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.

$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

./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.

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).