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:
$ADFBIN/adf <<eor
TITLE Nitrogen dioxide
ATOMS
N 0.000000 0.000000 -0.016179
O 0.000000 1.098646 -0.492918
O 0.000000 -1.098646 -0.492918
END
BASIS
CORE NONE
TYPE DZP
END
XC
LDA SCF VWN
END
ANALYTICALFREQ
END
UNRESTRICTED
CHARGE 0 1
GEOMETRY
Converge grad=1.0e-5
END
eor
mv TAPE21 NO2.t21
rm logfile
# We are using an already optimized geometry for the second calculation but in a
# real experiment one should run geometry optimization first
$ADFBIN/adf <<eor
TITLE Nitrite
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
BASIS
CORE NONE
TYPE DZP
END
XC
LDA SCF VWN
END
! Uncomment the 2 lines below if you copy this example
!GEOMETRY
!END
ANALYTICALFREQ
END
eor
mv TAPE21 NO2-.t21
rm logfile
# This runscript produces two TAPE21 files containing the frequencies and the
# normal modes for both charge states. Lets first look at the ground state to
# ground state overlap:
$ADFBIN/fcf <<eor
STATES NO2.t21 NO2-.t21
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.
$ADFBIN/fcf <<eor
STATES NO2.t21 NO2-.t21
QUANTA 20 20
TRANSLATE
ROTATE
eor
rm TAPE61 logfile
$ADFBIN/fcf <<eor
STATES NO2.t21 NO2-.t21
QUANTA 21 21
TRANSLATE
ROTATE
eor
rm TAPE61 logfile
$ADFBIN/fcf <<eor
STATES NO2.t21 NO2-.t21
QUANTA 0 20
TRANSLATE
ROTATE
SPECTRUM 0e3 20e3 1001
eor
rm TAPE61 logfile