3.6 Electronic Spectroscopy and Franck-Condon Principle

Electronic spectroscopy reveals how molecules interact with light, causing electrons to jump between energy levels. This topic dives into the principles behind these transitions, including selection rules and the types of electronic shifts that can occur in different molecular structures.

The Franck-Condon principle explains why some transitions are more likely than others. It connects electronic and vibrational changes, helping us understand the shapes of absorption and emission spectra and what they tell us about molecular geometry.

Electronic Spectroscopy Principles

Fundamental Concepts

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• Electronic spectroscopy involves the absorption or emission of photons that cause transitions between electronic states in atoms or molecules
• The energy of the absorbed or emitted photon corresponds to the energy difference between the initial and final electronic states involved in the transition
• Selection rules based on quantum mechanical principles determine which electronic transitions are allowed or forbidden
  • Allowed transitions have a higher probability of occurring than forbidden transitions
• The intensity of an electronic transition depends on the transition dipole moment, which measures the change in the electronic charge distribution during the transition

Types of Electronic Transitions

• Electronic transitions can be classified as σ → σ*, π → π*, n → σ*, or n → π*, depending on the molecular orbitals involved in the initial and final states
  • σ → σ* transitions involve the excitation of an electron from a bonding σ orbital to an antibonding σ* orbital (alkanes)
  • π → π* transitions occur when an electron is excited from a bonding π orbital to an antibonding π* orbital (conjugated systems, aromatic compounds)
  • n → σ* transitions involve the excitation of a non-bonding electron to an antibonding σ* orbital (alcohols, amines)
  • n → π* transitions occur when a non-bonding electron is excited to an antibonding π* orbital (carbonyl compounds)
• The energy of the electronic transitions depends on the electronic structure of the molecule, including the types of atoms, bonding, and molecular geometry
  • Molecules with more conjugated π systems typically have lower-energy π → π* transitions (carotenoids)
  • Molecules with heteroatoms (oxygen, nitrogen) often exhibit n → π* transitions at lower energies than π → π* transitions

Franck-Condon Principle for Vibronic Transitions

Vibronic Coupling

• The Franck-Condon principle states that electronic transitions occur much faster than the nuclei can respond, so the nuclear geometry remains essentially unchanged during the transition
• Vibronic transitions involve both electronic and vibrational excitations, where the vibrational levels of the initial and final electronic states are coupled
• The intensity of a vibronic transition depends on the overlap integral between the vibrational wavefunctions of the initial and final states, known as the Franck-Condon factor
  • The Franck-Condon factor is larger when the vibrational wavefunctions of the initial and final states have a significant overlap, leading to more intense vibronic transitions

Vertical Transitions and Vibrational Structure

• Vertical transitions, where the nuclear geometry remains unchanged, are typically the most intense vibronic transitions according to the Franck-Condon principle
  • Vertical transitions occur when the electron is excited to a higher electronic state without any change in the nuclear coordinates (absorption of a photon)
• The Franck-Condon principle can explain the vibrational structure observed in electronic spectra, including the presence of vibrational progressions and hot bands
  • Vibrational progressions appear as a series of peaks in the spectrum, corresponding to transitions to different vibrational levels of the excited electronic state (S0 → S1, v=0 → v=0, 1, 2, ...)
  • Hot bands arise from transitions originating from vibrationally excited levels of the ground electronic state (S0, v=1 → S1, v=0, 1, 2, ...)

Molecular Structure from Electronic Spectra

Energy and Vibrational Information

• Electronic spectra provide valuable information about the electronic structure and excited states of molecules
• The position of the absorption or emission bands in the spectrum corresponds to the energy of the electronic transitions, which can be used to determine the energies of the excited states relative to the ground state
  • The energy of the lowest-energy absorption band gives the energy of the first excited electronic state (S1) relative to the ground state (S0)
• The shape and width of the absorption or emission bands can provide information about the vibrational structure and the coupling between electronic and vibrational degrees of freedom
  • Broad, unstructured bands indicate strong coupling and significant geometry changes between the ground and excited states (charge-transfer transitions)
  • Sharp, well-resolved bands suggest weak coupling and similar geometries in the ground and excited states (rigid molecules, like benzene)

Structural and Symmetry Insights

• The presence of vibrational progressions in the spectrum indicates the excitation of specific vibrational modes in the excited state, which can be used to identify the types of vibrations involved
  • The spacing between the peaks in a vibrational progression corresponds to the frequency of the excited-state vibrational mode (C=C stretching, C-H bending)
• The relative intensities of the vibronic transitions in the spectrum can be analyzed using the Franck-Condon principle to gain insights into the geometry changes between the ground and excited states
  • A strong 0-0 transition (S0, v=0 → S1, v=0) suggests similar geometries in the ground and excited states
  • Intense transitions to higher vibrational levels of the excited state indicate significant geometry changes upon excitation
• The polarization of the absorption or emission bands can provide information about the symmetry of the electronic states and the orientation of the transition dipole moment
  • Polarized bands suggest that the transition dipole moment is aligned along a specific molecular axis (linear molecules, like diatomics)
  • Unpolarized bands indicate that the transition dipole moment is not aligned with any particular molecular axis (highly symmetric molecules, like tetrahedral or octahedral complexes)
• Comparing the electronic spectra of related molecules can reveal the effects of structural modifications on the electronic properties and excited state dynamics
  • Substitution of atoms or functional groups can shift the positions and intensities of the absorption or emission bands (adding electron-donating or electron-withdrawing groups to aromatic rings)
  • Changes in the molecular geometry can alter the vibrational structure and the Franck-Condon factors (cis-trans isomerization, conformational changes)