Radiative mechanism, description

Photosynthesis provides another source of stimulation for investigations in photophysics. The photochemistry of manganese prophyrins have been investigated because of their relevance to photosystem II.Related to this are the studies on the quenching of fluorescence of tetraphenylporphine. Freed has given a quantum mechanical description of the radiative and non-radiative characteristics of the lowest singlet states in chlorophyll hydrated dimers. 

The more general use of Eq, (5-128) is to obtain the set of total interchange areas AS"- which con stitute a complete description of the effect of shape,. size, and emi.s.sivity on radiative flux, independent of the pre.sence or absence of other tran.sfer mechanisms. It may be shown that... 

A relaxation process will occur when a compound state of the system with large amplitude of a sparse subsystem component evolves so that the continuum component grows with time. We then say that the dynamic component of this state s wave function decays with time. Familiar examples of such relaxation processes are the a decay of nuclei, the radiative decay of atoms, atomic and molecular autoionization processes, and molecular predissociation. In all these cases a compound state of the physical system decays into a true continuum or into a quasicontinuum, the choice of the description of the dissipative subsystem depending solely on what boundary conditions are applied at large distances from the atom or molecule. The general theory of quantum mechanics leads to the conclusion that there is a set of features common to all compound states of a wide class of systems. For example, the shapes of many resonances are nearly the same, and the rates of decay of many different kinds of metastable states are of the same functional form. 

The broadening Fj is proportional to the probability of the excited state k) decaying into any of the other states, and it is related to the lifetime of the excited state as r. = l/Fj . For Fjt = 0, the lifetime is infinite and O Eq. 5.14 is recovered from O Eq. 5.20. Unfortunately, it is not possible to account for the finite lifetime of each individual excited state in approximate theories based on the response equations (O Eq. 5.4). We would be forced to use a sum-over-states expression, which is computationally intractable. Moreover, the lifetimes caimot be adequately determined within a semiclassical radiation theory as employed here and a fully quantized description of the electromagnetic field is required. In addition, aU decay mechanisms would have to be taken into account, for example, radiative decay, thermal excitations, and collision-induced transitions. Damped response theory for approximate electronic wave functions is therefore based on two simplifying assumptions (1) all broadening parameters are assumed to be identical, Fi = F2 = = r, and (2) the value of F is treated as an empirical parameter. With a single empirical broadening parameter, the response equations take the same form as in O Eq. 5.4 with the substitution to to+iTjl, and the damped linear response function can be calculated from first-order wave function parameters, which are now inherently complex. For absorption spectra, this leads to a Lorentzian line-shape function which is identical for all transitions. 

In the above reaction scheme Solv" ", C-RH+, S represent the solvent cation, cyclohexane cation and hexafluorobenzene (HFB) anion respectively. The spin-dynamics of S and c-RH+ determine the magnetic field effect, since the spin wave-function for the ion pair (S / c-RH+) evolves differently at the different magnetic field strengths. The intensity of recombination fluorescence of the solution is determined by the rate of radiative deactivation of S [reaction (7)], which is accumulated within the simulation program. Although this model is not a complete description of the radiolysis of n-hexane which contains a solution of HFB and cyclohexane, it does however, take into account the most important aspect of the proposed relaxation mechanism, namely cross recombination. A more detailed reaction scheme for the radiolysis of n-dodecane is considered later in this chapter (in Sect. 8.6), which takes into account the excited state chemistry as well as spin-exchange reactions. 

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