Frank Condon principle

A natural question is In which temporal order do the reorganization processes and the proper electron transfer take place The answer is given by the Frank-Condon principle, which in this context states First the heavy particles of the inner and outer sphere must assume a suitable intermediate configuration, then the electron is exchanged isoenergetically, and finally the system relaxes to its new equilibrium... 

This equation is in accord with the Frank-Condon principle The nuclei stand still during an electronic transition, so that a good overlap between the nuclear wavefunctions is required for the transition. 

In the spirit of the adiabatic approximation, the transitions between two vibrational states (belonging to initial and final electronic states) must occur so rapidly that there is no change in the configurational coordinate Q. This is known as the Frank Condon principle and it implies that the transitions between i and / states can be represented by vertical arrows, as shown in Figure 5.12. Let us now assume our system to be at absolute zero temperature (0 K), so that only the phonon level = 0 is populated and all the absorption transitions depart from this phonon ground level to different phonon levels m = 0, 1, 2,... of the excited state. Taking into account Equation (5.25), the absorption probability from the = 0 state to an m state varies as follows ... 

Corresponding to the Frank-Condon principle is an associated concept called the Frank-Condon factors. Thus, when an electronic transition occurs from the vibrational levels of a lower vibrational state to the corresponding vibrational levels of a higher electronic state, there are various intensities of transition, depending on the vibrational states to which a transition is made. 

Development of the Frank-Condon principle in quantum mechanical terms (involving a transition dipole moment14) allows a calculation of the intensities referred to in terms of a series of Frank-Condon factors by which expressions for the transition probabilities are multiplied to obtain a net transition probability from one level to another for an electron-transfer process. 

In some presentations of this theory, the Frank-Condon principle is mentioned, (a) Why do you think that is (b) In what part of the theory do you see this principle applied ... 

Both types of reaction must obey the Frank-Condon principle,1000 which states that there must be no movement of the nuclei during the time of electron transfer. Consequently, the... 

An electron transfer occurs momentarily between neighboring molecules. No nuclear motions in the molecules occur during this transfer. [The Frank-Condon principle Transfer of an electron takes place much faster than nuclear movements]. Therefore, such a rapid electron transfer may take place only when the geometry of the ion radical and the parent molecule are similar (Warman 1982). Solvent relaxation is assumed to be much faster than... 

Normally, when a complex molecule is excited by radiation, a n-electron moves up into a Tt or band. This usually involves a n-electron of the singlet type and the Frank-Condon principle requires the transition to proceed into an excited state of the singlet type. The excited state of the singlet type is relatively short lived and is usually associated with fluorescence as a method of decay in molecules. If the n-electron is initially of a triplet type, it can transition directly into an excited state of the triplet type which is a longer life state usually related to phosphorescence as a method of decay. 

The mechanism of fluorescence is illustrated in the following figure. The incident light excites the molecule from the ground state, O. By the Frank-Condon principle this excitation should be vertically upwards along OD, producing a compressed excited molecules, which vibrates with a period of 10-13s as shown by the upper curve. Vibrational excitation is thus coupled to electronic... 

Information about further energy levels in a redox system can be derived from the theory of electron transfer between a redox system and an electrode, which has been derived by various authors [2-5]. In all these theories it is assumed that the vibration of redox molecules and their surrounding solvation shell is slow, compared to the actual electron transfer, i.e. it is assumed that the Frank-Condon principle is valid. As shown by Gerischer [44], this assumption leads to the consequence that the energy levels involved in the charge transfer differ from the thermodynamic value Ep, jox- This model leads to a distribution of empty and occupied states versus electron energy, as illustrated in Fig. 6. These electron states are not discrete energy levels, but are distributed over... 

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