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

12.4 Radiationless processes in photoexcited molecules 244
12.4 Radiationless processes in photoexcited molecules
I
Figure 12.2: Jablonski Diagram.
Elementary Photochemical Processes: Jablonski Diagram
Energy
RXN
(10 -14 .. 10 -6 s)
S 2
T 2
IC
S 2 -S 1 Abs.
T 1
T 2 -T 1 Abs.
IVR
IC
VET* S 1
ISC
(10 -9 ..10 -3 s)
S 0 VET* (10 -11 s)
IVR (10 -13 ..10 -9 s)
Absorption
(10 -18 s)
Fluorescence
(10 -9 ..10 -8 s)
Phosphorescence
(10 -3 ..10 -6 s)
*also known as VR
Physical Chemistry III: Chemical Kinetics • © F. Temps, IPC Kiel 253
12.4.1 The Born-Oppenheimer approximation and its breakdown
a) The full Hamiltonian
We consider a non-moving, non-rotating molecule in the laboratory framework. The
molecule is described by the Schrödinger equation (SE)
ˆ(r R) = (r R) (12.12)
or ³
ˆ − ´
(r R) =0 (12.13)
with being the energy eigenvalue associated with the wavefunction (r R) as function
of the electronic (e) coordinates r and the nuclear (N) coordinates R.
The Hamilton operator ˆ appearingintheSEcanbewrittenas
ˆ = ˆ + ˆ = ˆ (r)+ ˆ (R)+ (r R) (12.14)
where
ˆ = − ~2
2
X
=1
∇ 2 (12.15)
ˆ = − ~2 X
∇ 2 (12.16)
2
=1