Vavilov’s rule

The probability of intramolecular energy transfer between two electronic states is inversely proportional to the energy gap, AE, between the two states. The value of the rate constant for radiationless transitions decreases with the size of the energy gap between the initial and final electronic states involved. This law readily provides us with a simple explanation of Kasha s rule and Vavilov s rule. 

The independence of luminescence quantum yields on excitation wavelength is known as Vavilov s rule. There are however many exceptions to this rule, in particular for molecules which contain heavy atoms such as Br and I, or metals (e.g. organometallic complexes). The heavy atom effect makes intersystem crossings more efficient and these can compete with internal conversions. 

The heavy atom effect affects also the non-radiative transitions, as shown above in Figure 4.76. Transitions between higher excited states of different nominal multiplicities are efficient, so that the luminescence quantum yields depend on the excitation wavelength. (Vavilov s rule breaks down in such cases.)... 

Vavilov s rule states that the quantum yield of luminescence is generally independent of the wavelength of excitation. The quantum yield of luminescence is equal to the... 

Vavilov s Rule The fluorescence quantum efficiency is independent of the excitation wavelength. This implies that there is efficient nonradiative interconversion. 

Applying logarithms to this equation shows that a plot of log ( p (n) versus n should give a straight line with a slope equal to log[fev/(fev + pc)] and consequently from this, the ratio of ky/kpc can be obtained. This, by itself, showed that, for these molecules, the quantum yield was changing with energy, which was in contradiction with the known wisdom. Kasha s-Vavilov s rule. 

The emission behavior is embodied in two rules Kasha s rule and Vavilov s law [91]. Kasha s rule states that if a molecule emits a photon, it will always originate from the lowest excited state of a given spin multiplicity. If the emission occurs from the lowest singlet excited state it is called fluorescence and when the lowest excited state is a triplet it is known as phosphorescence. In addition, Vavilov s law implies that the fluorescence quantum yield (F) is essentially independent on the excitation wavelength. 

Polymer photophysics is determined by a series of alternating odd (B ) and even (Ag) parity excited states that correspond to one-photon and two-photon allowed transitions, respectively [23]. Optical excitation into either of these states is followed by subpicosecond nonradiative relaxation to the lowest excited state [90]. This relaxation is due to either vibrational cooling within vibronic sidebands of the same electronic state, or phonon-assisted transitions between two different electronic states. In molecular spectroscopy [146], the latter process is termed internal conversion. Internal conversion is usually the fastest relaxation channel that provides efficient nonradiative transfer from a higher excited state into the lowest excited state of the same spin multiplicity. As a result, the vast majority of molecular systems follow Vavilov-Kasha s rule, stating that FT typically occurs from the lowest excited electronic state and its quantum yield is independent of the excitation wavelength [91]. 

Luminescent Tr-conjugated polymers, like many other complex molecular systems, are expected to follow Vavilov-Kasha s rule. The independence of exciton generation yield on the excitation wavelength... 

This statement came to be known as Kasha s rule and lead to extensions, variously known as Vavilov s law and the Kasha-Vavilov rule, that the emission spectrum and photochemical quantnm yield are independent of excitation wavelength. 

The generalizations about photochemical reactions emerged in the 1950s are perhaps too narrow. The key photochemical steps, as shown in Sect. 7.3, involve absorption of one photon (according to the Stark-Einstein law, 10 -10 s ), internal conversion, and/or intersystem crossing down to the lowest excited singlet or the lowest triplet (Kasha-Vavilov rule, or ki c up to 10 s ) and emission or... 

---