Spectroscopy

[Worked example] A 600 nm photon: ν, E (J), E (eV), E (kJ/mol), ν̃?

ν = c/λ = 3×10⁸ / 6×10⁻⁷ = 5×10¹⁴ Hz. E = hν = 6.63×10⁻³⁴ × 5×10¹⁴ = 3.3×10⁻¹⁹ J = 2 eV ≈ 200 kJ/mol. ν̃ = 1/λ = 1.67×10⁴ cm⁻¹.

[UV/Vis ranges] Wavelength ranges: VUV, UVC, UVB, UVA, visible?

VUV ~100-200 nm; UVC ~200-280 nm (ozone absorbs ~200-290 nm); UVB ~280-315 nm; UVA ~315-400 nm; Visible ~400-750 nm (slide: ~390-780). Bees can see ~300-650 nm (into the UV). ★ exact UV band edges are standard values.

[Energy levels] What is the Boltzmann law?

Energy is quantised, and molecules distribute over the levels as n_u/n_g = exp(−ΔE/RT) (n_u = excited, n_g = ground; R gas constant; ΔE energy gap; T temperature). Bigger gap or lower T → fewer molecules in the excited state.

Order the transition types from HIGHEST to LOWEST energy

Inner-electron transitions (X-rays) > bonding/outer-electron transitions (UV/Vis, ~10⁵ J/mol) > molecular vibrations (IR, ~10⁴ J/mol) > electron spin + molecular rotations (microwaves) > nuclear spin flips (radiowaves, ~10⁻³ J/mol).

Which technique goes with which region?

X-rays: XAS/EXAFS (inner electrons). UV/Vis region: UV/Vis absorption, fluorescence, (resonance) Raman (outer electrons). IR: IR/Raman (vibrations). Microwaves: EPR (electron spin). Radiowaves: NMR (nuclear spin).

[Population: NMR vs UV/Vis] What are n_u/n_g for NMR vs UV/Vis, and what does it mean?

NMR: ΔE ~10⁻³ J/mol → n_u/n_g ≈ 0.99999 (levels almost equally populated). UV/Vis: ΔE ~10⁵ J/mol → n_u/n_g ~10⁻²¹ (essentially everything in the ground state). Greater population difference = greater sensitivity (less sample / lower concentration needed). So UV/Vis is intrinsically more sensitive than NMR.

What determines peak linewidth (Δν) and why does it matter?

Δν depends on the LIFETIME (τ) of the excited state (Δν ~ 1/τ). FAST decay → position uncertain → BROAD line. SLOW decay (e.g. NMR) → SHARP lines. Linewidth sets spectral resolution, so it affects the information content of the spectrum.

[Franck-Condon] State the Franck-Condon principle

Electronic transitions (~10⁻¹⁵ s) are much faster than nuclear motion (vibrations), so the nuclei do not move during the transition → on an energy-vs-r plot (Morse curves) the transition is drawn VERTICAL.

Name the processes on a Jablonski diagram

Absorption (S₀→S₁/S₂, ~10⁻¹⁵ s)

Vibrational relaxation (within a state, non-radiative).

Internal conversion (S₂→S₁, non-radiative).

Intersystem crossing (S₁→T₁, spin flip).

FLUORESCENCE (S₁→S₀, radiative, fast ~ns).

PHOSPHORESCENCE (T₁→S₀, radiative, slow µs-s, spin-forbidden).

Why is fluorescence emitted at a LONGER wavelength than the absorbed light?

Before emitting, the molecule loses some energy by vibrational relaxation / internal conversion, so the emitted photon has less energy (longer λ) than the absorbed one.

Why do selection rules exist?

E-field of the EM radiation only interacts effectively if there is a CHARGE DISPLACEMENT (change in dipole) when going between states

No charge displacement → transition 'forbidden' (weak or absent).

[Selection rules: UV/Vis] Which electronic transitions are allowed/forbidden?

1s→2s is FORBIDDEN (no charge displacement, Δl = 0). s→p is ALLOWED (Δl = ±1, charge moves) and π→π* is ALLOWED.

What is μ (transition dipole moment)?

A vector that quantifies the charge displacement during a g→e transition. Bigger charge displacement → bigger μ → more probable transition → stronger absorbance. Its DIRECTION depends on chemical structure (e.g. of a chromophore).

Why use spectroscopy to study materials?

