☀️Photochemistry Unit 6 – Radiative and Non–Radiative Transitions

Key Concepts and Definitions

• Radiative transitions involve the absorption or emission of photons as molecules transition between energy states
• Non-radiative transitions occur without the absorption or emission of photons and include processes such as internal conversion, intersystem crossing, and vibrational relaxation
• Quantum yield represents the efficiency of a photochemical process, defined as the number of molecules undergoing a specific event divided by the number of photons absorbed
• Excited state lifetimes refer to the average time a molecule spends in an excited state before returning to the ground state through radiative or non-radiative processes
  • Lifetimes can range from femtoseconds (10^-15 s) to seconds depending on the molecule and the specific excited state
• Franck-Condon principle states that electronic transitions occur much faster than nuclear motions, resulting in vertical transitions on potential energy surfaces
• Born-Oppenheimer approximation assumes that electronic and nuclear motions can be separated due to the significant difference in their masses and velocities
• Selection rules determine the allowed or forbidden nature of transitions based on the symmetry and spin of the involved states

Radiative Transitions: Types and Mechanisms

• Absorption occurs when a molecule absorbs a photon and transitions from a lower energy state to a higher energy state
  • Absorption spectra provide information about the energy differences between the ground and excited states
• Fluorescence is the emission of a photon as a molecule transitions from an excited singlet state to the ground singlet state
  • Typically occurs on timescales of nanoseconds (10^-9 s) to microseconds (10^-6 s)
• Phosphorescence involves the emission of a photon as a molecule transitions from an excited triplet state to the ground singlet state
  • Longer timescales compared to fluorescence, ranging from microseconds to seconds, due to the spin-forbidden nature of the transition
• Stimulated emission occurs when an incident photon interacts with an excited molecule, causing it to emit a photon of the same frequency, phase, and direction
• Resonance fluorescence happens when the incident light frequency matches the energy difference between the ground and excited states, leading to increased fluorescence intensity
• Delayed fluorescence arises from the reverse intersystem crossing from the excited triplet state back to the excited singlet state, followed by fluorescence emission

Non-Radiative Transitions: Types and Mechanisms

• Internal conversion is a transition between two electronic states of the same spin multiplicity (e.g., S2 to S1 or T2 to T1)
  • Occurs when the vibrational levels of the higher electronic state overlap with the vibrational levels of the lower electronic state
• Intersystem crossing involves a transition between electronic states of different spin multiplicities (e.g., S1 to T1)
  • Facilitated by spin-orbit coupling, which mixes the singlet and triplet states
• Vibrational relaxation is the rapid transition from higher vibrational levels to the lowest vibrational level within the same electronic state
  • Occurs through the transfer of vibrational energy to the surrounding medium (solvent or lattice) on timescales of picoseconds (10^-12 s)
• Collisional quenching happens when an excited molecule transfers its energy to another molecule during a collision, returning to the ground state without emitting a photon
• Förster resonance energy transfer (FRET) is a non-radiative energy transfer mechanism between two chromophores, where the emission spectrum of the donor overlaps with the absorption spectrum of the acceptor
• Dexter energy transfer is another non-radiative energy transfer mechanism that requires the overlap of the electron clouds of the donor and acceptor molecules

Energy Transfer Processes

• Radiative energy transfer involves the emission and absorption of photons between molecules
  • Occurs over longer distances compared to non-radiative energy transfer processes
• Förster resonance energy transfer (FRET) is a non-radiative, long-range (up to ~10 nm) dipole-dipole interaction between a donor and an acceptor molecule
  • Efficiency depends on the spectral overlap, distance, and relative orientation of the donor and acceptor
• Dexter energy transfer is a short-range (< 1 nm) non-radiative process that involves the exchange of electrons between the donor and acceptor
  • Requires the overlap of the electron clouds and conserves the total spin of the system
• Triplet-triplet annihilation occurs when two molecules in their triplet excited states interact, resulting in one molecule returning to the ground state and the other being promoted to a higher excited state
• Singlet fission is a process where one singlet excited molecule splits into two triplet excited molecules, potentially increasing the efficiency of solar cells
• Upconversion is an anti-Stokes process where two or more low-energy photons are absorbed, leading to the emission of a higher-energy photon

Quantum Yield and Lifetimes

• Quantum yield (Φ) is the ratio of the number of molecules undergoing a specific process to the number of photons absorbed
  • Φ = (number of events) / (number of absorbed photons)
• Fluorescence quantum yield (Φ_f) is the ratio of the number of photons emitted through fluorescence to the number of photons absorbed
  • Φ_f = (number of photons emitted) / (number of photons absorbed)
• Phosphorescence quantum yield (Φ_p) is the ratio of the number of photons emitted through phosphorescence to the number of photons absorbed
  • Φ_p = (number of photons emitted) / (number of photons absorbed)
• Excited state lifetime (τ) is the average time a molecule spends in the excited state before returning to the ground state
  • Related to the rate constants of radiative (k_r) and non-radiative (k_nr) processes: τ = 1 / (k_r + k_nr)
• Fluorescence lifetime (τ_f) is the average time a molecule spends in the excited singlet state before emitting a photon through fluorescence
• Phosphorescence lifetime (τ_p) is the average time a molecule spends in the excited triplet state before emitting a photon through phosphorescence
  • Usually longer than fluorescence lifetimes due to the spin-forbidden nature of the transition

