Franck-Condon transition probability intersection

A question that arises in consideration of the annihilation pathways is why the reactions between radical ions lead preferentially to the formation of excited state species rather than directly forming products in the ground state. The phenomenon can be explained in the context of electron transfer theory [34-38], Since electron transfer occurs on the Franck-Condon time scale, the reactants have to achieve a structural configuration that is along the path to product formation. The transition state of the electron transfer corresponds to the area of intersection of the reactant and product potential energy surfaces in a multidimensional configuration space. Electron transfer rates are then proportional to the nuclear frequency and probability that a pair of reactants reaches the energy in which they have a common conformation with the products and electron transfer can occur. The electron transfer rate constant can then be expressed as... 

Instead, the vibrational wavepacket created at zero pump/probe delay on the Nat X2Ej" state is built from low-u+ levels centered near the intersection of the probe pulse dotted arrow with the X2E+-state potential. The excess energy from the probe pulse must go into the kinetic energy of the ejected electron (in even-1 partial waves). The excitation by the probe pulse at the outer turning point (solid vertical arrow) has good Franck-Condon overlap with the 2E+-state repulsive potential. The g +- u optical selection rule requires that the low kinetic energy ejected electron depart in odd-1 (i.e., u symmetry) partial waves. Both electronic and vibrational transition probability factors favor excitation at the outer turning point. 

D14.2 The Franck-Condon principle states that because electrons are so much lighter than nuclei, an electronic transition occurs so rapidly compared to vibrational motions that the internuclear distance is relatively unchanged as a resu It of the transition. This implies that the most probable transitions vf <— vj are vertical. This vertical line will, however, intersect any number of vibrational levels Vf in the upper electronic state. Hence transitions to many vibrational states of the excited state will occur with transition probabilities proportional to the Frank-Condon factors which are in turn proportional to the overlap integral of the wavefunctions of the initial and final vibrational states. A vibrational progression is observed, the shape of which is determined by the relative horizontal positions of the two electronic potential energy curves. The most probable transitions are those to excited vibrational states with wavefunctions having a large amplitude at the internuclear position Re. 

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