Frank-Condon process

The nuclear sum of the state for Frank-Condon processes, such as are most of the chemical transformations, is given by ... 

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... 

Two main liminations have, however, become evident the hrst is that molecules whose gas-phase ionization energy exceeds > 9.5 eV cannot be oxidized by ionized solid Ar. The reason for this limitation is unclear, because the process is exothermic (the ionization energy of solid Ar is 13.9 eV, that of organic molecules in Ar is typically lowered by 1 eV in solid Ar relative to the gas phase ). Perhaps the localization of the spin and charge onto the substrate entails a Frank-Condon barrier that cannot easily be surmounted at 12 K. 

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. 

First, we present the dynamics of the initial wavepacket a. Initially the system stands at the equilibrium position of the electronic ground X. The temporal evolution of the wavepacket Pe generated in the electronic excited state is shown in the left-hand column of Fig. 5.9. Apparently, tp originates in the Frank-Condon (FC) region, which is located at the steep inner wall of the electronically excited A state. The repulsive force of the potential l 0 the drives e(t) downhill toward the saddle point and then up the potential ridge, where Pe(t) bifurcates into two asymptotic valleys, with Ye = 0.495 in channel f. The excitation achieved using this simple quadratically chirped pulse is not naturally bond-selective because of the symmetry of the system. The role played by our quadratically chirped pulse is similar to that of the ordinary photodissociation process, except that it can cause near-complete excitation (see Table 5.1 for the efficiency). This is not very exciting, however, because we would like to break the bond selectively. 

The photoinduced CO loss from Cr(CO)6 occurs following a symmetry and spin-allowed transition to produce the a 7 u MLCT excited state. A Jahn-Teller active (f2g bending) mode promotes motion to a conical intersection close to the Frank-Condon state. This provides an efficient barrierless transition to the E component derived from the a 7 g state. This process takes approximately 12.5 fs. The E component is unbound with respect to the M-CO interaction. As the M-CO bond lengthens a further conical intersection with the E component derived from the a 7, u state,... 

Femtosecond photochemistry (267 nm) of gas-phase M(C0)6, M = Cr, Mo, W, Fe(CO)5, and Ni(CO)4, has established multiple processes in the first 1000 fs after excitation. For example, Fe(CO)5 undergoes five consecutive processes. The first four of which occur within 3300 fs and represent a continuous pathway from the Frank-Condon region down to the lowest singlet state of Fe(CO)4. The fifth stage corresponds to loss of a second carbonyl group. A review of this work appeared in 2001. In the case of Fe(CO)5, CASSCF/MR-CCI calculations have been carried out on the excited states. ... 

The sequence of processes leading finally to decomposition may then be described as follows absorption of a photon promotes the molecule to the singlet excited state HN3( A") which in the first instance appears in the linear configuration of the ground state (Frank-Condon principle). Since the equilibrium configuration of HN ( A") is... 

In the Gerischer model, an electron transfer occurs from an occupied state in the metal or the semiconductor to an empty state in the redox system, as illustrated in Fig. 6.10. The reverse process occurs then from an occupied state in the redox system to an empty state of the solid (not shown). The electron transfer takes place at a certain and constant energy as indicated by arrows in Fig. 6.10. This means that the electron transfer is faster than any rearrangement of the solvent molecules, i.e. the Frank-Condon principle is valid. In this approach, the rate of an electron transfer depends on the density of energy states on both sides of the interface. For instance, in the case of an electron transfer from the electrode to the redox system the rate is given by... 

Ionization dnring colhsion of vibrationally excited molecules can be very important in non-equilibrium systems. Cross sections of such processes, however, are very low because of the smallness of the Frank-Condon factors. Consider the associative ionization (Rusanov Fridman, 1984) ... 

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