The Franck-Condon principle explains how electronic transitions happen in molecules. It's all about the speed of these transitions and how they affect a molecule's structure. This principle helps us understand why absorption and emission spectra look the way they do.

Advanced concepts build on this foundation, exploring vertical transitions and factors that influence vibronic transition intensity. These ideas are crucial for interpreting spectroscopic data and understanding molecular behavior during electronic excitation.

Fundamentals of the Franck-Condon Principle

Franck-Condon principle in electronic transitions

• Franck-Condon principle states electronic transitions occur without changes in nuclear positions grounded in Born-Oppenheimer approximation
• Electronic transitions happen much faster than nuclear motion typically ~$10^{-15}$ seconds
• Vertical transitions represented as vertical lines on potential energy diagrams
• Franck-Condon factor measures overlap between vibrational wavefunctions determines transition probability
• Principle explains intensity patterns in absorption and emission spectra (UV-Vis spectroscopy)

Vibrational structure of spectra

• Vibronic transitions involve simultaneous changes in electronic and vibrational states
• Intensity distribution in spectra reflects overlap of vibrational wavefunctions governed by Franck-Condon factor
• Absorption spectra show transitions from ground vibrational state to excited vibrational states intensity pattern relates to equilibrium geometry changes
• Emission spectra display transitions from lowest excited vibrational state to ground vibrational states often mirror image of absorption spectrum (exceptions exist)
• Vibrational progression appears as series of peaks corresponding to transitions to different vibrational levels
• Huang-Rhys factor quantifies displacement between potential energy curves relates to number of visible vibronic transitions

Advanced Concepts and Applications

Vertical transitions and Franck-Condon principle

• Vertical transitions occur without changes in nuclear coordinates illustrated as straight vertical lines between electronic states on potential energy diagrams
• Concept exemplifies instantaneous nature of electronic transitions in Franck-Condon principle
• Results in population of higher vibrational levels in excited state and non-equilibrium nuclear configuration immediately after transition
• Relaxation processes follow vertical transitions including vibrational relaxation to lowest vibrational level of excited state
• Stokes shift emerges as energy difference between absorption and emission maxima due to vertical transitions and subsequent relaxation

Factors in vibronic transition intensity

• Franck-Condon factor quantifies overlap of vibrational wavefunctions directly proportional to transition intensity
• Equilibrium geometry changes influence vibrational progression breadth and shape of potential energy curves
• Symmetry considerations determine allowed and forbidden transitions based on molecular symmetry (benzene)
• Temperature effects impact initial state population distribution leading to hot bands in absorption spectra at higher temps
• Solvent interactions modify potential energy surfaces affect vibronic coupling and transition intensities (solvatochromism)
• Vibronic coupling describes interaction between electronic and vibrational motions can cause intensity borrowing between electronic states
• Duschinsky effect involves mixing of normal modes between electronic states complicates interpretation of vibronic spectra