Franck-Condon overlap integral

Adiabatic and Condon." Since the Condon approximation separates the electronic and the vibrational parts of the problem (see Section 10c), most of the papers using this approximation emphasize the latter aspect. Specifically, they analyze the so-called Franck-Condon overlap integrals [the (Xm X ) of Eq. (42)] and the occupancy factors of these vibrational levels. Such analyses include (1) the influence of mode type and/or number as well as... 

Electronic transitions between two energy states are governed bytheFranck-Condon principle. In quantum mechanical terminology, the Franck-Condon overlap integral f xf x, dxv is important. xf and x" are, respectively, vibration wave functions for v in the final electronic state, and v" in the initial electronic state. 

Figure 5.2 Potential energy surface for So, S, and S2 and Franck-Condon overlap integral. Inset (A) Overlap integral between AJ 12 and SJ""° and (B) Sj and SJ ° states for horizontal transfer of energy.

J.R. Henderson, R.A. Willett, M.Muramoto and D.C. Richardson, Table of Hormonic Franck-Condon Overlap Integrals Including Displacement of Normal Coordinates, Douglas Aircraft Co. Report S.M. (1964)45807. 

According to the Franck-Condon principle (725), to evaluate the Franck-Condon overlap integral the vibrational wavefunctions for the ground and excited electronic states are expressed in terms of the Hermite polynomials, which include the displacement of the origin of the normal... 

The Franck-Condon overlap integrals are related to the relative intensities for the vibronic emission peaks represented in Eq. (19) ... 

In the case of internal conversion between states of equal multiplicity A = is the kinetic energy operator of the nuclei. In the case of weak coupling the matrix element of the perturbation operator can be split into an electronic part and a contribution due to the vibrational terms which, with the help of further simplifying assumptions, can be written as the Franck-Condon overlap integral ... 

Xg excitation of oxygen meant that the Franck-Condon overlap integrals controlling the size of should be determined primarily by the aromatic... 

The integral (9Tn 31 ) is the Franck-Condon overlap integral. Since the equilibrium nuclear configurations in the ground and excited states are not normally identical, this integral has some value for all p that permit the integral to be nonzero from symmetry considerations. If the ground and excited states had identical Qo for a particular p. then all (3lo , 91 ) would be zero except (atf" , aty ). Of course, (3l(V , is zero if the direct product of the two vibrational states does not contain the totally. symmetric rep. Since >s totally symmetric (zero point wavefunction) the transition moment of Eq. 8.46 will vanish unless p is a,... 

A number of different approaches may be subsumed under this heading—approaches which are not restricted to nonadiabatic reactions. In remote encounters, the initial and final states refer to separated reactants and products, respectively, and the transition probability may be computed from the corresponding energy defect this model is familiar for charge-transfer processes, but has been applied to chemical reactions. The effect of spin and symmetry conservation on such crossings has also been assessed qualitatively. The importance of the Franck-Condon overlap integral in determining the transition probability has also been treated semiempirically. In the theoretical discussion of nonadiabatic reactions, it is standard practice to compute the transition probability between the surfaces, for example, by Landau-Zener theory. ... 

The Franck-Condon factors, shown here for the process of absorption (blue line) followed by emission (green line). In a resonance Raman experiment, the LASER beam is tuned to be in resonance with an allowed electronic transition (indicated here by the blue arrow), which takes the electron from some initial state I to some intermediate state V. Unlike fluorescence, there is no vibrational relaxation of the excited state. The electron is scattered from the intermediate V state down to the i/ = 1 vibrational level of the ground electronic state, which we will call the final state F. The Franck-Condon overlap integrals involve the amount of overlap between the wave functions, which are shown on this diagram in brown. [ Mark M Samoza/CC-BY-SA 2.5/GFDL /Wimimedia Commons reproduced from http //en.wikipedia.org/wiki /Franck%E2%80%93Condon principle (accessed December 21,2013).]... 

The first integral represents a normal transition moment. The value of the second integral is not determined by orthonormality, because it represents different vibrational wavefunctions of different electronic states. This second integral is known as the Franck-Condon overlap integral, and it is a measure of the amount of overlap between two different vibrational wavefunctions. The larger the overlap (see Figure 15.14), the larger the transition probability. 

Figure 15.39 shows two vibronic levels of a molecule. Indicate which sets of energy levels should have the largest Franck-Condon overlap integral. Explain your answer. 

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