Kasha's rule
Encyclopedia
Kasha's rule is a principle in the photochemistry
of electronically excited
molecules. The rule states that photon emission (fluorescence
or phosphorescence
) occurs in appreciable yield only from the lowest excited state of a given multiplicity
. It is named for American spectroscopist Michael Kasha
, who proposed it in 1950.
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 Sn 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 transition
s. 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 wavefunction
s. 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.
rule, which states that the quantum yield
of luminescence is generally independent of the excitation wavelength. This can be understood as a consequence of the tendency – implied by Kasha's rule – for molecules in upper states to relax to the lowest excited state non-radiatively. Again there are exceptions: for example benzene
vapour.
Photochemistry
Photochemistry, a sub-discipline of chemistry, is the study of chemical reactions that proceed with the absorption of light by atoms or molecules.. Everyday examples include photosynthesis, the degradation of plastics and the formation of vitamin D with sunlight.-Principles:Light is a type of...
of electronically excited
Excited state
Excitation is an elevation in energy level above an arbitrary baseline energy state. In physics there is a specific technical definition for energy level which is often associated with an atom being excited to an excited state....
molecules. The rule states that photon emission (fluorescence
Fluorescence
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation of a different wavelength. It is a form of luminescence. In most cases, emitted light has a longer wavelength, and therefore lower energy, than the absorbed radiation...
or phosphorescence
Phosphorescence
Phosphorescence is a specific type of photoluminescence related to fluorescence. Unlike fluorescence, a phosphorescent material does not immediately re-emit the radiation it absorbs. The slower time scales of the re-emission are associated with "forbidden" energy state transitions in quantum...
) occurs in appreciable yield only from the lowest excited state of a given multiplicity
Multiplicity (chemistry)
Multiplicity in quantum chemistry is used to distinguish between several degenerate wavefunctions that differ only in the orientation of their angular spin momenta. It is defined as 2S+1, where S is the angular spin momentum....
. It is named for American spectroscopist Michael Kasha
Michael Kasha
Michael Kasha is an American physical chemist and molecular spectroscopist who is one of the original founders of the Institute of Molecular Biophysics at Florida State University . Born in Elizabeth, NJ to a family of Ukrainian immigrants, he earned his Ph.D...
, who proposed it in 1950.
Description and explanation
The rule is relevant in understanding the emission spectrumEmission spectrum
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted by the element's atoms or the compound's molecules when they are returned to a lower energy state....
of an excited molecule. Upon absorbing a photon, a molecule in its electronic ground state
Ground state
The ground state of a quantum mechanical system is its lowest-energy state; the energy of the ground state is known as the zero-point energy of the system. An excited state is any state with energy greater than the ground state...
(denoted S0, assuming a singlet state) may – depending on the photon wavelength
Wavelength
In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...
– be excited to any of a set of higher electronic states (denoted Sn where n>0). However, according to Kasha's rule, photon emission
Luminescence
Luminescence is emission of light by a substance not resulting from heat; it is thus a form of cold body radiation. It can be caused by chemical reactions, electrical energy, subatomic motions, or stress on a crystal. This distinguishes luminescence from incandescence, which is light emitted by a...
(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 transition
Vibronic transition
A vibronic transition denotes the simultaneous change of vibrational and electronic quantum number in a molecule. According to the separability of electronic and nuclear motion in the Born-Oppenheimer approximation, the vibrational transition and electronic transition may be described separately...
s. For a given pair of energy levels that differ in both vibrational and electronic quantum number
Quantum number
Quantum numbers describe values of conserved quantities in the dynamics of the quantum system. Perhaps the most peculiar aspect of quantum mechanics is the quantization of observable quantities. This is distinguished from classical mechanics where the values can range continuously...
, the Franck–Condon factor expresses the degree of overlap between their vibrational wavefunction
Wavefunction
Not to be confused with the related concept of the Wave equationA wave function or wavefunction is a probability amplitude in quantum mechanics describing the quantum state of a particle and how it behaves. Typically, its values are complex numbers and, for a single particle, it is a function of...
s. 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
Internal conversion (chemistry)
Internal conversion is a transition from a higher to a lower electronic state in a molecule or atom. It is sometimes called "radiationless de-excitation", because no photons are emitted...
(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
Azulene
Azulene is an organic compound and an isomer of naphthalene. Whereas naphthalene is colourless, azulene is dark blue. Its name is derived from the Spanish word azul, meaning "blue"...
: 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.
Kasha–Vavilov rule
A corollary of Kasha's rule is the Kasha–VavilovSergey Ivanovich Vavilov
Sergey Ivanovich Vavilov -Biography:Vavilov founded the Soviet school of physical optics, known by his works in luminescence. In 1934 he co-discovered the Vavilov-Cherenkov effect, a discovery for which Pavel Cherenkov was awarded a Nobel Prize in Physics in 1958...
rule, which states that the quantum yield
Quantum yield
The quantum yield of a radiation-induced process is the number of times that a defined event occurs per photon absorbed by the system. The "event" may represent a chemical reaction, for example the decomposition of a reactant molecule:...
of luminescence is generally independent of the excitation wavelength. This can be understood as a consequence of the tendency – implied by Kasha's rule – for molecules in upper states to relax to the lowest excited state non-radiatively. Again there are exceptions: for example benzene
Benzene
Benzene is an organic chemical compound. It is composed of 6 carbon atoms in a ring, with 1 hydrogen atom attached to each carbon atom, with the molecular formula C6H6....
vapour.
See also
- Stokes shiftStokes shiftStokes shift is the difference between positions of the band maxima of the absorption and emission spectra of the same electronic transition. It is named after Irish physicist George G. Stokes. When a system absorbs a photon, it gains energy and enters an excited state...
, the difference between the absorption and emission frequencies, related to Kasha's rule.