A material's function doesn't follow directly from its chemistry. Spectroscopy links structure (how molecules form chemically, are arranged and interact) to properties, and shows how stimuli (temperature, force, water, light) change the molecular landscape and can be used to process/shape the material.

What are the two components of electromagnetic radiation?

An electric field component and a magnetic field component. The electric field describes how photons travel through space; it is drawn as a wave, polarised when we select a single plane.

What is radiant power?

How many photons hit the detector per unit time. P is proportional to the amplitude squared (P ∝ A²).

Key wave relations (frequency, speed of light, wavenumber)

ν = 1/period; c = νλ (in vacuum/air); wavenumber ν̄ = 1/λ (in cm⁻¹).

Energy of a single photon

E = hν = hc/λ = hcν̄ (h = 6.63·10⁻³⁴ Js). Energy increases when wavelength decreases (wavenumber increases).

What kind of change does each EM region cause?

Long wavelength/low energy = subtle: NMR/ESR change spin

microwave changes orientation (rotation)

infrared changes configuration (bond vibrations)

UV-vis + X-ray change electron distribution

γ-rays change nuclear configuration (dramatic).

What can happen when radiation hits a sample?

Reflection, transmission, absorption or scattering. We use these phenomena to extract information about the material.

Emission/chemiluminescence spectroscopy: how does it work?

Non-radiative energy (thermal, electrical, chemical) excites molecules to a higher state; when they relax they emit photons (radiant). Wavelength λ = identity of the species; emitted power P_E = concentration. No light source needed.

Photoluminescence (fluorescence) spectroscopy: how does it work?

A light source + wavelength selector irradiates the sample, molecules go to an excited state and emit light as they fall back. You detect the emitted light (not the transmitted excitation light). Energy differences between levels determine the wavelength λ.

Absorption spectroscopy: principle and equation

Incident energy P0 must match the energy gap between levels

A = −log T = −log(P/P0) = εbc (Beer-Lambert)

Qualitative from λ (which bonds), quantitative from A (how much)

(c = concentration, b = path length, ε = molar absorptivity.)

Thick vs thin sample in transmission (4000-600 cm⁻¹)

A thick sample absorbs everything in some regions, so no light reaches the detector (saturation, ~0% transmission) and nothing can be concluded there. Fix: lower the concentration/path length (thinner sample) so that some light passes (A = εbc).

Continuum source vs line source

Continuum (e.g. a light bulb) has all wavelengths; changing wavelength is slow/gradual and gives poorly defined wavelength resolution. Line source: select one wavelength, switch it off and turn on another.

How does a monochromator select a wavelength?

Light with many wavelengths diverges and hits a concave mirror, which makes it parallel (collimated). A reflection grating disperses it by wavelength (angular dispersion); a second concave mirror focuses it onto the exit slit. Rotating the grating selects the wavelength.

Path of light in an FTIR interferometer

Source → slit → collimated beam → beam splitter (half transmitted, half reflected). One half goes to a stationary mirror, the other to a movable mirror; both return to the beam splitter, recombine and go through the sample to the detector.

When do the two beams interfere constructively/destructively?

Path difference δ = integer multiple of λ → constructive (waves in phase, stronger signal). δ = half-integer multiple of λ → destructive (signal cancels). Moving the mirror switches wavelengths on/off.

How do you get a spectrum from the interferometer?

Measure a blank without the sample first, then with the sample (the ratio removes the background). The detector records an interferogram (intensity vs mirror position); a Fourier transform converts it into the spectrum.

What determines spectral resolution in FTIR?

mirror displacement: Δν̄ = 1/x

larger displacement gives a finer resolution (e.g. x = 4 cm → 0.25 cm⁻¹)

FTIR coupled to a microscope: what does it add?

You can use an aperture to select a small area of a thin slice (patient, animal, plastic) and measure spectra there. Different proteins/structures look different in space, giving much higher spatial resolution than a bulk measurement.

IR vs Raman: what is the difference?

IR = absorption of photons

Raman = inelastic scattering (the photon exchanges energy with the matter)

Elastic = same energy in + out

They are complementary: bands missing in IR often appear in Raman

Practical advantage of Raman detection

Scattered light can be collected anywhere in space, so a simple probe/handheld scanner can record chemical information easily.

Selection rule for IR

The vibration must change the dipole moment (e.g. a polar bond whose + and − ends move when it stretches).

Selection rule for Raman

The vibration must change the polarisability (the electron cloud follows the light wave). Useful when there is no dipole change.

