Relaxation rates, excited states

Fast non-radiative relaxation of excited states leads to broadening of the spectral lines. The amount of broadening gives information about the nature and rate of the relaxation. We will discuss both qualitative and quantitative effects below. 

Back to the basic photophysics of organic chro-mophore, it has been stated earlier that an electronic transition is very fast, much faster than the vibrational motion. Why then is the vibrational relaxation occurring first Actually, it is not the transition itself that takes longer than the vibrational deactivation of the excited electronic state, but the probability of occurrence of this emissive transition that is much lower than the rate of the vibrational relaxation. The excited state is not so unstable that the electron has to immediately return to its original location. It can wait sometimes in the excited states. In fact, the notion of rates of deactivation is a statistical... 

The first type of interaction, associated with the overlap of wavefunctions localized at different centers in the initial and final states, determines the electron-transfer rate constant. The other two are crucial for vibronic relaxation of excited electronic states. The rate constant in the first order of the perturbation theory in the unaccounted interaction is described by the statistically averaged Fermi golden-rule formula... 

Table I reports the observed NMR linewidths for the H/3 protons of the coordinating cysteines in a series of iron-sulfur proteins with increasing nuclearity of the cluster, and in different oxidation states. We have attempted to rationalize the linewidths on the basis of the equations describing the Solomon and Curie contributions to the nuclear transverse relaxation rate [Eqs. (1) and (2)]. When dealing with polymetallic systems, the S value of the ground state has been used in the equations. When the ground state had S = 0, reference was made to the S of the first excited state and the results were scaled for the partial population of the state. In addition, in polymetallic systems it is also important to account for the fact that the orbitals of each iron atom contribute differently to the populated levels. For each level, the enhancement of nuclear relaxation induced by each iron is proportional to the square of the contribution of its orbitals (54). In practice, one has to calculate the following coefficient for each iron atom ...

The Orbach process is a two-phonon process that takes place via population of an excited electronic state with energy Eq. The temperature dependence of the relaxation rate is given by... 

Chemiluminescence is light emission from the relaxation of electrons populating excited states in an elementary step of a chemical reaction. Since, the process of population of excited states is related kinetically to the kinetics of the given chemical reaction, the emission of chemiluminescence over time should thus be related to the rate of the chemical reaction. 

The photolysis of Cr(CO)6 also provides evidence for the formation of both CO (69) and Cr(CO) species (91,92) in vibrationally excited states. Since CO lasers operate on vibrational transitions of CO, they are particularly sensitive method for detecting vibrationally excited CO. It is still not clear in detail how these vibrationally excited molecules are formed during uv photolysis. For Cr(CO)6 (69,92), more CO appeared to be formed in the ground state than in the first vibrational excited state, and excited CO continued to be formed after the end of the uv laser pulse. Similarly, Fe(CO) and Cr(CO) fragments were initially generated with IR absorptions that were shifted to long wavelength (75,91). This shift was apparently due to rotationally-vibrationally excited molecules which relaxed at a rate dependent on the pressure of added buffer gas. 

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