the C–H doublet at 2720/2820.
• Ketone: ~1715 cm⁻¹ saturated, ~1680 if α,β-unsaturated, ~1660 if aryl.
• Carboxylic acid: ~1710 cm⁻¹ plus that boulder-shaped O–H above 2500.
• Amide: ~1680 cm⁻¹ (amide I band) plus N–H bending (amide II) at ~1550. Lowest C=O of the lot.

IR vs Raman vs ATR vs near-IR

Technique	What gets absorbed/scattered	Selection rule	Sample type	Strength
Mid-IR (transmission)	4000–400 cm⁻¹ photons	Δ dipole ≠ 0	Thin films, KBr discs, gas cells	Quantitative; long history
FTIR-ATR	4000–400 cm⁻¹ via evanescent wave	Same as mid-IR	Neat liquids, powders, polymers	No sample prep; 30-second turnaround
Raman	Visible-laser inelastic scatter	Δ polarisability ≠ 0	Aqueous solutions, gemstones, art	Water-friendly; non-destructive; symmetric stretches
SERS (surface-enhanced)	Raman on roughened metal surface	Same as Raman	Trace analytes adsorbed on Au/Ag	10⁶–10¹⁰× enhancement; ppt detection
Near-IR (NIR)	4000–14000 cm⁻¹ overtones	Same as mid-IR but weaker	Pharma tablets, grain, milk powder	Penetrates packaging; non-contact PAT
Far-IR (terahertz)	400–10 cm⁻¹	Same	Crystalline solids, pharmaceutical polymorphs	Lattice vibrations; metal-ligand bonds

IR and Raman are complementary because their selection rules differ. Symmetric vibrations (e.g., C=C in trans-stilbene) that are weak in IR are bright in Raman and vice versa. A polar bond's stretch is strong in IR (large dipole change) but often weak in Raman (small polarisability change). For unknown identification, having both spectra eliminates almost all ambiguity.

Worked example: an unknown C₈H₈O₂

You collect the FTIR of a colourless oil and observe:

• Broad band centred at 2500–3300 cm⁻¹ (boulder shape).
• Sharp doublet at 3050 and 2940 cm⁻¹.
• Strong band at 1685 cm⁻¹.
• Multiple bands 1450–1600 cm⁻¹.
• Strong band at 1280 cm⁻¹.
• Two bands at 750 and 705 cm⁻¹.

Reasoning. The 2500–3300 boulder = carboxylic acid O–H. The 1685 cm⁻¹ C=O is shifted lower than typical 1710 — conjugation with an aromatic ring. The aromatic C–H at 3050 and ring stretches at 1450–1600 confirm the aromatic. The two low-frequency C–H out-of-plane bends at 750 and 705 are the diagnostic mono-substituted-benzene fingerprint. C₈H₈O₂ with COOH and an aryl group → benzoic acid? But benzoic acid has the formula C₇H₆O₂, not C₈H₈O₂. The extra CH₂ between ring and COOH gives phenylacetic acid, C₆H₅CH₂COOH — and the saturated CH₂ at 2940 cm⁻¹ confirms it. Phenylacetic acid.

Hardware: how a modern FTIR works

The heart of any FTIR is a Michelson interferometer. A broadband IR source (a heated SiC ceramic, ~1300 K) sends light through a beamsplitter; half goes to a fixed mirror, half to a moving mirror; the recombined beam carries an interference pattern that depends on the moving-mirror position. Pass the beam through the sample, detect the resulting modulated intensity, and apply a Fourier transform to recover the spectrum.

• Source. Globar (silicon carbide rod) for mid-IR, tungsten for near-IR.
• Beamsplitter. KBr-coated Ge for mid-IR; CaF₂ for near-IR.
• Detector. DTGS (deuterated triglycine sulfate) for routine work; MCT (mercury–cadmium–telluride) cooled to 77 K for high-sensitivity microscopy.
• Sampling accessory. ATR with diamond crystal is the modern default. Transmission cells (KBr, CaF₂ windows) for quantitative work. Diffuse-reflectance (DRIFTS) for powders. Specular reflectance for thin films on metal.

Real-world applications

• Pharmaceutical identification. The US Pharmacopeia and European Pharmacopeia accept FTIR-ATR as a primary identification method. A 30-second ATR scan of an incoming raw material is matched against the supplier's reference spectrum at > 95% correlation before release.
• Polymer recycling. Sorting facilities use NIR spectroscopy to distinguish PET, HDPE, PVC, LDPE, PP, PS at conveyor-belt speeds (5 m/s, 100 ms per particle). The diagnostic NIR overtones of the C–H, O–H and C=O groups separate every common consumer plastic.
• Atmospheric monitoring. The IASI satellite payload measures CO, CO₂, CH₄, O₃, N₂O and water vapour profiles globally with FTIR at 0.5 cm⁻¹ resolution. Each rotational-vibrational line is fit against pressure and temperature.
• Forensic drug ID. ATR-FTIR identifies seized cocaine, heroin, amphetamines and synthetic cannabinoids at trafficking levels in seconds. Field-deployable units with reference libraries replace bulky benchtop GC-MS in many roadside stops.
• Art conservation. Non-contact reflectance FTIR maps pigments, binders and varnishes on canvases and frescoes without sampling. Indigo at 1180 cm⁻¹, lead white at 1410 cm⁻¹, oil binder by C=O at 1740 cm⁻¹.
• Process analytical technology (PAT). In-line FTIR probes immersed in pharmaceutical reactors monitor reaction progress in real time — no aliquoting, no quenching. The shift of a starting-material C=O to a product C=O is the kinetic signal.

Common mistakes and pitfalls

• Calling every broad ~3300 cm⁻¹ band an alcohol. It might be a carboxylic acid (broader, lower), a primary amine (twin peaks), or just adsorbed water — check for corroborating bands.
• Ignoring CO₂ and water-vapour bands. CO₂ at 2350 cm⁻¹ and rotational H₂O lines at 1500–2000 and 3500–4000 cm⁻¹ leak in from atmosphere. Subtract a fresh background; purge the bench with N₂ for low-noise work.
• Trusting peak position to ±1 cm⁻¹. Hydrogen bonding, concentration, solvent and temperature can move bands by 5–30 cm⁻¹. Match to ranges, not point values.
• Forgetting the ATR depth dependence. The evanescent wave penetrates ~1 µm at 1500 cm⁻¹ but only ~0.4 µm at 4000 cm⁻¹. Bands at higher wavenumber appear weaker than in transmission spectra; ATR-correction algorithms compensate.
• Quantifying without Beer's law check. IR transmittance is non-linear; concentration plots use absorbance A = log₁₀(I₀ / I) and only stay linear up to A ≈ 1.5. Above that the detector saturates and your calibration curves bend.
• Assigning fingerprint-region peaks individually. Below 1500 cm⁻¹ the spectrum is dense and bands are coupled. Use it for compound matching, not for piecewise functional-group assignment.
• Confusing transmittance and absorbance scales. Old papers plot %T (peaks point down); modern software plots A (peaks point up). Mistaking one for the other reverses every intensity comparison.