Physical Chemistry 3: — Chemical Kinetics — - Christian-Albrechts ...

12.4 Radiationless processes in photoexcited molecules 248
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This breakdown of the BO approximnation leads to non-adiabatic coupling of
electronic states:
• For a diatomic molecule, the coupling leads to an avoided crossing of the two
electronic potential curves.
• For polyatomic molecules, the coupling can lead to a conical intersection (CI)
between the two electronic potential energy hypersurfaces.
As will be outlined in the following, the existence of conical intersections between different
excited electronic potential energy hypersurfaces and between an excited and
the ground electronic potential energy hypersurface has dramatic consequences for the
dynamics of photochemical reactions.
The recognition since about the years 2000 - 2005 that conical intersections in polyatomic
molecules are the rule rather than the exception has indeed revolutionized our
understanding of photochemical reactions.
12.4.2 Avoided crossings of two potential curves of a diatomic molecule
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Illustration of an avoided crossing using two diabatic model potential functions
+ coupling term:
1 () = 1 [1 − exp [− 1 ( − 1 )]] 2 (12.33)
2 () = 2 + exp [− 2 ( − 2 )] (12.34)
12 () = 1 [1 + tanh [− 2 ( − 12 )]] (12.35)
12 () is just a convenient model function with the physically correct behavior
12 () → 0 for →∞.
Figure 12.3: Diabatic model potential curves for a diatomic molecule.
Avoided Crossing of Two Potentials of a Diatomic Molecule
Diabatic model potential curves: V1
( R) 0
H
0 V2
( R)
1exp ( )
2
V R D
R R
1 1 1 1
exp ( )
V R D R R
2 2 2 2
Physical Chemistry III: Chemical Kinetics • © F. Temps, IPC Kiel 254