Franck-Condon factors

The photoionization transition probability may be written, to a good approximation, as
        Ã = |M_e(r; R₀)|² |<Y_v^”(R)|Y_v^’(R)>|²
The vibrational overlap integral in the above equation is called the Franck-Condon (FC)factor and is largely responsible for the relative intensities of the vibrational bands in photoionization transitions. This overlap integral does not vanish by orthogonality because Y_v^’(R) and Y_v^”(R) are vibrational functions belonging to different electronic states.

Franck-Condon principle

       The quantitative form of the Franck-Condon (FC) principle is derived from the expression for the transition moment. The wavefunctions of the initial and final states are the products of the respective electronic and vibrational wavefunctions. The intensity of a vibrational band in an electronically allowed transition is proportional to the absolute square of the overlap integral of the vibrational wavefunctions of the initial and final states. This statement (FC principle) rests on the assumption that the variation of M_e with R is slow and that M_e may be replaced by an average value of M_e(r; R₀). It is noted that Franck-Condon principle does not specify a “verticality” of electronic transitions nor the time duration of an electronic transition as determined from the mass disparity between electrons and nuclei. It indicates only that transitions are favored when there is a large overlap between the vibrational wavefunctions of the initial and final states of the transition. This condition favors, but not require, transitions in which the relative positions of the nuclei are the same in the initial and final states.

背景音樂: ["Fernando" by ABBA]
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