Excited state kinetic scheme

Photophysical processes, that is, ones not involving any change in composition of an A, have become of much interest to the inorganic photochemist, particularly in terms of excited state kinetic schemes. A brief discussion of the phenomenology and theory of radiative and nonradiative deactivations follows. 

In this chapter, we have described the fundamental parameters that should be obtained when characterising an electronic, singlet or triplet, excited state and how to determine them experimentally including methodologies and required equipment. These characteristics include electronic energy, quantum yields, lifetimes and number and type of species in the excited state. Within this last context, i.e., when excited state reactions give rise to additional species in the excited state we have explored several excited state kinetic schemes, found to be present when excimers, exciplexes are formed and (intra and intermolecular) proton transfer occurs. This includes a complete formalism (with equations) for the steady-state and dynamic approaches for two and three-state systems, from where all the rate constants can be obtained. Additionally, we have explored additional recent developments in photophysics the competition between vibrational relaxation and photochemistry, and the non-discrete analysis (stretched-exponential) of fluorescence decays. 

Fig. 1. Excited state kinetic scheme for a single monomer (M) and excimer (E) species. Kr denotes the rate constant for direct formation of excimers, k is the trapping rate function for monomer excitation energy at excimer-forming sites. See text for details.

Scheme 1. Three-state kinetic scheme as minimal basis to explain the photophysics of donor-acceptor substituted stilbenes. E (primary excited n, n state, essentially planar geometry) and P ( Phantom Singlet state , twisted double bond) are the classical states discussed for stilbene, A (twisted single bonds, state(s) of TICT nature, up to 4 different possibilities in donor-acceptor substituted stilbenes like DNS) correspond to motions along different reaction coordinates than for P ...

A kinetic scheme and a potential energy curve picture ia the ground state and the first excited state have been developed to explain photochemical trans—cis isomerization (80). Further iavestigations have concluded that the activation energy of photoisomerization amounts to about 20 kj / mol (4.8 kcal/mol) or less, and the potential barrier of the reaction back to the most stable trans-isomer is about 50—60 kJ/mol (3). 

The above reaction scheme was established by a combination of uv-visible absorption and fluorescence, ir isotopic substitution, esr and kinetic measurements (37). The important point to note here is that in 02 rich Xe matrices, ground state Cu(2Sj/2) cannot avoid reactive encounters with 02 to form Cu(02)2 and Cu(02) dioxygen complexes,whereas it is proposed that the formation of CuO, Cu(03) and 03 in dilute 02/Xe matrices arises from the reaction of a long lived mobile excited state Cu(2D) with 02. On the other hand the reactions of photoexcited Ag(2P) with 02 are different (37), electron transfer being favoured to form Ag 02. ... 

The time evolution of the fluorescence intensity of the monomer M and the excimer E following a d-pulse excitation can be obtained from the differential equations expressing the evolution of the species. These equations are written according to the kinetic in Scheme 4.5 where kM and kE are reciprocals of the excited-state lifetimes of the monomer and the excimer, respectively, and ki and k i are the rate constants for the excimer formation and dissociation processes, respectively. Note that this scheme is equivalent to Scheme 4.3 where (MQ) = (MM) = E and in which the formation of products is ignored. 

A well-known example of an exciplex is the excited-state complex of anthracene and N,N-diethylaniline resulting from the transfer of an electron from an amine molecule to an excited anthracene molecule. In nonpolar solvents such as hexane, the quenching is accompanied by the appearance of a broad structureless emission band of the exciplex at higher wavelengths than anthracene (Figure 4.9). The kinetic scheme is somewhat similar to that of excimer formation. 

Under pH conditions where the back reaction is too slow to take place during the excited-state lifetime (k 3 [H30+] 1/ft), the kinetic scheme is simplified and leads to the following equations ... 

