====== 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 [[doi>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//.

<note tip>
You should run these calculations on your virtual machine. We will make severe approximation to fit this on your QM. 
Download, as usual, the **commented** files from the wiki {{exercise_7.tgz|}}.
Please use command  **  tar xvzf exercise_7.tgz  **  to extract files.
</note>

===== 1. Task: Computing vibrational spectra for methanol and benzene =====
<code>
$cp2k.ssmp -i vibmet.inp > vibmet.out
$cp2k.ssmp -i vibc6h6.inp > vibc6h6.out

</code>

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.

<code>
&VIBRATIONAL_ANALYSIS
 INTENSITIES
 DX 0.001
   &PRINT
     &PROGRAM_RUN_INFO ON
     &END
   &END
&END
</code>

<note warning>The ** .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.  
</note>



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

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:
<code>
 &DFT
    BASIS_SET_FILE_NAME ./BASIS_MOLOPT
    POTENTIAL_FILE_NAME ./GTH_POTENTIALS
    &PRINT
      &MOMENTS
       PERIODIC FALSE
      &END
    &END
</code>

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**. 

<note important>
  
  * $ ./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.
</note>



===== 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).

<note important>  - Check the result. **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 [[https://www.cfa.harvard.edu/hitran/vibrational.html|Vibrational modes]] **
</note>