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