Franck-Condon factors complexes

Another consequence of the stronger interactions upon ionization is that the equilibrium geometry of the ionized complex may differ signihcantly from that of the neutral states. Broadened ionization onsets are frequently attributed to the spectral superposition of ionization into several vibrational levels for which Franck-Condon factors are more favorable. As a result, the adiabatic ionization potential may be considerably lower than the vertical potential, and the observed ionization onsets may occur above the adiabatic potential. Another factor to be considered is the conformation-dependent efifect, due to the different conformations of the solvent molecules. The most populated form of a complex may involve a less stable form of the solvent. After photoionisation, the lowest-energy dissociation channel in the complex ion leads to the most stable form of isolated solvent, which has to be taken into account for the estimate of the binding energy. 

Equation (33) assumes that IV// is large compared to 2J (i.e., no electronic and vibrational recurrences). In addition, Eq. (33) deals only with population dynamics Interferences between different Franck-Condon factors are neglected. These interferences do influence the rate, and the interplay between electronic and vibrational dynamics can be quite complex [25], Finally, as discussed by Jean et al. [22], Eq. (33) does not separate the influence of pure dephasing (T-T) and population relaxation (Ti). These two processes (defined as the site representation [22]) can have significantly different effects on the overall rate. For example, when (T () becomes small compared to Eq. (33) substantially overestimates the rate compared to... 

In this paper we will first review the manner in which spin-free permutation and point group symmetry arise. Some general concepts concerning time-dependent processes will be discussed. Spin-free processes in which spin is conserved will be studied, and spin-free spin conservation rules and examples will be given. Special attention will be given to processes in which spin apparently is not conserved, but is in actuality. In addition, we will treat processes in which spin is not conserved. The role of doublepoint group symmetry and of Franck-Condon factors will be developed. Special emphasis is given to spin-forbidden processes in methylene, benzene, and chromium(III) complexes. 

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. 

Figure 7.12 compares the measured and the theoretical absorption spectra for CH30N0(S i), the latter being obtained in a three-dimensional wavepacket calculation (Untch, Weide, and Schinke 1991a). The energy spacing of the main progression reflects the vibrational frequency of NO in the Si complex. The ratio of the peak intensities is mainly determined by the one-dimensional Franck-Condon factors... 

In Equation 6.88, K0 is the equilibrium constant for the formation of the collision complex, (V) 2 is the electronic coupling, and F is the Franck-Condon factor. In contrast to the radiationless relaxation, the energy transfer process cannot be rationalized only in the limit of the strong and weak coupling limits shown in Figure 6.16. 

The denominator of (2.81) presents an imaginary part in two distinct cases Either (1) g0 (and absorbing state is diluted in the two-particle-state continuum, or (2) the real part of the denominator vanishes, f being real, for discrete values of z, and we have absorption by a discrete state. The calculated absorption spectra are presented in Fig. 2.6 for various values of the linear coupling ( ) and the quadratic coupling (AD = De - /20) the corresponding Franck-Condon factors are given by (2.44). 

Now, and Robertson pointed out, the Franck-Condon factors may be significantly different for the HC1 and for the DC1 complexes. Because of the lesser... 

A more general definition of the FCWD includes overlap integrals of quantum nuclear modes. The definition given by Eq. [19] includes only classical solvent modes (superscript s ) for which these overlap integrals are identically equal to unity. An extension of Eq. [19] to the case of quantum intramolecular excitations of the donor-acceptor complex is given below in the section discussing optical Franck-Condon factors. 

The collision-assisted predissociation in iodine B O + state merits a detailed discussion. It is well known that B state is weakly coupled to the dissociative A 1m state by rotational and hyperfine-structure terms in the molecular Hamiltonian. The natural predissociation rate strongly depends on the vibrational quantum number (pronounced maxima for o=5 and u = 25, a minimum for u= 15), this dependence being due to a variation of the Franck-Condon factor. " The predissociation rate is enhanced by collisions. In absence of a detailed theoretical treatment of the colhsion-assisted 12 predissociation, one can suppose that the asymmetric perturbation (breakdown of the orbital symmetry) in the collisional complex affects electronic and rotational wavefimctions but does not change the nuclear geometry. 

With this formulation of the problem the calculation of quenching rate constants is reduced to evaluating various matrix elements of the type y of Franck-Condon factors for the complex, and of the density of states factor p. 

Franck-Condon Factors. In the limit of weak coupling of M and O2 the vibrational wavefunction for the complex may be written as a product of the vibrational wavefunctions for the two components ... 

We, therefore, anticipate that most of the vibrational excitation will be deposited in M rather than in O2 (formation of a strong M-02 complex might somewhat relax this selection rule ). Consequently, the variation of Fif with Ac will be almost entirely conditioned by variations in fm, the Franck-Condon factor for the molecule. Fortunately, semi-empirical formulas for evaluating fm have been developed (19, 24, 48), and one such expression is given in Equation 6. 

The description of the radiationless processes which lead to the transfer of excitation energy from one excited state to another in heavy metal complexes has been discussed by several authors (JI, 17, 22). Spin-orbit coupling must be included in the description of the initial and final states for the radiationless process but may also contribute to the coupling terms responsible for this process (II, 17). There are also vibronic coupling terms which arise from breakdown of the Bom-Oppen-heimer approximation which presumably play some role in radiationless energy transfer processes in both heavy- and light-atom molecules (II, 17). Beyond these electronic terms, there are vibrational contributions to the rate constant for a radiationless process, and these contributions are generally expressed as Franck-Condon factors (II). 

The two collision partners form a collision complex that is excited by absorption of the photon hv at a relative distance Rc, where the energy difference AE = fCAM) — (AM) between the two potential curves just equals the photon energy h V (Fig. 8.33a) and the Franck-Condon factor has a maximum value [1089]. This complex decays after a short time into A - - M. 

Thus, the interpretation of ZEKE signal intensities can be more complex than expected purely on the basis of Franck-Condon factors. 

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