Evaluation of Franck-Condon factors

The Franck-Condon principle couples electronic and vibrational properties.

Franck-Condon factors in CH4

Forces

We may get a good structure for methane from ase.build. This will not be the ground state structure according to the EMT calcuator though. Therfore EMT predicts finite forces:

from ase.build import molecule
from ase.calculators.emt import EMT

atoms = molecule('CH4')
atoms.calc = EMT()

# evaluate forces in this configuration
forces_a = atoms.get_forces()

Vibrational properties

These forces can be used to calculate the corresponding Franck-Condon factors for transitions from the EMT ground state. First we need the EMT ground state and the vibrational properties:

from ase.optimize import BFGS
from ase.vibrations import Vibrations

# relax and get vibrational properties
opt = BFGS(atoms, logfile=None)
opt.run(fmax=0.01)

vibname = 'vib'
vib = Vibrations(atoms, name=vibname)
vib.run()
vib.summary()

Huang-Rhys factors

The Huang-Rhys factors describe the displacement energy in each vibrational coordinate relative to the vibrational energy. We may get them by:

from ase.vibrations.franck_condon import FranckCondon

# FC factor for all frequencies
fc = FranckCondon(atoms, vibname)

HR_a, freq_a = fc.get_Huang_Rhys_factors(forces_a)

Franck-Condon factors

The Franck-Condon factors depend on temperature due to occupation of vibrational states. We may get them for 293 K by:

FC, freq = fc.get_Franck_Condon_factors(293, forces_a)

where FC[0] contains the Franck-Condon factors and freq[0] the corresponding frequencies.

It is also possible to evaluate higher order transitions. Two vibrational quanta might be considered by increasing the order:

FC, freq = fc.get_Franck_Condon_factors(293, forces_a, order=2)