Movatterモバイル変換

[0]ホーム

Jump to content

Kasha's rule

Edit links

From Wikipedia, the free encyclopedia

Law of photochemistry

Scheme of Kasha's rule. A photon with energy $h\nu _{1}$ excites an electron of fundamental level, of energy $E_{0}$ , up to an excited energy level (e.g. $E_{1}$ or $E_{2}$ ) or on one of the vibrational sub-levels. Vibrational relaxation then takes place between excited levels, which leads to dissipation of part of the energy ( $\Delta E_{d}$ ), taking the form of a transition (internal conversion) towards the lowest excited level. Energy is then dissipated by emission of a photon of energy $h\nu _{2}$ , which allows the system to go back to its fundamental state.

{\displaystyle h\nu _{1}} — Scheme of Kasha's rule. A photon with energy $h\nu _{1}$ excites an electron of fundamental level, of energy $E_{0}$ , up to an excited energy level (e.g. $E_{1}$ or $E_{2}$ ) or on one of the vibrational sub-levels. Vibrational relaxation then takes place between excited levels, which leads to dissipation of part of the energy ( $\Delta E_{d}$ ), taking the form of a transition (internal conversion) towards the lowest excited level. Energy is then dissipated by emission of a photon of energy $h\nu _{2}$ , which allows the system to go back to its fundamental state.

Kasha's rule is a principle in thephotochemistry ofelectronically excited molecules. The rule states that photon emission (fluorescence orphosphorescence) occurs in appreciable yield only from the lowest excited state of a givenmultiplicity. It is named after American spectroscopistMichael Kasha, who proposed it in 1950.^[1]^[2]

Description and explanation

[edit]

The rule is relevant in understanding theemission spectrum of an excited molecule. Upon absorbing a photon, a molecule in its electronicground state (denotedS₀, assuming asinglet state) may – depending on the photonwavelength – be excited to any of a set of higher electronic states (denotedS_n wheren>0). However, according to Kasha's rule,photon emission (termed fluorescence in the case of anS 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 theFranck–Condon factors forvibronic transitions. For a given pair of energy levels that differ in both vibrational and electronicquantum numbers, the Franck–Condon factor expresses the degree of overlap between their vibrationalwavefunctions. 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 thevibrationless levels of the electronic states coupled by the transition (where the vibrational quantum numberv 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 betweenS₁ andS₀ is greater, so here fluorescence occurs, since it is now kinetically competitive withinternal conversion (IC).^[4]^[5]

Exceptions to Kasha's rule arise when there are large energy gaps between excited states. An example isazulene: the classical explanation is that theS₁ andS₂ states lie sufficiently far apart that fluorescence is observed mostly fromS₂.^[4]^[5] In 2023, an explanation was proposed which pointed out that theS₁ excited state hasantiaromatic character while theS₂ excited state isaromatic.^[6]

Vavilov rule

[edit]

A corollary of Kasha's rule is theVavilov rule, which states that thequantum 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 examplebenzene vapour.^[4]