Infrared (IR) Spectroscopy

What IR spectroscopy actually measures

Shine a beam of infrared light through a sample and some of it gets swallowed. The wavelengths that vanish are not random — a molecule absorbs an IR photon only when that photon's energy exactly matches the energy needed to make one of its bonds vibrate harder. Plot how much light survives at each frequency and you get an IR spectrum: a series of downward dips (absorption bands) at the frequencies where the molecule's bonds resonate.

The key idea is that a chemical bond behaves like a tiny spring connecting two masses. Push the atoms together or pull them apart and the spring restores them; left alone, they oscillate at a characteristic frequency. Because different bonds have different stiffnesses and connect different atoms, each bond type oscillates at its own frequency — and IR light lets you interrogate every spring in the molecule at once.

Chemists don't plot frequency in hertz; they use wavenumber ν̃ (in cm⁻¹), which is just 1/λ. It is proportional to frequency and energy, and it gives convenient numbers: the whole informative range of the mid-IR runs from 4000 cm⁻¹ down to about 400 cm⁻¹. A band's position on that axis tells you what kind of bond is present; the pattern of many bands together tells you which specific molecule you have.

The mechanism: photon in, vibration up

Here is the step-by-step of what happens to a single molecule during an absorption event:

1. A bond sits in its vibrational ground state. Even at absolute zero a bond isn't still — quantum mechanics gives it a zero-point vibration in the v = 0 level.
2. An IR photon arrives with just the right energy. Vibrational levels are quantized and roughly evenly spaced (ΔE = hν). The photon must carry exactly ΔE to be absorbed — too much or too little energy and it sails through untouched.
3. The oscillating field couples to the molecular dipole. IR light is an oscillating electric field. It can only do work on the bond if the bond has a dipole that changes as it stretches. The field grabs that changing dipole and pumps energy in — this is the gross selection rule: the vibration must change the dipole moment.
4. The bond jumps to v = 1. The molecule is now vibrating with a larger amplitude in that mode. The photon is gone; the missing energy shows up as an absorption dip in the transmitted beam.
5. The energy dissipates. Collisions relax the excited vibration back to the ground state as heat, and the bond is ready to absorb again.

That third step is why symmetry matters so much. A stretch of homonuclear O₂ or N₂ keeps the molecule symmetric — its dipole stays exactly zero throughout — so no coupling, no absorption, IR-silent. A polar bond like C=O has a big permanent dipole that swells and shrinks as it stretches, giving one of the strongest bands in all of IR spectroscopy.

The physics: Hooke's law sets the frequency

Model the bond as a harmonic oscillator — two masses m₁ and m₂ joined by a spring of force constant k. The vibrational wavenumber is:

    ν̃  =  (1 / 2πc) · √(k / μ)          with reduced mass   μ = (m₁·m₂)/(m₁+m₂)

    ν̃  = wavenumber (cm⁻¹)
    c  = speed of light (2.998 × 10¹⁰ cm/s)
    k  = force constant / bond stiffness (N/m)
    μ  = reduced mass of the two atoms (kg)

Two levers move every band on the spectrum:

• Bond stiffness k pushes wavenumber up. Triple bond > double bond > single bond. A C≡C (k ≈ 1600 N/m) absorbs near 2150 cm⁻¹, a C=C (k ≈ 1000 N/m) near 1650 cm⁻¹, a C-C (k ≈ 500 N/m) near 1000 cm⁻¹. Since ν̃ ∝ √k, quadrupling the stiffness only doubles the frequency.
• Reduced mass μ pushes wavenumber down. Because μ is dominated by the lighter atom, any bond to hydrogen (μ ≈ 1 amu) lands at high wavenumber. That is why C-H, N-H, and O-H stretches all cluster at 2800-3700 cm⁻¹ while C-Cl, C-Br, and C-I sit down below 800 cm⁻¹.

A worked estimate: for a C=O bond, k ≈ 1200 N/m and μ = (12·16)/(12+16) = 6.86 amu = 1.14 × 10⁻²⁶ kg. Plugging in,

    ν̃ = (1 / (2π · 3.0×10¹⁰)) · √(1200 / 1.14×10⁻²⁶)
       = (5.31×10⁻¹²) · √(1.05×10²⁹)
       = (5.31×10⁻¹²) · (3.24×10¹⁴)
       ≈ 1720 cm⁻¹

which is spot-on for a ketone carbonyl. The whole predictive power of IR comes from this one equation.

