Electronic and Vibrational Spectroscopy

Electronic spectroscopy (UV-Visible)

Principle

Absorption of ultraviolet (200–400 nm) or visible (400–800 nm) radiation promotes an electron from a filled molecular orbital to an empty one. The energies involved are 1–10 eV, comparable to bond energies, which is why these are the transitions that produce colour.

Types of electronic transition

In order of decreasing energy:

Only the last two are analytically useful, because only they fall in the accessible range above 200 nm. Ordinary solvents and air absorb below that, so $\sigma \rightarrow \sigma^*$ requires evacuated instruments and is not routine work.

$\pi \rightarrow \pi^*$ is intense ($\varepsilon \sim 10^4$) and $n \rightarrow \pi^*$ is weak ($\varepsilon \sim 10$–$100$), because the $n$ and $\pi^*$ orbitals occupy different regions of space and overlap poorly. That intensity difference identifies which transition is which.

Chromophores, auxochromes and shifts

A chromophore is the group responsible for absorption: C=C, C=O, N=O, benzene ring. An auxochrome (–OH, –NH₂, –OR) does not absorb usefully itself but shifts and intensifies the chromophore's absorption when attached.

• Bathochromic (red) shift — to longer wavelength.
• Hypsochromic (blue) shift — to shorter wavelength.
• Hyperchromic / hypochromic — increase / decrease in intensity.

The role of conjugation

This is the central idea of the topic.

Extending conjugation raises the highest occupied orbital and lowers the lowest unoccupied one, so the HOMO–LUMO gap narrows. Since $\lambda = hc/\Delta E$, absorption moves to longer wavelength.

It is the particle-in-a-box result again: delocalising electrons over a longer system is enlarging the box, and $E \propto 1/L^2$.

Extend conjugation far enough and absorption enters the visible, so the compound is coloured. β-carotene absorbs blue light at 450 nm and therefore looks orange — the pigment of carrots. Nearly every organic dye and pigment is an extensively conjugated system, and this is why.

Instrumentation

Radiation source — deuterium lamp for UV, tungsten-halogen for visible; instruments switch between them around 350 nm. Monochromator — prism or diffraction grating, selecting a narrow band. Sample and reference cells — quartz for UV, since glass absorbs below 350 nm; glass or plastic acceptable for visible only. Detector — photomultiplier tube or photodiode array. Readout — absorbance against wavelength.

A double-beam instrument splits the light between sample and reference cells and compares them continuously, cancelling lamp drift and solvent absorption. That is why it is standard for scanning spectra.

Applications

Quantitative determination via Beer-Lambert; detection of conjugation and functional groups; purity checking; monitoring reaction kinetics by following absorbance with time; and determining equilibrium and dissociation constants.

Vibrational spectroscopy (Infrared)

Principle

Absorption of infrared radiation, typically 4000–400 cm⁻¹, excites molecular vibrations — stretching and bending of bonds. A bond behaves as two masses joined by a spring:

where $k$ is the force constant and $\mu$ the reduced mass. So stronger bonds and lighter atoms vibrate at higher frequency — which is why C≡C appears above C=C above C–C, and why C–H stretches sit high at around 3000 cm⁻¹.

The selection rule

A vibration is infrared active only if it changes the dipole moment of the molecule.

A symmetric vibration in a symmetric molecule leaves the dipole unchanged and is infrared inactive — it absorbs nothing, however vigorously the atoms move. Homonuclear diatomics such as N₂ and O₂ have no infrared spectrum at all, which is precisely why they are not greenhouse gases despite making up 99% of the atmosphere.

Number of vibrational modes

For a molecule of $N$ atoms:

Each atom has three degrees of freedom, giving $3N$ in total; three are translation of the whole molecule and three are rotation — but a linear molecule has only two rotational degrees of freedom, since rotation about its own axis moves no atom. Hence the 5 rather than 6.

CO₂ — linear, N = 3

1. Symmetric stretch (~1340 cm⁻¹) — both oxygens move outward together. The dipole stays zero by symmetry, so this mode is infrared INACTIVE.
2. Asymmetric stretch (~2349 cm⁻¹) — one bond lengthens as the other shortens, creating a dipole. Active. 3 and 4. Two bending modes (~667 cm⁻¹) — in-plane and out-of-plane, identical in energy, so they are degenerate and appear as a single band. Bending breaks the linearity and creates a dipole. Active.

So CO₂ has 4 modes but only 3 distinct absorption bands, and only 2 observed frequencies because two are degenerate.

Why this matters beyond the exam: the asymmetric stretch and bend absorb strongly in the infrared that Earth radiates to space, which is what makes CO₂ a greenhouse gas — the subject of Module 4.

H₂O — non-linear (bent, 104.5°), N = 3

1. Symmetric stretch (~3657 cm⁻¹). Because the molecule is bent, even this changes the dipole. Active.
2. Asymmetric stretch (~3756 cm⁻¹). Active.
3. Bending (~1595 cm⁻¹). Active.

All three are infrared active — the contrast with CO₂ is entirely due to the bent geometry. Water's strong, broad infrared absorption is why aqueous samples are difficult in IR spectroscopy and why water vapour is the most significant greenhouse gas by quantity.

Applications

Functional group identification, since each group absorbs in a characteristic range; the fingerprint region below 1500 cm⁻¹, which is complex and essentially unique to a compound, so a match confirms identity; purity and reaction monitoring; and polymer and surface analysis.