Kasha's rule

Kasha's rule states that appreciable luminescence normally originates from the lowest excited electronic state of a given spin multiplicity. In the familiar molecular notation, fluorescence is usually associated with $S_1$ and phosphorescence with $T_1$, even when absorption initially prepares a higher state. The rule is a spectroscopic regularity, rather than a guarantee that all excited molecules emit.

Michael Kasha presented the underlying classification of electronic transitions in 1950, discussing the connection between radiationless conversion and the lowest emitting level.^[ref] Molecular internal conversion provides a route from a higher electronic state to a lower state of the same multiplicity before appreciable higher-state emission occurs.

An original rate-competition model makes the condition quantitative. For an initially populated $S_2$ state, let $k_{21}$ be conversion to $S_1$, $k_{2r}$ upper-state radiative decay and $k_{2x}$ other loss. The fraction emitting directly from $S_2$ isWith stipulated $k_{21}=10^{12}{\mathrm{s}}^{-1}$, $k_{2r}=10^8{\mathrm{s}}^{-1}$ and no other loss, this fraction is about $10^{-4}$. Fast conversion suppresses upper-state emission even though the molecule absorbs into that state. If conversion is slowed until it competes with radiation, appreciable higher-state emission becomes possible. These values illustrate kinetics, not universal molecular constants.

The rule concerns the emitting electronic state. It does not by itself assert an excitation-wavelength-independent fluorescence quantum yield; that is the separate Kasha-Vavilov rule. Competing photochemistry, intersystem crossing and state preparation can affect the number of emitted photons even when the eventual fluorescence band comes from $S_1$.

A proposed experimental test compares emission spectra after excitation into different absorption bands, correcting for absorbed photon counts and detector response. Similar emission-band shapes support a common emitting state, while time-resolved measurements test whether a fast relaxation precedes emission. A different band requires checking sample purity, distinct species and instrumental artifacts before assigning emission from a higher electronic state.

The rate argument also explains why a rigid drawing of one downward arrow is insufficient evidence. Measure which states are populated, how fast they exchange population and which transitions radiate. This connects an empirical rule with a falsifiable kinetic model, while preserving the distinction between a common behaviour and an exception-free law.

The Kasha-Vavilov rule states that the quantum yield of luminescence is normally independent of excitation wavelength. IUPAC explicitly notes exceptions.^[ref] The statement concerns emitted photons per absorbed photon, not equal detector counts under equal incident optical power.

An original photon-accounting model writesfor monochromatic incident power $P$, wavelength $\lambda$ and absorbance $A$. Comparing raw fluorescence at different wavelengths without correcting incident photon number and absorbed fraction can therefore give a misleading yield comparison.

For equal incident powers and equal absorbed fractions at 400 and 500 nm, the absorbed photon rates have ratio $500/400=1.25$. A molecule obeying the rule with unchanged yield then emits 25% more photons per second under the 500 nm condition. Unequal raw emission is entirely consistent with equal emitted-per-absorbed-photon yield.

Absorbed-photon normalization in quantum-yield comparisons also needs detector-response correction. The observation system measures a selected fraction of an emission spectrum, not automatically all emitted photons. Keep excitation and emission spectral responses, sample geometry and optical density in the comparison.

The distinction from Kasha's rule is physical as well as verbal. Kasha's rule concerns the emitting electronic state. Suppose a wavelength-dependent fraction $f(\lambda )$ of absorbed excitations reaches the same emitting state, whose radiative and nonradiative rates are $k_r,k_{nr}$. ThenThe same emitting state and band shape can coexist with a wavelength-dependent yield if upstream branching changes. Fast molecular internal conversion can make the simple wavelength-independent approximation useful, but does not prove it for every system.

A proposed experiment compares corrected integrated emission with absorbed photon counts while checking concentration, chemical stability and competing absorption. A persistent excitation-dependent yield after those corrections is a scientific result to explain, rather than something to normalize away by assuming the rule in advance.

Absorbed-photon normalization in quantum-yield comparisons compares emitted events with the photons actually absorbed by the sample. The quantum yield uses absorbed photons as its denominator; equal incident optical power does not generally establish equal absorbed photon rates.^[ref]

For monochromatic incident power $P$, excitation wavelength $\lambda$ and absorbance $A$, the idealized absorbed photon flux isThis model assumes that the measured attenuation is attributed appropriately to absorption rather than unaccounted scattering or other optical losses. If background-corrected detected count rate is $D=\eta \Phi {\dot{N}}_{\mathrm{abs}}$, where $\eta$ includes the specified collection and detection efficiency, thenDifferent emission spectra or collection conditions can change $\eta$; treating it as equal requires justification.

An original example uses equal incident powers at 400 and 600 nm, with absorbed fractions $1/2$ and $3/4$. The absorbed photon rates have ratioIf count rates are 10,000 and 22,500 per second at equal detection efficiency, the inferred yield ratio is one. A raw brightness increase by 2.25 is entirely consistent with unchanged fluorescence quantum yield.

The weak-absorption approximation $1-10^{-A}\simeq (\log 10)A$ needs its stated range. At $A={\log }_{10}2$, the exact absorbed fraction is 0.5 while the approximation gives $\log 2\approx 0.693$. Using it here would overestimate absorbed photons by about 39 percent and underestimate the inferred yield.

NIST's primary fluorescence-calibration guide separately treats emission response, excitation-beam intensity and relative quantum-yield measurement, including refractive-index corrections in its comparison model.^[ref] Its framework motivates independently checking excitation and detection corrections. Inner filter effects, photobleaching and chemical changes can also defeat a naive comparison. Normalization corrects a specified measurement model; it should not force the Kasha-Vavilov rule to hold when corrected yields genuinely differ.