Lifetime of an excited state

Chemical reactions can be studied at the single-molecule level by measuring the fluorescence lifetime of an excited state that can undergo reaction in competition with fluorescence. Reactions involving electron transfer (section C3.2) are among the most accessible via such teclmiques, and are particularly attractive candidates for study as a means of testing relationships between charge-transfer optical spectra and electron-transfer rates. If the physical parameters that detennine the reaction probability, such as overlap between the donor and acceptor orbitals. 

The lifetime of an excited state of a molecular entity (in the absence of any radiationless transition). Radiative... 

An excited state has a finite lifetime and so it has static properties, such as molecular shape (median bond lengths and angles) and dipole moment, like those of a ground-state molecule, that can in principle be determined experimentally. However, the lifetime of an excited state is short, often very short, and this restricts the range of techniques that can be employed to study such properties. Most of the available information comes from high-resolution absorption 01 emission spectra, particularly of small or symmetrical model compounds. The geometry of most other excited organic molecules has to be inferred from such results. 

If the time period for creation of excited states and relaxation of electronic shells is much less than the lifetime of an excited state and if interference effects between various processes binding the same initial and final states may be neglected, then the creation and decay of excited states may be treated separately as a two-step process. Such an approach is widely used in X-ray and electron spectroscopy. 

With regard to lifetimes, it is often the case that the experimentally measured lifetime represents the decay of a specific excited state and can thus be equated to the mechanistic lifetime of that state. However, this need not be so. For example, the decay of E-type fluorescence follows the lifetime of the phosphorescing state (14). In principle, the radiative lifetime of an excited state can be determined indirectly from the integrated extinction coefficient of the absorption transition that connects the same two states as the emission. In practice, however, several difficulties are encountered in such a determination (6,8,14). 

Natural lifetime, t The radiative lifetime of an excited state the time period during which the concentration of the reactant in a first-order process decreases to Me of its original value. Nebulization The transformation of a liquid into a spray of small droplets. 

The natural width of a spectral line is due to the finite lifetime of an excited state (t). The corresponding halfwidth in terms of the frequency is given by ... 

The chemical exchange rate(s) between two or more vanadium species can lie in about the same time window as the relaxation rates (lifetime of an excited state in an NMR... 

D23.6 The shortening of the lifetime of an excited state is called quenching. Quenching effects may be studied by monitoring the emission from the excited state that is involved in the photochemical process. The addition of a quencher opens up an additional channel for the deactivation of the excited singlet state. 

The natural lifetime of an excited state is inversely proportional to the strength of absorption to that state, usually expressed as the molar extinction coefficient , which is defined as e = 1/cl log (lo/I), where c is the concentration in moles per liter, I is the length of the absorption path in cm., and (/o//) is the fraction of the incident light which is transmitted. In the near ultraviolet, the following approximation can be used for estimating the lifetime of excited states. 

There is a relationship between the lifetime of an excited state and the bandwidth of the absorption band associated with the transition to the excited state. This relationship is a consequence of the Heisenberg uncertainty principle, which states that at the microscopic level the... 

In this formulation, the lifetime of the excited singlet state in the absence of Q is denoted x, while that in the presence of Q is indicated as r. Often, r° is used to represent the lifetime of an excited state in the absence of quencher and x to represent the lifetime of an excited state in the presence of quencher. In that case, the Stern-Volmer relationship becomes... 

The lifetime of an excited state of a molecule is one of its fundamental characteristics the others being its energy, quanmm yields of decay processes and their respective rate constants. After generation of an excited population of molecules of concentration cq in the lowest vibronic state of Sj, the concentration c(f) at the time t after excitation decreases exponentially with time, according to the law c t) = where tq is the reciprocal of the sum of the rate constants of all the... 

The lifetime of an excited state can be calculated by measuring its concentration as a function of time. Most lifetime-measuring techniques are indeed based on the reeording of the excited state concentration as a function of time, and are eoUeetively referred to as time-domain measurements. The techniques described... 

In any case, taking into account both time-domain and frequency-domain techniques, there are basically four methods to measure the lifetime of an excited state, as described in detail in the next Sect. 7.2. The first three methods use the time-domain approach to rebuild the intensity-time curve the fourth one uses the frequency-domain approach and is based on the phase shift between excitation and emission. 

S = Kronecker delta h = Planck s constant divided by 2ir /3r = Branching ratio for radiative relaxation to a particular final state tr = Radiative lifetime of an excited state tt = Total lifetime (radiative and non-radiative) of an excited state Wt = Non-radiative relaxation rate of an excited state Pe = Density of states... 

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