Electronic excitation occurs rapidly compared with nuclear motion. In the Condon approximation, vibronic intensities are proportional to squared overlaps of initial and final vibrational wavefunctions; vertical arrows on a potential diagram summarize this overlap rather than a nuclear trajectory.
The squared vibrational overlap entering a vibronic intensity when the electronic transition moment is treated as constant over nuclear coordinates.
For equal-frequency harmonic ground and excited molecular potentials displaced by , the low-temperature vibrational overlap has the Poisson weights in the title, with . Optical lines occur at , apart from broadening and slowly varying electronic or optical prefactors. The normalized weights sum to one and have mean vibrational excitation . Unequal frequencies, several vibrations, hot initial states and intermolecular coupling modify this simple Franck-Condon principle model.
The dimensionless displacement strength for the equal-frequency single-vibration model in displaced-oscillator Franck-Condon progression. It equals the mean number of excited vibrational quanta in its zero-temperature overlap distribution.
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The Franck-Condon principle is a fundamental concept in molecular spectroscopy that pertains to the behavior of molecules during electronic transitions. It provides insight into why certain electronic transitions are favored over others in terms of their ability to absorb or emit light. The principle is based on the idea that during an electronic transition, such as the absorption or emission of a photon, the nuclei of the molecules do not have time to move significantly due to the very short timescales involved in electronic transitions.