1.2 Light-matter interactions: absorption, emission, and scattering

Light-Matter Interactions: Fundamental Processes

Light-matter interactions form the basis of photochemistry. Every photochemical process begins when light encounters a molecule, and the outcome depends on whether that light is absorbed, emitted, or scattered. Understanding these three processes is essential for interpreting spectroscopic data and designing photochemical reactions.

When molecules absorb light, electrons are promoted to higher energy states. These transitions follow quantum mechanical selection rules and can lead to several outcomes: fluorescence, phosphorescence, non-radiative decay, or photochemical reaction.

Absorption vs. Emission vs. Scattering

Absorption occurs when matter takes in photon energy, causing an electron to jump to a higher energy state. This only happens when the photon's energy matches the energy gap between two electronic states. Absorption decreases the intensity of transmitted light, which is the basis of UV-visible spectroscopy.

Emission is the reverse: an excited electron returns to a lower energy level and releases a photon. There are two types:

• Spontaneous emission occurs without any external trigger. Fluorescence is a common example.
• Stimulated emission occurs when an incoming photon prompts an excited molecule to emit a second, identical photon. This is the principle behind lasers.

Scattering involves a change in the direction of light upon interacting with matter. Unlike absorption, the molecule doesn't retain the photon's energy.

• Elastic scattering (Rayleigh): the scattered photon keeps its original wavelength. This is why the sky appears blue, since shorter wavelengths scatter more strongly.
• Inelastic scattering (Raman): the scattered photon gains or loses energy, shifting its wavelength. Raman spectroscopy exploits this effect to probe molecular vibrations.

Electronic Transitions in Light Interactions

Electronic transitions occur when electrons move between quantized energy levels in atoms or molecules. Quantum mechanical selection rules determine which transitions are "allowed" (high probability) and which are "forbidden" (low probability, but not necessarily zero).

During absorption, an electron jumps from the ground state to an excited state by absorbing a photon of the correct energy. The Franck-Condon principle governs which vibrational level the electron lands in: transitions are most probable when the vibrational wavefunctions of the initial and final states have maximum overlap. Because nuclei are much heavier than electrons, the nuclear geometry doesn't change during the electronic transition (a vertical transition on a potential energy diagram).

During emission, the excited electron drops back to the ground state and releases a photon whose energy equals the energy difference between the two states involved.

The common types of electronic transitions, ordered from highest to lowest energy:

• $\sigma \to \sigma^*$: requires high-energy UV light. Found in saturated molecules like alkanes, which is why they're transparent in the near-UV and visible range.
• $n \to \sigma^*$: moderate-energy UV transitions. Seen in molecules with lone pairs on heteroatoms, such as alcohols and amines.
• $\pi \to \pi^*$: lower energy, often in the near-UV or visible region. Characteristic of conjugated systems like dienes and aromatic rings. These are typically strong, allowed transitions.
• $n \to \pi^*$: also lower energy, but these transitions are symmetry-forbidden, making them weaker (lower molar absorptivity). Common in carbonyl compounds like ketones and aldehydes.

Photoluminescence and Efficiency Factors

Principles of Fluorescence and Phosphorescence

Fluorescence is a rapid emission process, typically occurring on the nanosecond timescale. The transition occurs between states of the same spin multiplicity (usually $S_1 \to S_0$, singlet-to-singlet). Before emission, the molecule undergoes vibrational relaxation within the excited state, losing some energy as heat. This means the emitted photon always has less energy (longer wavelength) than the absorbed photon. The difference in wavelength between absorption and emission maxima is called the Stokes shift.

Phosphorescence is a much slower process, lasting from milliseconds to even hours. Here's why it's slow:

1. The molecule absorbs light and reaches an excited singlet state ($S_1$).
2. Intersystem crossing (ISC) occurs: the electron's spin flips, converting the molecule to a triplet state ($T_1$). This spin-forbidden process is facilitated by spin-orbit coupling, which is stronger in molecules containing heavy atoms.
3. The molecule emits from $T_1 \to S_0$. Because this transition involves a change in spin multiplicity, it's formally forbidden, which is what makes it so slow.
4. Phosphorescence exhibits a larger Stokes shift than fluorescence because the triplet state is lower in energy than the corresponding singlet.

The Jablonski diagram is the standard way to visualize all of these processes. It maps out the singlet and triplet electronic states as horizontal lines, with arrows showing absorption (upward), fluorescence (downward from $S_1$), phosphorescence (downward from $T_1$), and wavy arrows for non-radiative processes like internal conversion and intersystem crossing.

Efficiency Factors in Light-Matter Interactions

Not every absorbed photon leads to emission. Several factors determine how efficiently a molecule converts absorbed light into emitted light or photochemical products.

Absorption cross-section ($\sigma$) quantifies how likely a molecule is to absorb a photon at a given wavelength. A larger cross-section means higher absorption probability. It depends on both the molecular structure and the wavelength of incident light.

Quantum yield ($\Phi$) is the ratio of photons emitted to photons absorbed:

$\Phi = \frac{\text{number of photons emitted}}{\text{number of photons absorbed}}$

A quantum yield of 1.0 means every absorbed photon produces an emitted photon. In practice, competing non-radiative pathways (internal conversion, intersystem crossing, collisional quenching) reduce the quantum yield below 1.

Factors that affect emission efficiency:

• Molecular rigidity reduces non-radiative decay. Rigid molecules like rhodamine dyes have high quantum yields because they can't easily dissipate energy through bond rotations.
• Solvent and temperature matter because collisions with solvent molecules and increased thermal motion both promote non-radiative relaxation.
• Quenchers are species that deactivate excited states through energy transfer or electron transfer, reducing emission intensity.
• Concentration can cause self-quenching at high levels, where emitted photons are reabsorbed by neighboring molecules.

Oscillator strength ($f$) is a dimensionless quantity that indicates the probability of an electronic transition. Higher values correspond to stronger, more probable transitions. Allowed transitions like $\pi \to \pi^*$ have oscillator strengths near 1, while forbidden transitions like $n \to \pi^*$ have values closer to 0.01 or lower.

The Beer-Lambert Law connects absorption measurements to molecular concentration:

$A = \varepsilon b c$

• $A$ = absorbance (dimensionless)
• $\varepsilon$ = molar absorptivity ($\text{L mol}^{-1} \text{cm}^{-1}$), a measure of how strongly a substance absorbs at a given wavelength
• $b$ = path length through the sample (cm)
• $c$ = molar concentration ($\text{mol L}^{-1}$)

This law assumes dilute solutions and monochromatic light. At high concentrations, deviations occur due to molecular interactions and scattering effects.