# 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)
```