1.1 Radiation and transitions #
1.1.1 The spectrum as an energy ladder #
The energy of one photon is
Cd Spectrum
E = hฮฝ = hc / ฮป
where h is Planckโs constant, ฮฝ is frequency, c is the speed of light, and ฮป is wavelength. A shorter wavelength is a larger energy. Vibrational spectra are usually plotted in wavenumber, ฮฝฬ = 1/ฮป, in cmโปยน, because wavenumber is proportional to energy. The photon either matches a gap in the molecule or it does not. Whether that match produces a signal depends on the selection rule and on how many molecules are in the beam.
Thermal energy kT at room temperature is about 2.5 kJ molโปยน. Gaps much smaller than kT are almost equally populated both ways, which is why NMR is insensitive. Gaps much larger than kT are occupied only in the ground state, which is why an ultraviolet photon can promote an electron and a radiofrequency photon cannot.
| Region | Scale, about | What the energy matches |
|---|---|---|
| Radiofrequency | tens to hundreds of MHz in an NMR magnet | nuclear spin flips |
| Microwave | centimetres; electron resonance often near 9 GHz | electron spin flips; molecular rotation in the gas phase |
| Mid-infrared | about 2.5โ25 ยตm (4000โ400 cmโปยน) | bond vibrations |
| Visible | about 400โ700 nm | electronic transitions of conjugated cofactors and dyes |
| Near-ultraviolet | about 250โ400 nm | electronic transitions of aromatic side chains and bases |
| Far-ultraviolet | below about 250 nm; water and oxygen cut the window near 180 nm | electronic transitions of the peptide bond |
| X-rays | about 0.1 nm | core electrons if absorbed; electron clouds if scattered |
A 500 nm photon carries about 240 kJ molโปยน. An amide I vibration near 1650 cmโปยน carries about 20 kJ molโปยน, enough to report a hydrogen-bonded carbonyl and not enough to break it. A proton resonance near 500 MHz is a fraction of a joule per mole, so only about one nucleus in 10โต sits in the excess population the detector can use.
1.1.2 Absorption, emission, and scattering #
Absorption removes photons whose energy matches an allowed gap and leaves the molecule excited. The transmitted beam is weaker, and an absorption spectrum is that missing intensity. Emission is a photon leaving as the molecule returns to a lower state; fluorescence and phosphorescence are the cases that matter here, and the emitted photon is almost always of lower energy than the one absorbed. Scattering redirects the wave. Elastic (Rayleigh) scattering keeps the photon energy and is the basis of dynamic light scattering. Inelastic (Raman) scattering gains or loses a vibrational quantum. X-ray diffraction is coherent elastic scattering from a periodic electron density. It is not an absorption spectrum of the protein.
A detector cannot tell these events apart unless the instrument forces the distinction. Transmission at the incident colour is absorption. Light at a longer colour, behind a filter, is emission. Light off the straight-through beam is scatter. If two of them reach the same detector, the number is no longer the quantity the experiment named.
1.1.3 Selection rules, briefly #
A transition is seen only if the radiation can couple to it. Infrared absorption needs a vibration that changes the dipole moment, so a peptide carbonyl is strong and a symmetrical non-polar stretch is often silent. Raman scattering needs a change in polarisability, the ease with which the electron cloud distorts. The two rules are complementary: a band missing from the infrared may dominate the Raman spectrum. NMR needs a nucleus with a magnetic moment. EPR needs an unpaired electron, so a paired, diamagnetic molecule is silent however concentrated it is. โThe sample contains that bondโ does not mean โthe spectrum will show itโ.
1.2 The aqueous sample #
The study of The aqueous sample provides fundamental principles governing cellular architecture, molecular interactions, and physiological regulation.
Aqueous Potassium Ferricyanide Magnetic Circular Dichroism
1.2.1 Why the sample is in water #
Cells are aqueous. A spectrum in hexane, in vacuum, or in a crystal answers a different question from a spectrum in buffer. Water sets the dielectric constant, hydrogen-bonds to carbonyls, and controls side-chain ionisation, so pH and ionic strength can move a peak or change an extinction coefficient without any covalent change. A biological spectrum belongs to a molecule in a stated solvent, temperature, and pH.
Water is also 55 mol Lโปยน. Whatever the macromolecule does at micromolar concentration, water does a million-fold more of, if water can do it at all. Paths around that fact are the practical story of infrared spectroscopy, far-ultraviolet circular dichroism, and proton NMR.
1.2.2 Where water is opaque #
Liquid water has a strong OโH stretch near 3400 cmโปยน and an HโOโH bend near 1640 cmโปยน. The bend sits on the amide I band, the main infrared reporter of backbone carbonyls, so a centimetre path of water is black across much of the mid-infrared. Aqueous infrared work uses a micrometre path, an evanescent wave at a crystal surface, or DโO, whose bend lies near 1200 cmโปยน. In the far-ultraviolet the peptide bond, chloride, many buffer ions, dissolved oxygen, and water itself cut transmission below about 180 nm. Ordinary glass stops the beam below about 320 nm, so 260 and 280 nm need quartz. Between those two difficult regions water is transparent, which is why absorbance, fluorescence, and light microscopy are everyday methods and infrared and far-ultraviolet CD are not.
1.2.3 A master table #
| Method | Motion or transition | Biological question |
|---|---|---|
| Ultravioletโvisible absorption | valence electronic transition | how much chromophore; whether a cofactor is oxidised, reduced, or liganded |
| Circular dichroism | difference in absorption of left and right circularly polarised light | secondary structure in the far-UV; aromatic packing in the near-UV |
| Fluorescence | emission after electronic excitation | environment, binding, and distance on the 2โ10 nm scale |
| Infrared absorption | vibration that changes a dipole | polar bonds; secondary structure from amide I, if water is dealt with |
| Raman scattering | vibration that changes polarisability | the same vibrational questions, with less interference from water |
| NMR | nuclear spin flip | environment, bonded neighbours, near neighbours in space, dynamics |
| MRI | the same nuclear spin flip, almost always of water | anatomy and a few physiological contrasts, not a molecular structure |
| EPR | electron spin flip | radicals, paramagnetic metals, distances between spin labels |
| X-ray diffraction | coherent scattering from electron density, not a valence transition | crystal spacings; electron density only after phases are recovered |
| Dynamic light scattering | elastic scatter from a moving particle | a diffusion coefficient and a hydrodynamic radius |
Later chapters leave the spectrum. Mass spectrometry measures mass-to-charge. Chromatography and electrophoresis measure differential migration. Calorimetry measures heat. Force methods measure piconewtons and nanometres. Electrical recording measures current and voltage. They are in this course because of the quantity and the artefact, not because a photon is involved.
1.3 Key terms, summary, and self-check #
Key terms. Wavelength; wavenumber; absorption; emission; Rayleigh scattering; Raman scattering; selection rule; dipole moment; polarisability; amide I; far-ultraviolet.
Summary. Photon energy sets which degree of freedom a method can see: nuclear spin, electron spin, rotation, vibration, or electronic excitation. Absorption, emission, and scattering are different events and must not reach the detector together unrecognised. Water is the biological solvent and is also the absorber that closes much of the infrared and the far-ultraviolet.
Self-check.
1. A 280 nm photon and a 1650 cmโปยน photon match which molecular transitions?
2. Why is a rotational microwave spectrum not a routine measurement on a protein in water?
3. What must change in the molecule for infrared absorption, and what must change for Raman scattering?
4. Why can a centimetre cuvette of buffer be used at 280 nm and not for a transmission amide I spectrum?
5. Why is X-ray diffraction listed as scattering rather than as an electronic absorption method?
