where ${\delta\rho_i},{\pi_i}$ are the mass normalized position and momentum vectors. The above equation corresponds to a set of **uncoupled harmonic oscillators**:
The **molden** file contains the eigenvalues and eigenvectors of the Hessian matrix. The eigenvectros corresponds to the atomic displacements and the eigenvalues are the vibrational frequencies. Your task is to devise a method to display the vibrational modes, making use of the *vibr_displacements* and *atoms*(ase.Atoms object) returned by the function *read_molden*.
For the purpose, complete the skeleton function *get_trajectory*, which is initialized in a cell below, and make use of the ase.Atoms class, which is initialized with a list of atomic elements and their respective coordinates.
**Hint**: Write the equation of motion (Lagrangian) for the equation above and find the time evolution of the atoms for a given normal mode.
%% Cell type:markdown id: tags:
### Task 2
- Compare the vibrational frequencies 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.
%% Cell type:markdown id: tags:
## Funcitons:
**read_molden(file):**
input:
file - molden filename
return:
atoms - ase.Atom object
frequency - vibrational frequencies
vibr_displacements - vibrational atomic displacements in Angstrom
**get_trajectory(mode):**
input:
mode - mode number
return:
trajectory - trajectory of atomic displacements for specified mode
where ${\delta\rho_i},{\pi_i}$ are the mass normalized position and momentum vectors. The above equation corresponds to a set of **coupled harmonic hoscillators**:
The **molden** file contains the eigenvalues and eigenvectors of the Hessian matrix. The eigenvectros corresponds to the atomic displacements and the eigenvalues are the vibrational frequencies. Your task is to devise a method to display the vibrational modes, making use of the *vibr_displacements* and *atoms*(ase.Atoms object) return by the function *read_molden*.
For the purpose, complete the skeleton function *get_trajectory*, which is initialized in a cell below, and make use of the ase.Atoms class, which is initialized with a list of atomic elements and their respective coordinates.
**Hint**: Write the equation of motion (Lagrangian) for the equation above and find the time evolution of the atoms for a given normal mode.
%% Cell type:markdown id: tags:
### Task 2
- Compare the vibrational frequencies 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.
%% Cell type:markdown id: tags:
## Funcitons:
**read_molden(file):**
input:
file - molden filename
return:
atoms - ase.Atom object
frequency - vibrational frequencies
vibr_displacements - vibrational atomic displacements in Angstrom
**get_trajectory(mode):**
input:
mode - mode number
return:
trajectory - trajectory of atomic displacements for specified mode