Electronic transition

A change between electronic energy eigenstates of a chemical atom or another system.

A radiationless transition changes a system's electronic state without absorption or emission of a photon in that transition. Energy is redistributed among coupled degrees of freedom; it does not disappear. In molecular photophysics, the electronic change can populate vibrational motion before subsequent energy transfer to the surroundings.^[ref]

Molecular internal conversion connects electronic states of the same spin multiplicity, while intersystem crossing connects states of different multiplicity. These must be distinguished from vibrational relaxation within an electronic state and from nuclear internal conversion. A radiationless step need not instantaneously deliver all the electronic energy as heat to a solvent.

A simple competing-rate experiment illustrates why a dark channel can be inferred from light measurements. Suppose an emitting excited population loses members by fluorescence at rate $k_r$ and by nonfluorescent channels at total rate $k_{nr}$. With no population returning,These are the stated one-population assumptions of the fluorescence quantum yield model. For chosen rates $k_r=10^7{\mathrm{s}}^{-1}$ and $k_{nr}=4\times 10^7{\mathrm{s}}^{-1}$, the lifetime is $20\mathrm{ns}$ and the yield is $0.20$. A shorter lifetime here does not mean a larger radiative rate.

With a measured lifetime and yield, the model gives $k_r={\Phi }_f/\tau$ and $k_{nr}=(1-{\Phi }_f)/\tau$. Measuring only an emission intensity is less specific because it also depends on absorbed excitation and detection efficiency. Additional intermediate states, energy transfer or population return require a more complete model; the inferred missing fluorescence does not uniquely identify one radiationless mechanism.

Time-resolved emission paired with transient absorption can therefore test a proposed pathway: the first observes photons from an emitting state, while the second can reveal population in a state that does not emit in the monitored band. A mechanism must account for both signals and their time dependence.

An initially stationary isolated chemical atom of rest mass $M$ absorbing a single photon must recoil. If the internal excitation changes its rest mass by $\Delta M=\Delta E/c^2$, conservation of energy and conservation of momentum give $M{c}^2+h\nu =\sqrt{(M{c}^2+\Delta E{)}^2+(h\nu {)}^2}$ and hence the exact formula in the title. The additional positive energy supplies recoil. An external body sharing the momentum, or an initially moving chemical atom, changes this laboratory resonance condition.

A two-index arrangement of vibronic transition wavenumbers. Differences along rows isolate lower-state spacings; differences down columns isolate upper-state spacings. Deviations from exact separability can expose measurement uncertainty, rotational structure or incorrect assignments.

A sequence of vibronic transitions sharing a lower vibrational level and reaching successive vibrational levels of another electronic state. frequency differences remove the common electronic origin and reveal vibrational spacings.

Electronic excitation occurs rapidly compared with nuclear motion. In the Condon approximation, vibronic intensities are proportional to squared overlaps of initial and final vibrational wavefunctions; vertical arrows on a potential diagram summarize this overlap rather than a nuclear trajectory.

The squared vibrational overlap $|⟨{\chi }_{v^{\prime }}|{\chi }_{v^{\prime \prime }}⟩{|}^2$ entering a vibronic intensity when the electronic transition moment is treated as constant over nuclear coordinates.

For equal-frequency harmonic ground and excited molecular potentials displaced by $\Delta Q$, the low-temperature vibrational overlap has the Poisson weights in the title, with $S=M{\omega }_v(\Delta Q{)}^2/(2\hslash )$. Optical lines occur at $E_{00}+\nu \hslash {\omega }_v$, apart from broadening and slowly varying electronic or optical prefactors. The normalized weights sum to one and have mean vibrational excitation $S$. Unequal frequencies, several vibrations, hot initial states and intermolecular coupling modify this simple Franck-Condon principle model.

The dimensionless displacement strength for the equal-frequency single-vibration model in displaced-oscillator Franck-Condon progression. It equals the mean number of excited vibrational quanta in its zero-temperature overlap distribution.