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What is the FranckCondon principle? 
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#1
Feb913, 09:43 PM

P: 17

hi guys
I want to know what is the FranckCondon principle?.... please in details thanks for all 


#2
Feb1013, 07:34 AM

Sci Advisor
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#3
Feb1113, 01:14 AM

P: 5

From the BO approximation, we have the product of the electronic [itex]\varphi_i(r,R)[/itex] and the nuclear [itex]\eta_i(R)[/itex] wavefunction. For the transition, we use Fermi's Golden rule, where the DipoleOperator [itex]\mu[/itex] "initiates" the transition. So we end up in
[itex]r_{i\rightarrow j}=\left\langle \eta_i(R) \varphi_i(r,R) \mu \varphi_j(r,R) \eta_j(R) \right\rangle[/itex]. Here we have an inner integral over the electron coordinates [itex]r[/itex] and an outer integral over the nuclei coordinates [itex]R[/itex]. It is important to note here that the inner integral [itex]\left\langle \varphi_i(r,R) \mu \varphi_j(r,R) \right\rangle[/itex] is a function of [itex]R[/itex]. The approximation is now that this inner integral is taken out of the outer interal, even though the former one is dependent of [itex]R[/itex]  which is the integration variable of the outer integral. Now the above equation looks like this: [itex]r_{i\rightarrow j}= \left\langle\varphi_i(r,R) \mu \varphi_j(r,R) \right\rangle \cdot\left\langle \eta_i(R)\eta_j(R) \right\rangle[/itex] So actually the electronic integral is handled independently of the nuclei integral. The former one is a usual transition (with an operator for the transition according to Fermi's Golden rule), while the latter one is only an overlap of wavefunctions any more! 


#4
Feb1113, 01:33 AM

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What is the FranckCondon principle?
Schafspelz, the approximation you made can be justified further by using diabatic electronic states ##\eta_j## instead of the adiabatic electronic wavefunctions. The diabatic states depend only very little on R.
A second step in the FranckCondon approximation is to replace the dipole integral by a semiclassical expression so that only the neighbourhoods of the turning points of the nuclear motion contribute to the integrand. 


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