Bond polarity vs electronegativity difference

ΔEN 0-0.4 = nonpolar covalent (dipole ≈ 0); 0.4-2.0 = polar covalent (one atom more negative); >2.0 = ionic (very high dipole moment).

Example: vibrational modes of CO₂ (IR/Raman)

Symmetric stretch (both O move outward): no dipole change → not IR active, Raman active.

Asymmetric stretch (one O out, one in): dipole changes → IR active.

Bending: dipole changes → IR active.

Also rocking, twisting, wagging. Correct for background CO₂ or you get its peaks.

Hooke's law model for stretching vibrations

Two atoms act as a harmonic oscillator: F = −k_f·x, parabolic potential V = ½k_f(R−R_eq)². Closer than R_eq → repulsion, further → attraction. Gives ν̄ = (1/2πc)·√(k_f/m_eff). Effective mass: m_eff = (m_A·m_B)/(m_A+m_B).

How do bond order and mass change the wavenumber?

Higher force constant (triple > double > single, shorter bond, stronger) → higher wavenumber.

Heavier atoms (larger m_eff) → LOWER wavenumber.

Coupled vibrations (e.g. CH₂)

One bond type, two vibrations: the antisymmetric stretch comes at a higher wavenumber than the symmetric stretch.

Fermi resonance

An overtone (higher wavenumber, ~2×, 3× the fundamental, weak) coincides with a fundamental. They mix and give a strong peak that may consist of two peaks. Overtones can therefore change the spectrum.

Electronic effects on band position

Induced by substituents/neighbours. Inductive effect: + lowers ν̄, − raises ν̄. Mesomeric: bond gets longer, k_f ↓, ν̄ ↓. Field effect: ν̄ can go up or down.

Example: the amide bond and the mesomeric effect

amide has 2 resonance forms (C=O/N and C-O⁻/N⁺=C) + we observe the average

C=O bond becomes longer, the force constant drops + carbonyl shifts to lower wavenumber.

Effect of hydrogen bonding on IR bands

Changes electron distribution, force constant and bond length: the stretch shifts to lower wavenumber (and broadens).

How do you read a spectrum? (high wavenumber vs fingerprint)

Split it into regions: high wavenumber (O-H, N-H, C-H stretches) and the fingerprint region (how the molecule organises itself in space). Leave out empty regions (no peaks) to see the peaks; assign bands with handbooks of IR/Raman characteristic frequencies.

Example: how to tell N-H from O-H when bands overlap?

Treat the sample with heavy water (D₂O). The N-H proton exchanges to N-D, increasing m_eff, so the band moves to a lower wavenumber (shifted peaks = exchangeable N-H/O-H).

Polarised FTIR microscopy: principle

Select one plane of polarised light. If it is aligned with the bond's axis, the band is seen; if not, it isn't. Rotate the polariser to find the orientation of the structure; subtracting the 0° and 90° spectra gives resolved peaks.

Example: FTIR imaging of PLLA/PDLA interfaces

Lactic acid has a chiral carbon (CH₃ on either side = mirror images L and D). PLLA and PDLA attract each other strongly (stereocomplex) and anchor layers. Print them, cut a cross-section (L on one side, D on the other) and use an aperture on the interface to prove it is there.

Mapping vs transmission imaging in FTIR imaging

Mapping: light in + out point by point (ATR contact can drag/contaminate the sample)

Transmission with a camera: scan the whole area + each pixel is an IR spectrum (info in space; e.g. 3 different spectra in an ink example).

How does nano-IR beat the diffraction limit?

A ~1 nm AFM tip scans the surface and records a near-field optical signal/local expansion. This gives spectral information with nanometre resolution plus topography/mechanical maps next to chemical IR maps.

[UV/Vis] Range and what is a chromophore?

UV/Vis spectroscopy: ~200-750 nm. A CHROMOPHORE is a molecule/group that absorbs in this range. Examples: aromatic amino acids (Trp, Tyr, Phe), nucleotide bases, NADH, flavins, chlorophyll, haem, some transition metals.

[Beer-Lambert calculation] ε = 5,500 M⁻¹cm⁻¹, A = 0.55, l = 1 cm. Concentration?

c = A/(ε·b) = 0.55 / (5,500 × 1) = 1×10⁻⁴ M = 100 µM.

Which residues absorb in proteins and at what wavelengths?

