Excited state Decay times

The maximum fluorescence quantum yield is 1.0 (100 %) every photon absorbed results in a photon emitted. Compounds with quantum yields of 0.10 are still considered quite fluorescent. The fluorescence lifetime is an instance of exponential decay. Thus, it is similar to a first-order chemical reaction in which the first-order rate constant is the sum of all of the rates (a parallel kinetic model). Thus, the lifetime is related to the facility of the relaxation pathway. If the rate of spontaneous emission or any of the other rates are fast, the lifetime is short (for commonly used fluorescent compounds, typical excited state decay times for fluorescent compounds that emit photons with energies from the UV to near infrared are within the range of 0.5-20 ns). The fluorescence lifetime is an important parameter for practical applications of fluorescence such as fluorescence resonance energy transfer. There are several rules that deal with fluorescence. 

In a typical LIF measurement, wavelength or excited-state decay time are fixed to produce a fluorescent signal from the sample. Calibration is done by... 

The assumed energy gap law, in combination with the calculated density of vdW states, determines the calculated energy dependence of IVR transition rates. The calculations predict that for aniline(Ar)i IVR from the initially excited state is far slower than subsequent IVR transitions. Thus, the calculated final state rise times closely match the initially excited state decay times, in agreement with the experimental results. 

Working the other way, from decay curves to intensities, for a single lumophore decaying exponentially the integrated intensity across the decay (7ss) is related to the excited state decay time by ... 

In pulse-fluorometry the sample is excited with a pulse of light (Figure 25.2). The width of the pulse is made as short as possible, and is preferably much shorter than the excited state decay time T of the sample. The time-dependent intensity is measured following the excitation pulse, and the decay time r is calculated from the slope of a plot of log I(t) versus t, or from the time at which the intensity decreases to 1/e of the intensity at t = 0. 

Zr(IV), and Ce(IV) as the central metal ion. Copper(II) porphyrins are among the most studied of the paramagnetic metalloporphyrins. The Cu(II) complexes show a low-temperature luminescence that arises from the and states that exist in thermal equilibrium. These two states are derived from the lowest excited triplet state on the porphyrin ring, which is split because of the presence of a unpaired electron on the Cu(II) center. Transient absorption measurements show that the ambient temperature excited-state decay times are lowered when a ligand is associated with the axial coordination positions of the tetracoordinate Cu(Il) porphyrin complex. The excited state lifetimes of Cu(II) porphyrin complexes in solution can be either dependent or independent of the temperature and solvent. For the octaethylporphyrin complex Cu(OEP) the excited state lifetime increases as the temperature is lowered, and also as the solvent polarity is increased. By contrast, the excited state lifetime of the tetraphenylporphyrin Cu(TPP) is insensitive to both the temperature and the polarity of the solvent. This difference in their photophysical behavior is likely due to a difference in the energy gap between the charge transfer state and the T/ T states in the pair of complexes. 

If now we consider a large number of molecules N0, the fraction still in the excited state after time t would be N/N0 — e kt where N is the number unchanged at time t. This exponential law is familiar to chemists and biological scientists as the first-order rate law and by analogy fluorescence decay is a first-order process—plots of fluorescence intensity after an excitation event are exponential and each type of molecule has its own characteristic average lifetime. 

The concentration of the iron porphyrins was adjusted to be between 0.2 and 0.3 OD for 2 mm cell at 530 nm. All relaxation times were calculated from the first order kinetic curves of excited state decay or ground state reappearance. This procedure eliminates error in delay times between the excitation and different wavelength probe pulses ("chirp") since constant delay times are subtracted out of the kinetic curves. There may, however, be some error introduced in the shorter decay times because of the excitation pulse and the probe pulse may overlap at the earliest points of the kinetic curve calculations. 

The Photoactive Yellow Protein (PYP) is the blue-light photoreceptor that presumably mediates negative phototaxis of the purple bacterium Halorhodospira halophila [1]. Its chromophore is the deprotonated trans-p-coumaric acid covalently linked, via a thioester bond, to the unique cystein residue of the protein. Like for rhodopsins, the trans to cis isomerization of the chromophore was shown to be the first overall step of the PYP photocycle, but the reaction path that leads to the formation of the cis isomer is not clear yet (for review see [2]). From time-resolved spectroscopy measurements on native PYP in solution, it came out that the excited-state deactivation involves a series of fast events on the subpicosecond and picosecond timescales correlated to the chromophore reconfiguration [3-7]. On the other hand, chromophore H-bonding to the nearest amino acids was shown to play a key role in the trans excited state decay kinetics [3,8]. In an attempt to evaluate further the role of the mesoscopic environment in the photophysics of PYP, we made a comparative study of the native and denatured PYP. The excited-state relaxation path and kinetics were monitored by subpicosecond time-resolved absorption and gain spectroscopy. 

As for electron transfer in the normal region, based on the results of time dependent perturbation theory, electron transfer in the inverted or excited state decay region is also determined by the... 

Time-resolved spectroscopies of various kinds have proven useful in probing the life of an excited state. As an excited state decays, perhaps through a chain of species, time-resolved spectroscopy (e.g., luminescence, excitation, resonance Raman) can provide data for these various steps. Such studies have led, for example, to the view that the first MLCT excited state in [Ru(bipyridine)3]2+, is localized in one bipyridine ring rather than delocalized over all three rings. 

Fig. 11 Normalized time and frequency resolved emission spectrum of the CC P4. A 6 ps time averaging has been carried out to mimic the apparatus function of the single photon detector. Radiative and non-radiative decay has been accounted for by a common chromophore excited-state life time of 5 ns.

It describes single chromophore excited state decay where the statistical operator Rme defines intra chromophore vibrational equilibrium in the excited electronic state. The whole mefl has to be taken at time argument t — t and, then, to be multiplied to A (f,f k) in Eq. (68). 

Fig. 8.20 a Differential absorption spectra (visible and near-infrared) obtained upon femtosecond flash photolysis (420 nm) of 8 in toluene with several time delays between 0 and 3000 ps at room temperature see color code for details. Arrows illustrate the changes, b Time-absorption profile of the spectra shown above at 457 nm (black spectrum) and 495 nm (red spectrum), reflecting the singlet excited-state decay and triplet excited-state formation, respectively... 

The DMC method achieves the lowest-energy eigenfunction by employing the quantum mechanical evolution operator in imaginary time [25], For an initial function expanded in eigenstates, one finds that contributions of the excited states decay exponentially fast with respect to the ground state. 

Figure 3 Recombination of oppositely charged, statistically independent carriers (e, h) can lead to the creation of an emitting excited state through a Coulombically correlated charge pair (e—h). The charge pair formation time (diffusion motion time) and its capture time are indicated in the figure as im and tc, respectively. The excited states decay radiatively (hi/) with the rate constant k and non-radiatively with an overall rate constant kn. After Ref. 21a.

The nature of the excited state decay processes is studied by the technique of laser flash photolysis, a full description of which has been given elsewhere (25). Briefly, flash photolysis involves irradiating a sample with a short (nanosecond) intense pulse from a laser, then observing by rapid response spectrophotometry the spectral changes that occur on the time scale nanoseconds to milliseconds. 

---