# Example: Franck-Condon Factors: NO2¶

Download FranckCondon_NO2.run

#!/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

Properties
NormalModes True
End

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:

$AMSBIN/fcf <<eor STATES NO2.results/adf.rkf NO2_minus.results/adf.rkf QUANTA 0 0 TRANSLATE ROTATE eor rm TAPE61 logfile # Here, zero vibrational quanta are specified for both charge states, which # corresponds to the vibrational ground state. Looking at the standard output, # we see for NO2 : # ================================================ # | Frequency (cm^-1 ) | lambda (dimensionless) | # | 756 | 1.979 | # | 1380 | 1.489 | # | 1716 | 0.000 | # ================================================ # And for NO_2^- : # ================================================ # | Frequency (cm^-1 ) | lambda (dimensionless) | # | 785 | 1.552 | # | 1265 | 0.000 | # | 1338 | 2.231 | # ================================================ # Both states have two vibrational modes with a significant electron-phonon # coupling. The ground state to ground state Franck-Condon factor is therefore # expected to be quite small. And indeed, looking at the output, we see that it # is 0.349*10^-1 , less than four percent of the total. # Since NO2 has only three vibrational modes, many quanta can be included, and # this indeed turns out to be necessary. Setting the maximum number of quanta at # 20 results in 1771 permutations for both states and a total of 3136441 Franck- # Condon factors. Even with so many factors, the average sum is still only # 0.463. Including one extra vibrational quanta results in an additional 960135 # Franck-Condon factors, but an average sum of only 0.473, i.e. a percent more. # This one percent is smeared out over so many factors that their individual # contributions become negligible.$AMSBIN/fcf <<eor
QUANTA 20 20
TRANSLATE
ROTATE
eor

rm TAPE61 logfile

$AMSBIN/fcf <<eor STATES NO2.results/adf.rkf NO2_minus.results/adf.rkf QUANTA 21 21 TRANSLATE ROTATE eor rm TAPE61 logfile$AMSBIN/fcf <<eor