Experimental Techniques and Measurements

• Absorption spectroscopy measures the absorption of light as a function of wavelength, providing information about the energy levels and electronic transitions of molecules
  • Follows the Beer-Lambert law: A = ε * l * c, where A is absorbance, ε is the molar attenuation coefficient, l is the path length, and c is the concentration
• Fluorescence spectroscopy measures the emission of light from a sample after excitation at a specific wavelength
  • Stokes shift is the difference between the maximum absorption and emission wavelengths, arising from the energy loss due to vibrational relaxation and solvent reorganization
• Time-resolved spectroscopy techniques, such as time-correlated single photon counting (TCSPC) and transient absorption spectroscopy, allow for the measurement of excited state lifetimes and the study of ultrafast processes
• Quantum yield measurements involve the comparison of the emission intensity of a sample to that of a reference compound with a known quantum yield
  • Relative method: Φ_sample = Φ_ref * (I_sample / I_ref) * (A_ref / A_sample) * (n_sample^2 / n_ref^2), where I is the integrated emission intensity, A is the absorbance at the excitation wavelength, and n is the refractive index of the solvent
• Transient absorption spectroscopy is a pump-probe technique that measures the change in absorption of a sample following excitation by a short laser pulse
  • Provides information about the dynamics of excited states, intermediate species, and photochemical reactions on timescales ranging from femtoseconds to microseconds
• Fluorescence anisotropy measurements can reveal information about the size, shape, and flexibility of molecules, as well as the viscosity of the surrounding medium

Applications in Photochemistry

• Photodynamic therapy (PDT) uses photosensitizers that generate reactive oxygen species upon light irradiation to selectively destroy cancer cells or other targeted tissues
  • Relies on the efficient intersystem crossing of the photosensitizer to generate long-lived triplet states that can interact with molecular oxygen
• Solar energy conversion utilizes the principles of radiative and non-radiative transitions to convert sunlight into electrical or chemical energy
  • Dye-sensitized solar cells (DSSCs) employ dye molecules that absorb light and inject electrons into a semiconductor, while the dye is regenerated by an electrolyte
• Photocatalysis involves the use of light to activate catalysts that can drive chemical reactions, such as water splitting or CO2 reduction
  • Semiconductor nanoparticles (e.g., TiO2) can absorb light and generate electron-hole pairs that participate in redox reactions
• Fluorescence imaging and sensing rely on the sensitive detection of fluorescence signals to visualize biological processes or detect specific analytes
  • Fluorescent proteins (e.g., green fluorescent protein, GFP) and small-molecule fluorophores are widely used in microscopy and bioassays
• Optogenetics employs genetically encoded light-sensitive proteins (e.g., channelrhodopsin) to control the activity of specific neurons or other cell types in living organisms
  • Relies on the efficient absorption and conformational changes of these proteins upon light irradiation
• Photolithography is a crucial process in the fabrication of microelectronic devices, where light is used to pattern photoresist materials on semiconductor substrates
  • Involves the photochemical reactions of the photoresist, such as photopolymerization or photocleavage, to create high-resolution patterns

Challenges and Future Directions

• Improving the efficiency of solar energy conversion devices by developing new materials with enhanced light absorption, charge transport, and stability
  • Strategies include the design of novel sensitizers, the optimization of device architectures, and the use of nanostructured materials
• Enhancing the selectivity and efficacy of photodynamic therapy by developing targeted photosensitizers and optimizing light delivery methods
  • Nanoparticle-based delivery systems and two-photon absorption techniques can improve the spatial and temporal control of PDT
• Expanding the scope of photocatalysis to enable more efficient and selective chemical transformations
  • Developing visible-light-responsive photocatalysts and exploring new reaction pathways, such as photoredox catalysis and proton-coupled electron transfer (PCET)
• Advancing the spatial and temporal resolution of fluorescence imaging techniques to study biological processes at the molecular level
  • Super-resolution microscopy methods (e.g., STED, PALM, STORM) and ultrafast spectroscopy can provide unprecedented insights into cellular dynamics
• Integrating optogenetics with other techniques, such as electrophysiology and functional imaging, to gain a comprehensive understanding of neural circuits and behavior
  • Developing new optogenetic tools with improved specificity, sensitivity, and spectral properties
• Pushing the limits of photolithography to create smaller and more complex nanostructures for advanced electronic and photonic devices
  • Extreme ultraviolet (EUV) lithography and directed self-assembly (DSA) are promising approaches to overcome the resolution limits of conventional photolithography
• Exploring the potential of quantum technologies, such as quantum dots and single-photon emitters, for secure communication, quantum computing, and ultra-sensitive sensing applications