# Example: Franck-Condon Factors: NO2¶

```
#!/bin/sh
# As an example of a Franck-Condon calculation, lets look at the transition of
# NO2 to NO2 - . NO2 is a small molecule with only three vibrational modes.
# Putting an extra electron on the molecule will cause a big displacement,
# resulting in large electron-phonon couplings.
# In general, the larger the molecule, the smaller the displacement and hence
# the electron-phonon couplings and Franck-Condon factors. Moreover, larger
# molecules have more vibrational modes, meaning that the already smaller
# displacement will generally be smeared out over more modes, resulting in an
# additional decrease in electron-phonon couplings. This is fortunate, since the
# number of Franck-Condon factors increases factorially with the number of
# vibrational modes, making it prohibitively expensive to take more than a few
# vibrational quanta into account for most molecules.
# In order to calculate the Franck-Condon factors for Nitrite and Nitrogen
# dioxide, the equilibrium positions of the nuclei and the vibrational modes
# have to be obtained:
AMS_JOBNAME=NO2 $AMSBIN/ams <<eor
System
atoms
N 0.000000 0.000000 -0.016179
O 0.000000 1.098646 -0.492918
O 0.000000 -1.098646 -0.492918
end
end
Task GeometryOptimization
GeometryOptimization
Convergence
Gradients 1.0e-5
End
End
Properties
NormalModes True
End
Engine ADF
basis
core NONE
type DZP
end
spinpolarization 1
title Nitrogen dioxide
unrestricted
xc
lda SCF VWN
end
EndEngine
eor
# We are using an already optimized geometry for the second calculation but in a
# real experiment one should run geometry optimization first
AMS_JOBNAME=NO2_minus $AMSBIN/ams <<eor
System
atoms
N 0.000000 0.000000 0.126041
O 0.000000 1.070642 -0.555172
O 0.000000 -1.070642 -0.555172
end
charge -1.0
end
Task SinglePoint
Properties
NormalModes True
End
Engine ADF
basis
core NONE
type DZP
end
title Nitrite
xc
lda SCF VWN
end
EndEngine
eor
# This runscript produces two adf.rkf files containing the frequencies and the
# normal modes for both charge states. Lets first look at the ground state to
# ground state overlap:
$AMSBIN/fcf <<eor
STATE1 NO2.results/adf.rkf
STATE2 NO2_minus.results/adf.rkf
TRANSLATE
ROTATE
eor
rm TAPE61 logfile
```