Franck-Condon factors
The
photoionization transition probability may be written, to a good approximation,
as
Ã
= |Me(r; R0)|2
|<Yv”(R)|Yv’(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 Yv’(R)
and Yv”(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 Me with R is slow and that Me may be replaced by an average value of Me(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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