Vibrational frequency analysis

Note

The scripts for this section of the tutorial can be found in li_mgo/4_li-mgo_vib. It is worth highlighting that the transition state structure cimg.pun was obtained from the _dl_find.pun file generated in the oxygen 7-5 NEB calculation.

This section of the tutorial will cover how to perform a vibrational frequency analysis on the equatorial hole migration transition state.

First, the transition state is read into ChemShell using the script vib_analysis.py. The rest of the script is similar to the geometry optimisation in Localising the electron hole section, with the exception of the thermal=True argument in the optimisation method. This specifies that a vibrational frequency analysis should be performed rather than an optimisation. This involves the construction of a finite-difference Hessian from which thermal contributions will be calculated.

Caution

It is necessary to use the same active region as used in Localising the electron hole section (regions 1-3) to obtain meaningful results. Therefore, it is highly recommended to use the taskfarmed parallelisation to ensure timely completion of the calculation.

Near the end of the ChemShell output file, DL-FIND will report the symmetrised Hessian matrix, eigenvalues and thermochemical analysis results. The key parameters that are of attention are the vibrational frequency modes, zero-point energy and the energetic and entropic vibrational contributions. The thermochemical analysis results should look similar to the condensed output illustrated below:

Thermochemical analysis
Temperature:     300.00 Kelvin
Modes assumed to have zero vibrational frequency:  0
 Mode     Eigenvalue Frequency Vib.T.(K)        ZPE (H)   Vib. Ene.(H)      - T*S (H)
    1  -0.0000536602    37.656i
    2   0.0010256750   164.630   236.866   0.0003750549   0.0006238386  -0.0011988288
    3   0.0010404380   165.811   238.564   0.0003777444   0.0006218450  -0.0011923846

...

total vibrational energy correction to E_electronic   0.2612139968 H
total ZPE     864987.58705 J/mol
total E vib   325126.72265 J/mol
total S vib     1680.99020 J/mol/K
Crossover temperature for tunnelling        8.62271 K

You should find that the thermochemical analysis results contain one mode with an imaginary frequency. Given that a transition state should only have one imaginary frequency, these results are consistent with the climbing image being representative of the equatorial hole migration transition state.