What is Kasha's Rule?

Kasha's rule states that photon emission (fluorescence or phosphorescence) only happens from the lowest-energy excited electronic state of a photoactive molecule. The exact quote from the seminal paper by Michael Kasha is:

“The emitting level of a given multiplicity is the lowest excited level of that multiplicity”

Multiplicity refers to the spin angular momentum of the energy level, where singlet states have a multiplicity of 1 and triplet states have a multiplicity of 3. Therefore, the Kasha rule states:

• Fluorescence will always occur from the vibrational ground state of the lowest singlet excited state S₁
• Phosphorescence will always occur from the vibrational ground state of the lowest triplet excited state T₁

Fluorescence and phosphorescence will always happen from the vibrational ground state of their respective multiplicities regardless of the initial level the molecule is excited to. As a result, the photoluminescence spectrum obtained from a material is entirely independent of the excitation wavelength.

The reason radiative emission only occurs from the vibrational ground state is because the rate constants for the non-radiative processes internal conversion and vibrational relaxation are so much faster than the radiative emission rate constant.

Internal conversion describes the movement between the different electronic excited states. The rate of internal conversion between two electronic levels is inversely proportional to the energy splitting between those levels (energy gap law).

Energy Gap Law

The energy gap law predicts that the probability of non-radiative decay (vibronic relaxation and internal conversion) increases exponentially as the energy gap decreases. The smaller the energy gap, the more efficient the non-adiabatic coupling becomes, facilitating faster and more probable non-radiative decay. The higher the electronic excited state the closer they are in energy to their surrounding electronic excited state. As a result, when a molecule is excited to a higher excited electronic state, E_{n > 1}, it will rapidly undergo internal conversion and vibrational relaxation to the vibrational ground state of the E₁ before undergoing photoluminescence. Only E₁ to E₀ radiative decay will be observed.

Related Photophysical Concepts

Stokes Shift

Kasha’s rule ensures that photon emission always happens from the lowest excited state (S₁), which typically has less energy than the initially absorbed state. The Stokes shift refers to the difference between the wavelength (or energy) of absorbed light and the wavelength of emitted light. When a molecule absorbs a high-energy photon, the emission occurs at a longer wavelength (lower energy) due to energy loss during relaxation.

The Stokes shift magnitude depends on how much energy the molecule loses during internal conversion and vibrational relaxation before emitting light. Kasha’s rule explains why emission comes from the lower-energy state, and the Stokes shift is a consequence of the energy lost between absorption and emission.

Vavilov's Rule

The exact definition of Vavilov's rule:

“The quantum yield of luminescence is independent of the wavelength of exciting radiation”

Vavilov's rule states photoluminescence quantum yield (PLQY) is independent of the excitation wavelength. This is related to Kasha's rule because molecules tend to relax into the lowest excited state non-radiatively. No matter the excitation wavelength (as long as it has enough energy to excite the molecule), photon emission will always only occur from the same electronic state. As a result, the efficiency of the radiative process (PLQY) remains constant, even though the initial excitation state may vary.

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