Correcting the entropy for errors introduced by low modes

useful papers

"Pitfalls in Computational Modeling of Chemical Reactions and How To Avoid Them" https://pubs.acs.org/doi/10.1021/acs.organomet.8b00456

"Use of Solution-Phase Vibrational Frequencies in Continuum Models for the Free Energy of Solvation" https://pubs.acs.org/doi/abs/10.1021/jp205508z

"Supramolecular Binding Thermodynamics by Dispersion-Corrected DensityFunctional Theory" https://onlinelibrary.wiley.com/doi/epdf/10.1002/chem.201200497

why the correction is needed

low energy modes can be; cluster breathing and torsion modes, real vibrations or the result of hindered rotors, and they can also be due to computational artefacts. Changes in convergence or in geometry can shift these modes in wavenumber.
this combines to be an important issue because low energy modes contribute significantly to the entropy term, after-all these modes are about sampling configuration space, the lower the mode, the more space can be sampled the larger the entropy
close to 0cm^-1 small changes in frequency can lead to large changes in entropy corrections!
in addition vibrations and rotations contribute through different formulae to the entropy
lastly small changes in geometry especially in loose clusters or transition states can move a mode in and out of the cut-off region used by many codes
the cut-off at which point some treatment of low modes needs to be made differs, but generally modes under 50-150cm^-1 can be simply missed out or set to a given value to avoid large errors, (this number is for room tem 298.15 Kelvin, and should be increased for higher temperatures!)

how to carry out the correction

GoodVibes is a python code available to calculate corrections to the entropy for Gaussian output files https://github.com/bobbypaton/GoodVibes

Cramer and Truhlar approach all frequencies below the cut-off are uniformly shifted up to the cut-off value before entropy calculation in the RRHO approximation

Grimme approach all frequencies below the cut-off are obtained from the free-rotor approximation, for those above the RRHO expression is retained

the program will attempt to parse the level of theory and basis set used in the calculations and then try to apply the appropriate vibrational (zpe) scaling factor aken from the Truhlar group database.

install the code as instructed on the website
example

python -m goodvibes test.log -q grimme -f 100 -t 298.15 -v 1.0

the -m allows python codes not in the standard path be used, however one problem is that you cannot have any other python codes in the directory!

-q truhlar or -q grimme, Grimme is the default

-f x specifies a cut-off frequency in wavenumbers, the default is 100

-t x specifies the temperature in Kelvin

-c corrects for liquids (gas is the standard 1atm) but a liquid should be 1 mol/L

-v x applies a scaling factor for harmonic frequencies based on Truhlar group, use -v 1.0 when no scaling is desired, gaussian uses 1/1.2=0.8929 by default

there are more options see the program notes!

the TS should and G(T) should match what gaussian has!
the T•qh-S and qh-G(T) stands for quasi-harmonic and are the numbers you want