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 after American spectroscopist Michael Kasha, who proposed it in 1950. [1] [2]
The rule is relevant in understanding the emission spectrum 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. [3]
The rule can be explained by the Franck–Condon factors for vibronic transitions. For a given pair of energy levels that differ in both vibrational and electronic quantum numbers, the Franck–Condon factor expresses the degree of overlap between their vibrational wavefunctions. The greater the overlap, the more quickly the molecule can undergo a 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. However, the energy gap between S1 and S0 is greater, so here fluorescence occurs, since it is now kinetically competitive with internal conversion (IC). [4] [5]
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. [4] [5] In 2023, an explanation was proposed which pointed out that the S1 excited state has antiaromatic character while the S2 excited state is aromatic. [6]
A corollary of Kasha's rule is the Vavilov rule, which states that the quantum yield of luminescence is generally independent of the excitation wavelength. [4] [7] 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. [4]
Diatomic molecules are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen or oxygen, then it is said to be homonuclear. Otherwise, if a diatomic molecule consists of two different atoms, such as carbon monoxide or nitric oxide, the molecule is said to be heteronuclear. The bond in a homonuclear diatomic molecule is non-polar.
Fluorescence is the emission of light by a substance that has absorbed light or other electromagnetic radiation. It is a form of luminescence. In most cases, the emitted light has a longer wavelength, and therefore a lower photon energy, than the absorbed radiation. A perceptible example of fluorescence occurs when the absorbed radiation is in the ultraviolet region of the electromagnetic spectrum, while the emitted light is in the visible region; this gives the fluorescent substance a distinct color that can only be seen when the substance has been exposed to UV light. Fluorescent materials cease to glow nearly immediately when the radiation source stops, unlike phosphorescent materials, which continue to emit light for some time after.
A quantum mechanical system or particle that is bound—that is, confined spatially—can only take on certain discrete values of energy, called energy levels. This contrasts with classical particles, which can have any amount of energy. The term is commonly used for the energy levels of the electrons in atoms, ions, or molecules, which are bound by the electric field of the nucleus, but can also refer to energy levels of nuclei or vibrational or rotational energy levels in molecules. The energy spectrum of a system with such discrete energy levels is said to be quantized.
Photoluminescence is light emission from any form of matter after the absorption of photons. It is one of many forms of luminescence and is initiated by photoexcitation, hence the prefix photo-. Following excitation, various relaxation processes typically occur in which other photons are re-radiated. Time periods between absorption and emission may vary: ranging from short femtosecond-regime for emission involving free-carrier plasma in inorganic semiconductors up to milliseconds for phosphoresence processes in molecular systems; and under special circumstances delay of emission may even span to minutes or hours.
Chemiluminescence is the emission of light (luminescence) as the result of a chemical reaction. There may also be limited emission of heat. Given reactants A and B, with an excited intermediate ◊,
The emission spectrum of a chemical element or chemical compound is the spectrum of frequencies of electromagnetic radiation emitted due to electrons making a transition from a high energy state to a lower energy state. The photon energy of the emitted photons is equal to the energy difference between the two states. There are many possible electron transitions for each atom, and each transition has a specific energy difference. This collection of different transitions, leading to different radiated wavelengths, make up an emission spectrum. Each element's emission spectrum is unique. Therefore, spectroscopy can be used to identify elements in matter of unknown composition. Similarly, the emission spectra of molecules can be used in chemical analysis of substances.
Photochemistry is the branch of chemistry concerned with the chemical effects of light. Generally, this term is used to describe a chemical reaction caused by absorption of ultraviolet, visible light (400–750 nm) or infrared radiation (750–2500 nm).
Fluorescence spectroscopy is a type of electromagnetic spectroscopy that analyzes fluorescence from a sample. It involves using a beam of light, usually ultraviolet light, that excites the electrons in molecules of certain compounds and causes them to emit light; typically, but not necessarily, visible light. A complementary technique is absorption spectroscopy. In the special case of single molecule fluorescence spectroscopy, intensity fluctuations from the emitted light are measured from either single fluorophores, or pairs of fluorophores.
