# Infrared spectroscopy with molecular dynamics

In this exercise, we will compare the vibrational spectrum of two molecules (methanol and benzene) computed with a static method (diagonalization of the dynamical matrix) and with molecular dynamics. The spectra for methanol are available in this paper 10.1039/c3cp44302g. As in the last lectures, to make this exercise computationally feasible, we will use for MD the efficient Density Functional based Tight Binding (DFTB) method. It requires only a minimal basis but delivers nevertheless reasonable results due to an empirical correction term called *repulsion potential*.

**commented**files from the wiki exercise_7.tgz. Please use command

**tar xvzf exercise_7.tgz**to extract files.

## 1. Task: Computing vibrational spectra for methanol and benzene

$cp2k.ssmp -i vibmet.inp > vibmet.out $cp2k.ssmp -i vibc6h6.inp > vibc6h6.out

To compute the vibrational spectra, we first need to find a minimum energy structure for the systems. The files optc6h6.xyz and optmet.xyz, present in exercise-10.1.tar.gz, contain minimum energy structures. Geometry **optc6h6.xyz** will be the input for the **vibc6h6.inp** and **optmet.xyz** will be the input for the **vibmet.inp**. The following important section (present in the input files) computes the vibrational spectra.

&VIBRATIONAL_ANALYSIS INTENSITIES DX 0.001 &PRINT &PROGRAM_RUN_INFO ON &END &END &END

**.mol**file for c6h6 and methanol obtained with better precision (basis set) is already in the directory. (

**C6H6-VIBRATIONS-1.ref.mol**) Using the command

**diff vib.c6h6.inp vib.c6h6.ref**you can see the difference in the input parameters.

./cp2k.ssmp -i vibmet.inp > vibmet.out

For the intensities, the derivative of the dipole along the normal modes is necessary (see lecture). So the moments are computed in the standard non-periodic fashion:

&DFT BASIS_SET_FILE_NAME ./BASIS_MOLOPT POTENTIAL_FILE_NAME ./GTH_POTENTIALS &PRINT &MOMENTS PERIODIC FALSE &END &END

This code will generate frequencies and intensities of the IR spectrum in the files ** C6H6-VIBRATIONS-1.mol ** and ** MET-VIBRATIONS-1.mol **.
This file can be read by the visualization program **molden**.

* $ ./molden C6H6-VIBRATIONS-1.mol * Use the "normal mode" check in the graphical interface. The spectrum appears. - Compare the one of methanol with experiments (see paper) and the one of benzene with literature on the internet. - Which kind of modes will correspond to stretching of CH and CC bonds? - Try to animate some frequencies, and report the kind of mode corresponding to all peaks. - In the methanol case, you can compare the result you obtained with the one with better basis set and convergence. - Examine the differences between the file vib.c6h6.inp and the vib.c6h6.ref, and the difference in spectra. Discuss.

## 2. Task: Computing vibrational spectra using DFTB molecular dynamics

You will find a fortran program in the repository, called ** dipole_correlation.f90 ** . This is already compiled and the executable is dipole.x.
This program computes the correlation function of the (derivative of) the dipole moment and performs the Fourier transform.

Run ** cp2k ** with the ** md*.inp ** input files (for the two molecules). Note that the dipole moment and derivatives are extracted from simulation and saved in a file dip*traj (check the input). Run first 5000 steps, then edit the file dipole.in and run ** ./dipole.x < dipole.in **.

This will generate the autocorrelation function of the dipole derivative (why?) and its Fourier transform (frequency domain).

**gnuplot**with the command

**plot “file” u 1:2 w l**will help. Is it satisfactory with respect to the DFT static calculation and literature? Why?

- Run 40000 more steps. Check the new results. Discuss what you obtained. Discuss the behavior of the autocorrelation in the time domain.
**WEB SITE Vibrational modes**