Vibrational modes — not every wobble is a stretch

A nonlinear molecule of N atoms has 3N − 6 vibrational modes (3N − 5 if linear). Only some are simple bond stretches; the rest bend, wag, rock, scissor, and twist:

• Stretching — atoms move along the bond axis. Symmetric and antisymmetric stretches of a CH₂ or CO₂ group appear as two separate bands; the antisymmetric one is usually higher in frequency.
• Bending (scissoring, rocking, wagging, twisting) — the bond angle changes. Bends need less energy than stretches, so a CH₂ scissor sits near 1465 cm⁻¹ while its stretches are up near 2900 cm⁻¹.

CO₂ is the classic teaching case: it has a symmetric stretch (IR-silent — no dipole change), an antisymmetric stretch at 2349 cm⁻¹ (strongly IR-active), and a doubly-degenerate bend at 667 cm⁻¹. Those last two bands are exactly the ones that trap outgoing heat and drive the greenhouse effect — planetary-scale IR spectroscopy.

Reading a spectrum: the four zones and the fingerprint

Practicing chemists mentally divide the axis into blocks and scan left to right:

Region (cm⁻¹)	What lives there	Diagnostic value
3700-2500	X-H stretches: O-H, N-H, C-H	Broad O-H = alcohol/acid; sharp N-H = amine; C-H just left/right of 3000 splits sp²/sp³
2300-2000	Triple bonds: C≡N, C≡C	A lonely peak here almost always means a nitrile or alkyne
1850-1650	C=O stretches	The single most useful band in IR — position pins the carbonyl type
1680-1450	C=C, aromatic ring, N-H bend	Confirms unsaturation and aromatic rings
1500-500	Fingerprint region	Dense coupled skeletal modes; unique to each molecule — match against a reference to prove identity

The 3000 cm⁻¹ line is a free ruler: C-H stretches just above 3000 come from sp² carbons (alkenes, aromatics), and those just below from sp³ carbons (alkanes). The two carbonyl-versus-hydroxyl signposts and this 3000 line let you classify most organic samples in seconds.

Worked example: is it an aldehyde, a ketone, or an acid?

You are handed an unknown C₃ compound and a spectrum. Walk the axis:

1. Look at 3700-2500. No broad hump, no smear down to 2500 — rules out alcohol and carboxylic acid.
2. Look for a carbonyl. A strong sharp band at 1725 cm⁻¹ — there is a C=O.
3. Look for the aldehyde tell. Two weak bands at 2820 and 2720 cm⁻¹ — the Fermi-doublet C-H stretch of the aldehyde H-C=O group. That doublet is diagnostic; a ketone would not show it.
4. Conclusion. C=O at 1725 cm⁻¹ plus the 2820/2720 doublet = propanal (CH₃CH₂CHO), not acetone.

The carbonyl position is itself a fine ruler. Ring strain and conjugation shift it in predictable ways:

    carboxylic acid dimer   ~1710 cm⁻¹   (plus broad 3300-2500 O-H smear)
    aldehyde                ~1725 cm⁻¹
    ketone (acyclic)        ~1715 cm⁻¹
    ester                   ~1735 cm⁻¹   (plus strong C-O near 1200)
    amide                   ~1650 cm⁻¹   (lowered by N lone-pair donation)
    conjugated enone        ~1680 cm⁻¹   (lowered ~30 by conjugation)
    cyclopentanone          ~1745 cm⁻¹   (raised by ring strain)
    cyclobutanone           ~1780 cm⁻¹   (raised more by tighter strain)
    acyl chloride           ~1800 cm⁻¹   (raised by electron-withdrawing Cl)

Conjugation and lone-pair donation soften the C=O (lower ν̃); ring strain and electron-withdrawing neighbours stiffen it (higher ν̃). A single carbonyl number, read carefully, distinguishes an ester from an amide from a strained ketone.

