The Franck-Condon principle and the sudden approximation

Area of Science:

• Quantum mechanics
• Molecular spectroscopy
• Physical chemistry

Background:

• Franck-Condon factors (FCFs) traditionally assume instantaneous electronic transitions.
• Deviations from instantaneous transitions can influence spectral intensities.
• The concept of a finite transition time (t(0)) requires theoretical investigation.

Purpose of the Study:

• To investigate corrections to conventional Franck-Condon factors (FCFs).
• To evaluate the impact of a non-zero electronic transition time (t(0)) on molecular electronic spectra.
• To provide a theoretical framework for detecting and estimating non-zero transition times.

Main Methods:

• Application of a theory based on the sudden approximation.
• Derivation of an explicit expression for vibrational progressions using a harmonic oscillator model.
• Analysis of calculated corrections for various spectral cases.

Main Results:

• The study provides an explicit expression for vibrational progressions (k'<--0'').
• Calculations indicate that non-zero t(0) effects are typically very small in molecular electronic spectra.
• Significant corrections are predicted for certain long vibrational progressions, potentially detectable experimentally.

Conclusions:

• The assumption of a non-zero electronic transition time can lead to detectable corrections in FCFs.
• Experimental observation of these corrections would validate the concept of finite transition times.
• The findings offer a method for estimating the magnitude of t(0) in specific molecular systems.