# Vibrational modes of the H2O molecule¶

Density functional theory can be used to calculate vibrational frequencies of molecules, e.g. either in the gas phase or on a surface. These results can be compared to experimental output, e.g. from IR-spectroscopy, and they can be used to figure out how a molecule is bound to the surface. In this example we will calculate the vibrational frequencies for a water molecule.

• For a simple molecule, like CO, there is only one stretching mode. How would you calculate the vibrational frequency of this mode?

• For a general molecule with N atoms, how many modes are there? How many of them are vibrational modes? How would you do a calculation for the vibrational modes? Describe in detail which steps have to be performed.

• Read the script below and try to understand what it does.

```from math import cos, sin, pi

from ase import Atoms
from ase.optimize import QuasiNewton
from ase.vibrations import Vibrations

from gpaw import GPAW

# Water molecule:
d = 0.9575
t = pi / 180 * 104.51

H2O = Atoms('H2O',
positions=[(0, 0, 0),
(d, 0, 0),
(d * cos(t), d * sin(t), 0)])

H2O.center(vacuum=3.5)

calc = GPAW(h=0.2, txt='h2o.txt', mode='lcao', basis='dzp')

H2O.calc = calc

QuasiNewton(H2O).run(fmax=0.05)

"""Calculate the vibrational modes of a H2O molecule."""

# Create vibration calculator
vib = Vibrations(H2O)
vib.run()
vib.summary(method='frederiksen')

# Make trajectory files to visualize normal modes:
for mode in range(9):
vib.write_mode(mode)
```
• Run the script and look at the output frequencies. Compare them to literature values, which are 1595cm-1 for the bending mode, 3657cm-1 for the symmetric stretching mode and 3756cm-1 for the anti-symmetric stretching mode. How good is the accuracy and what are possible error sources?

• Now we want to look at the modes to see how the atoms move. For this we use the files `vib.?.traj` where `?` is the number of the mode counted in the order they are printed out. You can look at these trajectories with the ase gui command - click Play to play the movie. Do they look like you expected and what would you have expected (you may have learned something about symmetry groups at one point)? Did you assign the modes correctly in the previous question?