Intersystem crossing perturbation

The third process sensitive to heavy-atom perturbation is the radiative decay from the triplet to the ground state (phosphorescence). Since phosphorescence is commonly not observed in fluid solution at room temperature, the rate of phosphorescence in the presence of heavy-atom perturbation relative to the rate of intersystem crossing and nonradiative decay need not be considered. At low temperatures in a rigid glass, however, phosphorescence... 

In addition, it can be shown that second-order vibronic perturbation will make possible some intersystem crossing to the 3B3u(n, tt ) state. However, this second-order perturbation should be much less important than the first-order spin-orbit perturbation.(19) This will produce the unequal population of the spin states shown in Figure 6.1. In the absence of sir the ratios of population densities n are given by the following equations ... 

It has been possible to employ the heavy-atom solvent effect in determining the rate constants for the various intercombinational nonradiative transitions in acenaphthylene and 5,6-dichIoroacenaphthylene.<436,c,rate constants, which are not accessible in light-atom solvents due to the complexity of the mechanism and the low efficiency of intersystem crossing from the first excited singlet to the first excited triplet, can be readily evaluated under the influence of heavy-atom perturbation. 

A heavy-atom effect on the photocycloaddition of acenaphthylene to acrylonitrile has also been observed.<68) The effect of heavy atoms in this case is seen as an apparent increase in the quantum yield of product formation in heavy-atom solvents as opposed to cyclohexane (the time to achieve about 42% reaction in cyclohexane is greater than that required to produce the same conversion in dibromoethane by a factor of ten). An increase in the rate of acenaphthylene intersystem crossing due to heavy-atom perturbation was proposed to explain this increase in reaction rate. 

Finally, in many of the perturbation calculations of the effect of substituents and other structural changes, an important tacit assumption is made and it is far from obvious that it is always fulfilled. As already discussed, the physical argument on which the calculation is based is that the value of the initial slope, or the height of a small barrier along the way, determine the rate at which the photochemical reaction occurs. However, the experimental value with which comparison is made usually is not the reaction rate but the quantum yield, which of course also depends on rates of other competing processes and these may be affected by substitution as well. For instance, the rate at which fluorescence occurs is related to the absorption intensity of the first transition, the rate of intersystem crossing may be affected by introduction of heavy atoms... 

A time-dependent process, such as radiative absorption, internal conversion, intersystem crossing, unimolecular isomerization, or collision, may be treated in terms of a zero-order Hamiltonian H0 and a perturbation T. An unperturbed eigenstate of H0 evolves in time, since it is not an eigenstate to the perturbed Hamiltonian... 

It is possible to perturb a spin equilibrium by photoexciting one of the isomers. Among the possible radiative and nonradiative fates of the excited state is intersystem crossing to the manifold of the other spin state. Internal conversion within this manifold ultimately results in the nonequilibrium population of the ground state. If these processes are rapid compared with the relaxation time of the spin equilibrium, then the dynamics of the ground state spin equilibrium can be observed. This experiment was first performed for spin equilibria with a coordination-spin equilibrium of a nickel(II) complex (85). More recently a similar phenomenon has been observed in the solid state at low temperatures (41). The nonequilibrium distribution can be trapped for long periods at... 

The results obtained from thermal spin equilibria indicate that AS = 1 transitions are adiabatic. The rates, therefore, depend on the coordination sphere reorganization energy, or the Franck-Condon factors. Radiationless deactivation processes are exothermic. Consequently, they can proceed more rapidly than thermally activated spin-equilibria reactions, that is, in less than nanoseconds in solution at room temperature. Evidence for this includes the observation that few transition metal complexes luminesce under these conditions. Other evidence is the very success of the photoperturbation method for studying thermal spin equilibria intersystem crossing to the ground state of the other spin isomer must be more rapid than the spin equilibrium relaxation in order for the spin equilibrium to be perturbed. 

The spin state lifetimes in solution of the complexes II and III have been measured directly with the laser Raman temperature-jump technique189). Changes in the absorbance at 560 nm (CT band maximum) following the T-jump perturbation indicate that the relaxation back to equilibrium occurs by a first-order process. The spin-state lifetimes are r(LS) = 2.5 10 6 s and r(HS) =1.3 10 7 s. The enthalpy change is AH < 5 kcal mol-1, in good agreement with that derived from x(T) data in Ref. 188. The dynamics of intersystem crossing processes in solution for these hexadentate complexes and other six-coordinate ds, d6, and d7 spin-equilibrium complexes of iron(III), iron(II), and cobalt(II) has been discussed by Sutin and Wilson et al.u°). 

Bound electronic states exhibit a discrete spectrum of rovibrational eigenstates below the dissociation energy. The interaction between discrete levels of two bound electronic states may lead to perturbations in their rovibrational spectra and to nonradiative transitions between the two potentials. In the case of an intersystem crossing, this process is often followed by a radiative depletion. Above the dissociation energy and for unbound states, the energy is not quantized, that is, the spectrum is continuous. The coupling of a bound state to the vibrational continuum of another electronic state leads to predissociation. 

Much more is becoming known about the rates of the physical processes in competition with proton exchange reactions in excited states. (For an excellent review see Henry and Siebrand, 1973.) The factors which determine the rate constants (k) for internal conversion and intersystem crossing are neatly summarized in the Golden Rule of time-dependent perturbation theory ... 

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