Kasha's Rule - Description and Explanation

Description and Explanation

The rule is relevant in understanding the emission spectrum of an excited molecule. Upon absorbing a photon, a molecule in its electronic ground state (denoted S₀, assuming a singlet state) may – depending on the photon wavelength – be excited to any of a set of higher electronic states (denoted S_n where n>0). However, according to Kasha's rule, photon emission (termed fluorescence in the case of an S state) is expected in appreciable yield only from the lowest excited state, S₁. Since only one state is expected to yield emission, an equivalent statement of the rule is that the emission wavelength is independent of the excitation wavelength.

The rule can be explained by the Franck–Condon factors for vibronic transitions. For a given pair of energy levels that differ in both vibrational and electronic quantum number, the Franck–Condon factor expresses the degree of overlap between their vibrational wavefunctions. The greater the overlap, the quicker the molecule can undergo transition from the higher to the lower level. Overlap between pairs is greatest when the two vibrational levels are close in energy; this tends to be the case when the vibrationless levels of the electronic states coupled by the transition (where the vibrational quantum number v is zero) are close. In most molecules, the vibrationless levels of the excited states all lie close together, so molecules in upper states quickly reach the lowest excited state, S₁, before they have time to fluoresce. This process is known as internal conversion (IC). However, the energy gap between S₁ and S₀ is greater, so here fluorescence occurs, since it is now kinetically competitive with IC.

Exceptions to Kasha's rule arise when there are large energy gaps between excited states. An example is azulene: the classical explanation is that the S₁ and S₂ states lie sufficiently far apart that fluorescence is observed mostly from S₂. However, recent research has put forward that this may not be the case, and that fluorescence is seen from S₂ because of crossing in the N-dimensional potential surface allowing very fast internal conversion from S₁ to S₀.