Peptide bond ~200 nm. Above 230 nm: Trp (λmax 280 nm, ε ≈ 5,500 M⁻¹cm⁻¹) > Tyr (274 nm, ε ≈ 1,490) ≫ Phe (257 nm, weak, ε ≈ 200) plus cystine S-S (ε ≈ 125). Trp + Tyr dominate the A280.

[Nucleic acids UV] Where do nucleic acids absorb and how is concentration found?

230-290 nm, mainly from the BASES, λmax ≈ 258-260 nm (DNA 258, RNA 258). Use A260. Slide values: 0.020 (dsDNA) and 0.027 (ssDNA and RNA) in mL·µg⁻¹·cm⁻¹. ⚠ Slide writes the units as µg·mL⁻¹·cm⁻¹ (wrong way round). Rule of thumb: A260 = 1 ≈ 50 µg/mL dsDNA (=1/0.020), ~33 µg/mL ssDNA, ~40 µg/mL RNA ★.

What does IR detect and in what range?

Molecular VIBRATIONS. Observable range ν̃ = 700-4,000 cm⁻¹ (λ = 14-2.5 µm).

Two main limitations of IR?

(1) Large number of peaks: 3n−6 vibrations for a non-linear n-atom molecule (3n−5 if linear) → problems with resolution and with assigning peaks to specific vibrations. (2) Strong absorption by solvents (water!) and sample cells.

[Amide bands] What are amide I and amide II?

Characteristic IR bands of proteins from vibrations of the planar PEPTIDE group. Their positions are sensitive to secondary structure (α-helix vs β-sheet). ★ Amide I ≈ 1650 cm⁻¹ (mostly C=O stretch); amide II ≈ 1550 cm⁻¹ (N-H bend + C-N stretch).

What is Raman scattering?

Inelastic scattering of laser light (frequency ν₀): a change in the vibrational state of the molecule changes the scattering, so scattered light shifts in wavelength

Gives info on vibrational states + depends on change in polarisability.

[Raman lines] Rayleigh vs Stokes vs anti-Stokes?

RAYLEIGH: same frequency as laser (no change in vibrational state)

STOKES: scattered light at LOWER frequency (molecule ends in a higher vibrational level)

ANTI-STOKES: scattered light at HIGHER frequency (molecule started in an excited vibrational level)

Order of scattering intensities in Raman?

Rayleigh (static) ≫ Stokes > anti-Stokes

Rayleigh is ~10⁶ stronger than Raman

Anti-Stokes is weaker because few molecules start in an excited vibrational level (Boltzmann)

[Raman enhancement] Raman is weak: how is sensitivity boosted?

RESONANCE Raman: laser ν₀ tuned to excite an electronic transition of a chromophore → strong signal from that chromophore's vibrations.

SERS (surface-enhanced Raman spectroscopy): sample on a roughened metal surface → huge signal enhancement.

Difference between ORD and CD?

ORD = differential ROTATION of left (L) vs right (R) circularly polarised light; not very sensitive for biological use. CD = differential ABSORPTION of L vs R. CD and ORD are equivalent, but CD is more common in biology.

How is circular dichroism (CD) used for protein structure?

Compare the far-UV CD curve with curves generated from standards (α-helix, β-sheet, random coil) → estimate the secondary-structure content.

How does X-ray absorption work (XAS)?

High-energy X-rays are absorbed by INNER electrons: an electron is ejected from the K shell

K hole is refilled by an outer electron → X-ray fluorescence (XRF), characteristic of the atom type

useful for metalloproteins.

The two regions of an XAS spectrum?

(i) EDGE: sharp rise in absorption when the X-ray energy reaches the core-electron transition

(ii) EXAFS: wiggles above the edge from INTERFERENCE between the outgoing ejected electron wave + waves BACKSCATTERED from neighbouring atoms → info on neighbours (distance, number, type)

X-ray crystallography: Steps from crystal to structure?

Crystal → X-rays → diffraction pattern → phases → electron density map → fitting an atomic model → refinement (loop back to phases).

Phase problem: detectors record intensities not phases.

Protein in water: IR or Raman, and why?

Raman is easier: water is a weak Raman scatterer but absorbs IR strongly (IR limitation). IR is still possible with thin cells, ATR-FTIR or D₂O.

Name 3 ways to get protein secondary structure from spectra

Far-UV CD (compare with standard curves); IR amide I/amide II band positions; (Raman amide bands). All sensitive to α-helix vs β-sheet.