Franck control

We have seen in Chapter 1 that absorption and emission spectra are controlled at least in part by the Franck-Condon principle. However, this is only one of three major factors that must be considered. 

In Chapters 2 and 4, the Franck-Condon factor was used to account for the efficiency of electronic transitions resulting in absorption and radiative transitions. The efficiency of the transitions was envisaged as being related to the extent of overlap between the squares of the vibrational wave functions, /2, of the initial and final states. In a horizontal radiationless transition, the extent of overlap of the /2 functions of the initial and final states is the primary factor controlling the rate of internal conversion and intersystem crossing. 

In the previous section, we alluded to the Franck Condon factors (FCF) in controlling electron transfer rates. For this topic, detailed reviews of theory and experiment are provided elsewhere. In sum, it is now well known that the reaction free energy required to transfer charge can be reduced by the reaction free energy, AG°, as summarized in the famous Marcus equation AG = (AG° — where X, the reorganization energy, is related to the degree of... 

The basic theory of the kinetics of charge-transfer reactions is that the electron transfer is most probable when the energy levels of the initial and final states of the system coincide [5] following the Franck-Condon principle. Thus, the efficiency of the redox reaction processes is primarily controlled by the energy overlap between the quantum states in the energy bands of the semiconductor and the donor and acceptor levels of the reactants in the electrolyte (Fig. 1). In the ideal case, the anodic current density is given by the... 

Spiders are an important order of carnivorous arachnids having a great impact on many ecosystems. Because most of their prey consists of insects, they can play an important role in controlling pest insects in agricultural crops. There are currently about 36000 described species, out of an estimated overall number of 60000-80000 species (Platnick, 1999). Unlike the situation with insects (Francke and Schulz, 1999), pheromones and other semiochemicals of arachnids, and especially spiders, have received little attention from researchers. What information is available on the use of semiochemicals by spiders will be reviewed and discussed in this chapter. 

Collisions in solution are diffusion-controlled and hence depend on the viscosity of the solvent. Due to Franck-Rabinowitch cage effect they occur in sets called encounters . 

Adiabatic control of bond distance in selective non Franck-Condon transitions... 

Consider, to be specific, a molecule like Na2. In Fig. 1(a) we show some singlet electronic potential curves. A selective transition between the initial state (x) and the ground state of the excited potential Vn3(a ), o(x), is highly non Franck-Condon and thus involves a large displacement of the molecular bond. If the transition between these states can be adiabatically controlled, then it will be in principle possible to follow or control the bond length as the transition proceeds. The first problem involves the smallness of... 

We study two adiabatic schemes that, use a sequence of time-delayed transform limited pulses. The first one, known as STIRAP (Stimulated Raman adiabatic passage) controls the population transfer between three vibrational states. The frequency of the first pulse (t)[ is tuned in resonance with the transition from 4> (x) to the intermediate state (f>i0 x), and the frequency of the second pulse [ 2(t)] is resonant with the transition from i0 x) to 4>q x) i0 x) is the intermediate state that maximizes the Franck-Condon factors for both transitions at the same time, working as an efficient wave function bridge between the initial and target wave functions [5]. Using counterintuitive pulses, such that (t) precedes x (t), the wave function of the system has the interesting form [3]... 

The finer structure within each feature state corresponds to the dynamics of the Franck-Condon bright state within a four-dimensional state space. This dynamics in state space is controlled by the set of all known anharmonic resonances. The state space is four dimensional because, of the seven vibrational degrees of freedom of a linear four-atom molecule, three are described by approximately conserved constants of motion (the polyad quantum numbers) thus 7-3 = 4. 

The acetylene A <- X electronic transition is a bent <- linear transition that would be electronically forbidden ( - ) at the linear structure. The usual approximation is to ignore the possibility that the electronic part of the transition moment depends on nuclear configuration and to calculate the relative strengths of vibrational bands as the square of the vibrational overlap between the initial and final vibrational states (Franck-Condon factor). A slightly more accurate picture would be to express the electronic transition moment as a linear function of Q l (the fra/w-bending normal coordinate on the linear X1 state) in such a treatment, the transition moment would be zero at the linear structure and the vibrational overlap factors would be replaced by matrix elements of Qfl- Nevertheless, as long as one makes use of low vibrational levels of the A state, neglect of the nuclear coordinate dependence of the electronic excitation function is unlikely to affect the predicted dynamics or to complicate any proposed control scheme. 

The enrichment of the concentration of the polar solvent component in the cage and, therefore, the relative amount of the red shift of the fluorescence band is a function of viscosity, since the diffusion-controlled reaction time must be smaller than the excited-state lifetime. This lifetime limitation of the red shift is even more severe if the higher value of the excited-state dipole moment is not a property of the initial Franck-Condon state but of the final state of an adiabatic reaction. Nevertheless, the additional red shift has been observed for the fluorescence of TICT biradical excited states due to their nanosecond lifetime together with a quenching effect of the total fluorescence since the A to 50 transition is weak (symmetry forbidden) (Fig. 2.25). 

The absence of a substituent at C-2, usually able to influence the course of the glycosylation reaction, impedes control of the a (3 ratio. Marzabadi and Franck have compiled extensive data on the relevant glycosylation methods for 2-deoxy sugars.3... 

Figure 4 Opening of a fast radiationless decay channel via conical intersection for (a) a barrier controlled reaction, (b) a barrierless path, and (c) an uphill path without transition state (sloped conical intersection). M" is an excited state intermediate and FC is a Franck-Condon point.

In the control scheme [13,17] that we have focused on, the time evolution of the interference terms plays an important role. We have already discussed more explicit forms of Eq. (7.75). One example is the Franck-Condon wave packet considered in Section 7.2.2 another example, which we considered above, is the oscillating Gaussian wave packet created in a harmonic oscillator by an (intense) IR-pulse. Note that the interference term in Eq. (7.76) becomes independent of time when the two states are degenerate, that is, AE = 0. The magnitude of the interference term still depends, however, on the phase S. This observation is used in another important scheme for coherent control [14]. 

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