Intersystem crossing (ISC) is an isoenergetic radiationless process involving a transition between the two electronic states with different spin multiplicity.
In physics and physical chemistry, time-resolved spectroscopy is the study of dynamic processes in materials or chemical compounds by means of spectroscopic techniques. Most often, processes are studied after the illumination of a material occurs, but in principle, the technique can be applied to any process that leads to a change in properties of a material. With the help of pulsed lasers, it is possible to study processes that occur on time scales as short as 10−16 seconds. All time-resolved spectra are suitable to be analyzed using the two-dimensional correlation method for a correlation map between the peaks.
Stokes 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 Gabriel Stokes. Sometimes Stokes shifts are given in wavelength units, but this is less meaningful than energy, wavenumber or frequency units because it depends on the absorption wavelength. For instance, a 50 nm Stokes shift from absorption at 300 nm is larger in terms of energy than a 50 nm Stokes shift from absorption at 600 nm.
The Franck–Condon principle is a rule in spectroscopy and quantum chemistry that explains the intensity of vibronic transitions. The principle states that during an electronic transition, a change from one vibrational energy level to another will be more likely to happen if the two vibrational wave functions overlap more significantly.
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. It differs from intersystem crossing in that, while both are radiationless methods of de-excitation, the molecular spin state for internal conversion remains the same, whereas it changes for intersystem crossing. The energy of the electronically excited state is given off to vibrational modes of the molecule. The excitation energy is transformed into heat.
In particle physics, the quantum yield of a radiation-induced process is the number of times a specific event occurs per photon absorbed by the system.
In molecular spectroscopy, a Jablonski diagram is a diagram that illustrates the electronic states and often the vibrational levels of a molecule, and also the transitions between them. The states are arranged vertically by energy and grouped horizontally by spin multiplicity. Nonradiative transitions are indicated by squiggly arrows and radiative transitions by straight arrows. The vibrational ground states of each electronic state are indicated with thick lines, the higher vibrational states with thinner lines. The diagram is named after the Polish physicist Aleksander Jabłoński who first proposed it in 1933.
The zero-phonon line and the phonon sideband jointly constitute the line shape of individual light absorbing and emitting molecules (chromophores) embedded into a transparent solid matrix. When the host matrix contains many chromophores, each will contribute a zero-phonon line and a phonon sideband to the absorption and emission spectra. The spectra originating from a collection of identical chromophores in a matrix is said to be inhomogeneously broadened because each chromophore is surrounded by a somewhat different matrix environment which modifies the energy required for an electronic transition. In an inhomogeneous distribution of chromophores, individual zero-phonon line and phonon sideband positions are therefore shifted and overlapping.
In atomic physics, two-photon absorption, also called two-photon excitation or non-linear absorption, is the simultaneous absorption of two photons of identical or different frequencies in order to excite a molecule from one state to a higher energy, most commonly an excited electronic state. Absorption of two photons with different frequencies is called non-degenerate two-photon absorption. Since TPA depends on the simultaneous absorption of two photons, the probability of TPA is proportional to the square of the light intensity; thus it is a nonlinear optical process. The energy difference between the involved lower and upper states of the molecule is equal or smaller than the sum of the photon energies of the two photons absorbed. Two-photon absorption is a third-order process, with absorption cross section typically several orders of magnitude smaller than one-photon absorption cross section.
Photoelectrochemical processes are processes in photoelectrochemistry; they usually involve transforming light into other forms of energy. These processes apply to photochemistry, optically pumped lasers, sensitized solar cells, luminescence, and photochromism.
Vibronic spectroscopy is a branch of molecular spectroscopy concerned with vibronic transitions: the simultaneous changes in electronic and vibrational energy levels of a molecule due to the absorption or emission of a photon of the appropriate energy. In the gas phase, vibronic transitions are accompanied by changes in rotational energy also.
In atomic physics, non-degenerate two-photon absorption or two-color two-photon excitation is a type of two-photon absorption (TPA) where two photons with different energies are (almost) simultaneously absorbed by a molecule, promoting a molecular electronic transition from a lower energy state to a higher energy state. The sum of the energies of the two photons is equal to, or larger than, the total energy of the transition.
