= Molecular internal conversion
\b[Molecular internal conversion] is a radiationless transition between electronic states of the same <spin multiplicity>. Electronic and vibrational energy are redistributed without emission of a photon in the transition itself. IUPAC describes the step as isoenergetic: a lower electronic state can be reached with increased vibrational excitation, followed by subsequent relaxation.<IUPAC Compendium of Chemical Terminology, fifth edition (Gold Book)>[internal conversion, I03102]{ref}
This is distinct from <intersystem crossing>, which connects states of different multiplicity, and from <vibrational relaxation> within an electronic state. It is also distinct from nuclear <internal conversion>. A molecular singlet-to-singlet transition such as $S_2\to S_1$ fits the molecular definition; the energy need not be immediately transferred as heat to a surrounding solvent.
An original population model separates internal conversion from later decay. Suppose an impulsive excitation places population $N_0$ in $S_2$, transfer to $S_1$ occurs at rate $k_{21}$, and $S_1$ loses population at total rate $k_1$:
$$
\dot N_2=-k_{21}N_2,\qquad \dot N_1=k_{21}N_2-k_1N_1.
$$
For $k_{21}\ne k_1$,
$$
N_2=N_0e^{-k_{21}t},\qquad
N_1=\frac{N_0k_{21}}{k_{21}-k_1}(e^{-k_1t}-e^{-k_{21}t}).
$$
The lower-state population first rises and later decays. If only part of $k_1$ is radiative, fluorescence intensity is proportional to that radiative rate times $N_1$, not simply to the loss rate of $S_2$.
\Image[/internal-conversion-populations.png]
{title=Original sequential-population model with a 1 ps upper-state transfer scale and a 10 ns lower-state lifetime; no measured molecular rates are implied}
For stipulated $k_{21}=10^{12}\,\mathrm{s^{-1}}$ and $k_1=10^8\,\mathrm{s^{-1}}$, the transfer time scale is 1 ps while the lower-state lifetime is 10 ns. A fast population transfer can therefore precede much slower emission. These are model constants, not measured values assigned to every molecule.
An informative experiment resolves the time dependence of upper- and lower-state signals after a pulse and tests whether the proposed transfer accounts for both. A decay trace alone can have several explanations; spectral assignment and competing channels matter. <Sequential excited-state population kinetics> is one model to test against those measurements.
<Michael Kasha>'s 1950 analysis linked radiationless transitions among like-multiplicity states to emission from the lowest excited level of a given multiplicity.<Characterization of electronic transitions in complex molecules by Michael Kasha>[printed pp. 14–15, abstract and Internal Conversion]{ref} The rate competition supplies a physical motivation for <Kasha's rule>, while leaving room for molecules whose competing pathways behave differently.
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