⚛Molecular Physics Unit 9 – Electronic Spectroscopy & Franck-Condon

Key Concepts and Principles

• Electronic spectroscopy studies the interaction between matter and electromagnetic radiation in the UV-visible region
• Molecules absorb and emit light at specific wavelengths corresponding to energy differences between electronic states
• Electronic transitions occur between different electronic energy levels (ground state to excited states)
• Vibrational structure appears in electronic spectra due to simultaneous changes in vibrational energy levels during electronic transitions
• The Franck-Condon principle explains the intensity distribution of vibrational bands in electronic spectra
  • Based on the overlap of vibrational wavefunctions between initial and final electronic states
  • Transitions with the greatest wavefunction overlap have the highest intensity
• Selection rules determine which electronic transitions are allowed or forbidden based on symmetry and spin considerations
• Born-Oppenheimer approximation separates electronic and nuclear motions, allowing for the analysis of electronic transitions independently from vibrational and rotational motions

Electromagnetic Spectrum Basics

• Electromagnetic radiation consists of oscillating electric and magnetic fields propagating through space at the speed of light
• The electromagnetic spectrum spans a wide range of wavelengths and frequencies, from radio waves to gamma rays
• The energy of electromagnetic radiation is directly proportional to its frequency and inversely proportional to its wavelength ($E = hν = hc/λ$)
• UV-visible light falls between the wavelength range of 200-800 nm, with UV light having shorter wavelengths and higher energy than visible light
• Molecules interact with electromagnetic radiation through absorption, emission, or scattering processes
  • Absorption occurs when a molecule takes in energy from light and transitions to a higher energy state
  • Emission happens when a molecule releases energy as light and returns to a lower energy state
• The color of a substance is determined by the wavelengths of light it absorbs and reflects or transmits (complementary colors)

Molecular Energy Levels

• Molecules possess discrete energy levels, including electronic, vibrational, and rotational levels
• Electronic energy levels arise from the arrangement of electrons in molecular orbitals
  • The ground state is the lowest energy electronic configuration
  • Excited states are higher energy electronic configurations
• Vibrational energy levels are associated with the vibrations of atoms within a molecule
  • Each electronic state has its own set of vibrational levels
  • Vibrational levels are typically denoted by the vibrational quantum number (v = 0, 1, 2, ...)
• Rotational energy levels result from the rotation of the molecule about its axes
• The spacing between energy levels determines the wavelengths of light absorbed or emitted during transitions
• The Boltzmann distribution describes the population of molecules in different energy levels at thermal equilibrium
  • Lower energy levels have higher populations than higher energy levels
  • The population ratio depends on the temperature and energy difference between levels

Electronic Transitions

• Electronic transitions occur when a molecule absorbs or emits a photon, causing a change in its electronic state
• The energy of the absorbed or emitted photon must match the energy difference between the initial and final electronic states
• Allowed transitions follow selection rules based on the symmetry and spin of the electronic states involved
  • The most common selection rule is the spin selection rule, which states that transitions between states with different spin multiplicities are forbidden (ΔS = 0)
  • Laporte selection rule states that transitions between states with the same parity (gerade or ungerade) are forbidden in centrosymmetric molecules
• The probability of a transition depends on the transition dipole moment, which is a measure of the coupling between the initial and final states
• Transitions can be classified as π → π*, n → π*, σ → σ*, or n → σ* based on the types of molecular orbitals involved
• The energy and intensity of electronic transitions provide information about the electronic structure and properties of molecules

Vibrational Structure

• Electronic spectra often exhibit vibrational structure, which appears as a series of closely spaced bands within an electronic transition
• Vibrational structure arises from the simultaneous changes in vibrational energy levels during an electronic transition
• The spacing between vibrational bands corresponds to the vibrational energy level differences in the initial and final electronic states
• The intensity distribution of vibrational bands is governed by the Franck-Condon principle
  • Transitions with the greatest overlap between the vibrational wavefunctions of the initial and final states have the highest intensity
  • Vertical transitions, where the nuclear positions remain unchanged, are favored
• Progressions are series of vibrational bands corresponding to transitions from the ground vibrational state of the initial electronic state to different vibrational levels of the final electronic state
• Hot bands arise from transitions originating from excited vibrational levels of the initial electronic state
• The analysis of vibrational structure provides information about the vibrational frequencies and geometries of molecules in different electronic states

The Franck-Condon Principle

• The Franck-Condon principle is a key concept in understanding the intensity distribution of vibrational bands in electronic spectra
• It states that electronic transitions occur most favorably when the nuclear positions and momenta remain unchanged (vertical transitions)
• The probability of a transition is proportional to the square of the overlap integral between the vibrational wavefunctions of the initial and final states (Franck-Condon factor)
  • Transitions with the greatest wavefunction overlap have the highest intensity
  • The overlap integral depends on the relative positions and shapes of the potential energy curves of the initial and final electronic states
• The Franck-Condon principle explains the observation of vibrational progressions and hot bands in electronic spectra
• Transitions to higher vibrational levels of the final state are favored when there is a significant change in the equilibrium bond length between the initial and final electronic states
• The Franck-Condon principle is a consequence of the Born-Oppenheimer approximation, which separates electronic and nuclear motions

Spectroscopic Techniques

• Various spectroscopic techniques are used to study electronic transitions in molecules
• UV-visible absorption spectroscopy measures the attenuation of light as it passes through a sample
  • The absorbance is proportional to the concentration of the absorbing species (Beer-Lambert law)
  • Absorption spectra provide information about the energies and intensities of electronic transitions
• Fluorescence spectroscopy detects the emission of light from electronically excited states
  • Molecules are excited by absorbing light and then emit photons as they return to the ground state
  • Fluorescence spectra provide information about the energy differences between excited and ground states
• Phosphorescence spectroscopy measures the emission of light from triplet excited states
  • Transitions between states with different spin multiplicities are forbidden, leading to longer emission lifetimes compared to fluorescence
• Raman spectroscopy probes the vibrational structure of molecules through inelastic scattering of light
  • The energy differences between the incident and scattered light correspond to vibrational energy level spacings
• Time-resolved spectroscopy techniques (e.g., pump-probe, fluorescence upconversion) study the dynamics of electronic transitions on short timescales
• Spectroscopic techniques can be combined with computational methods (e.g., density functional theory) to aid in the interpretation of experimental data

Applications and Real-World Examples

• Electronic spectroscopy has a wide range of applications in various fields, including chemistry, biology, materials science, and environmental monitoring
• UV-visible spectroscopy is used for the quantitative analysis of compounds in solution (concentration determination)
  • Examples include measuring the concentration of proteins, nucleic acids, and chemical pollutants
• Electronic spectroscopy is employed in the characterization of organic compounds, including conjugated systems (dyes, pigments) and aromatic molecules
• The study of electronic transitions is crucial for understanding the photophysical and photochemical properties of molecules
  • Examples include the design of photosensitizers for photodynamic therapy and the development of organic photovoltaic materials
• Electronic spectroscopy is used to investigate the structure and function of biological molecules, such as proteins and enzymes
  • The absorption and fluorescence properties of amino acids (tryptophan, tyrosine) and cofactors (flavins, heme) provide information about their local environment and interactions
• Environmental monitoring applications include the detection and quantification of pollutants, such as pesticides and polycyclic aromatic hydrocarbons (PAHs)
• Electronic spectroscopy is employed in the quality control and analysis of pharmaceuticals, ensuring the purity and stability of drug compounds
• The study of electronic transitions is essential for the development of luminescent materials, such as organic light-emitting diodes (OLEDs) and fluorescent probes for imaging and sensing applications