IR vs the other spectroscopies

	Infrared (IR)	NMR	Mass spectrometry	UV-Vis
What it probes	Bond vibrations	Nuclear spin environment	Mass of ions/fragments	Electronic transitions
Best answers	Which functional groups?	Carbon-hydrogen skeleton, connectivity	Molecular weight, formula	Conjugation, concentration
Energy range	Vibrational (~1-50 kJ/mol)	Radio-frequency (tiny)	Ionizing (large)	Electronic (~150-600 kJ/mol)
Sample destroyed?	No	No	Yes — ionized/fragmented	No
Sample size	µg-mg, any phase	mg, in solution	ng-µg	µg, dilute solution
Time per run	~1 second (FTIR)	Minutes to hours	Seconds	Seconds
Silent to	Symmetric bonds (N₂, O₂)	Nuclei with no spin (¹²C, ¹⁶O)	Nothing (all ionizable)	Non-chromophores
Killer strength	Instant functional-group ID	Full structure elucidation	Exact mass / formula	Quantitation (Beer-Lambert)

In a real structure-elucidation workflow you rarely use one alone. IR spots the C=O in seconds, mass spec pins the formula, and NMR wires up the skeleton — IR is the fast, cheap, non-destructive first look that tells you which functional groups you are even dealing with.

The instrument: dispersive vs FTIR

Early IR spectrometers were dispersive: a prism or grating swept across the frequencies one at a time, and a detector recorded transmission at each wavelength. Slow, and you threw away most of the light.

Modern instruments are FTIR — Fourier-transform infrared. A Michelson interferometer with a moving mirror encodes all frequencies simultaneously into an interferogram (intensity versus mirror position). A computer runs a Fourier transform to recover intensity versus wavenumber. Two advantages fall out:

• Fellgett (multiplex) advantage. Every frequency is measured the whole time, not one at a time, so signal-to-noise improves by roughly √M for M resolution elements — a full spectrum in about a second.
• Jacquinot (throughput) advantage. No narrow slit is needed, so far more light reaches the detector than in a dispersive instrument.

Sampling is now easy too: ATR (attenuated total reflectance) presses the sample against a diamond or germanium crystal, and the evanescent wave from a totally internally reflected beam probes just the surface — no grinding KBr pellets, no Nujol mulls. You can drop a pill, a plastic chip, or a drop of oil onto the crystal and read the spectrum in seconds.

Who discovered it, and when

The story starts in 1800, when William Herschel put a thermometer just past the red end of a sunlight spectrum and watched the temperature climb — he had found invisible "calorific rays" beyond visible light, what we now call infrared. In the early 1900s W. W. Coblentz, later at the U.S. National Bureau of Standards, patiently recorded IR spectra of hundreds of compounds by hand, establishing that specific groups gave specific bands — the empirical foundation of the whole technique.

IR spectroscopy became a routine analytical tool during World War II, when the U.S. synthetic-rubber program needed fast quality control of hydrocarbon isomers and IR proved perfect for it. The transformative leap came in the 1960s-70s: cheap computers made the fast Fourier transform (Cooley and Tukey's 1965 algorithm) practical, turning the interferometer's raw data into spectra in real time and giving birth to FTIR. That is why a technique built on a physicist's thermometer from 1800 is now a one-second benchtop measurement.

Limitations and practical pitfalls

• Water is the enemy. O-H of liquid water absorbs enormously across the mid-IR and can swamp your bands. Use dry solvents, KBr optics (which dissolve in water), or ATR with a quick water-subtraction.
• IR alone rarely gives a full structure. It tells you the functional groups present, not how they are connected. A ketone band cannot tell 2-hexanone from 3-hexanone — you need NMR or MS for that.
• The fingerprint region is a match tool, not a decode tool. Don't try to assign every band below 1500 cm⁻¹. Its value is pattern-matching against a known reference spectrum.
• Symmetric and weakly polar bonds hide. A symmetric C=C in the middle of a molecule can give a vanishingly weak band because its dipole barely changes — its absence does not prove the bond is absent.
• Overtones and combination bands clutter. Weak bands at roughly 2× or the sum of fundamental frequencies (e.g. aromatic overtones at 2000-1650 cm⁻¹) can be mistaken for real functional-group bands if you are not careful.
• Concentration and path length are not free. Bands that are too strong flatten (clip at zero transmission) and you lose the ability to read their true shape; dilute or shorten the path.