The formation of a TICT state is often invoked even if no dual fluorescence is observed. For donor-acceptor stilbenes (PCT-2 and PCT-3), the proposed kinetic scheme contains three states the planar state E reached upon excitation can lead to state P (non-fluorescent) by double-bond twist, and to TICT state A by singlebond twist, the latter being responsible for most of the emission. 

Kelley and co-workers [70, 71] measured the dynamics of the excited-state intramolecular proton transfer in 3-hydroxyflavone and a series of its derivatives as a function of solvent (Scheme 2.9). The energy changes associated with the processes examined are of the order of 3 kcal/mol or less. The model they employed in the analysis of the reaction dynamics was based upon a tunneling reaction path. Interestingly, they find little or no deuterium kinetic isotope effect, which would appear to be inconsistent with tunneling theories. For 3-hydroxy-flavone, they suggest the lack of an isotope effect is due to a very large... 

An indirect method has been used to determine relative rate constants for the excitation step in peroxyoxalate CL from the imidazole (IM-H)-catalyzed reaction of bis(2,4,6-trichlorophenyl) oxalate (TCPO) with hydrogen peroxide in the presence of various ACTs . In this case, the HEI is formed in slow reaction steps and its interaction with the ACT is not observed kinetically. However, application of the steady-state approximation to the reduced kinetic scheme for this transformation (Scheme 6) leads to a linear relationship of l/direct measure of the rate constant of the excitation step. 

The unexpected formation of the blue crystalline radical cation (97) from the reaction of triazinium salt (98) with tetracyanoethylene has been reported and the product identified by its EPR spectrum and by X-ray crystallography (Scheme 42).199 Carboxylic acids react with the photochemically produced excited state of N-t-a-phenynitrone (PBN) to furnish acyloxy spin adducts RCOOPBN. The reaction was assumed to proceed via ET oxidation of PBN to give the PBN radical cation followed by reaction with RCO2H.200 The mechanism of the protodiazoniation of 4-nitrobenzenediazonium fluoroborate to nitrobenzene in DMF has been studied.201 Trapping experiments were consistent with kinetic isotope effects calculated for the DMF radical cation. The effect of the coupling of radicals with different sulfur radical cations in diazadithiafulvalenes has been investigated.202... 

This behavior can be rationalized in terms of the kinetic scheme I proposed by Grabowski et al.7,21 It involves the equilibrium of two excited states A and B and three temperature-independent... 

According to the kinetic scheme I, the excited B and A states can reach an equilibrium, at least above the characteristic temperature Tm introduced in Fig. 2.8. Since only the B state is excited directly, the equilibration involves, first, the depopulation of B toward A, and then the repopulation of B from A to reach equilibrium. 

Thus, it is very reasonable that the other factors involved in the excited state decay of [Ru(trpy)2]2+ include dissociation of at least one pyridyl ligator. Kirchhoff et al.258) have used an argument based on a kinetic scheme involving photolysis to rationalize inefficient luminescence in [Ru(trpy)2]2+ and related compounds however, they do not observe extensive photolysis in this system. 

Irradiation of 2,2-dimethyl chromene through Pyrex using a 550-W Hanovia lamp initiates a retro 4 + 2 reaction to form the extended quinone methide 4, which reacts with methanol to form a pair of methyl ethers (Scheme 6A).18 Flash photolysis of coniferyl alcohol 5 generates the quinone methide 6 (Scheme 6B) by elimination of hydroxide ion from the excited-state reaction intermediate.19 The kinetics for the thermal reactions of 6 in water were characterized,20 but not the reaction products. These were assumed to be the starting alcohol 5 from 1,8-addition of water to 6 and the benzylic alcohol from 1,6-addition of water (Scheme 6). A second quinone methide has been proposed to form as a central intermediate in the biosynthesis of several neolignans,21a and chemical synthesis of neolignans has been achieved... 

Fig. 13. Kinetic scheme for an excited state electron transfer reaction. For details, see text...

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