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I worked with gaussian to simulate vibrational IR and Raman spectra. For that purpose, I scaled the vibrational frequencies from my gaussian calculation with the scaling factors from this website:

https://cccbdb.nist.gov/vsfx.asp

I am writing my bachelor thesis now and wonder where the website found the scaling factors. On the bottom of the page is a reference to a paper.

Some of the above values were taken from
A.P. Scott, L. Radom, Harmonic Vibrational Frequencies: An Evaluation of Hartree-Fock, Moller-Plesset, Quadratic Configuration Interaction, Density Functional Theory and Semiempirical Scale Factors, J. Phys. Chem. 100, 16502, 1996
In this table many scale factors were assumed to be the same for different basis sets and similar methods.

I read the paper and did not find the scale factors I used in my work. For my thesis, I need papers to cite, so I want to ask, how did they assume the scale factors, or where did they find the other scale factors?

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I have a different page on the NIST website (https://cccbdb.nist.gov/vibscale.asp) that gives uncertainties in the scaling factors. I believe many of these were actually established by NIST themselves from the database itself.

But many of them are in the paper you cite, in Table 1:

table of vibrational scaling factors

As you probably know, one problem is that most quantum chemical methods calculate harmonic vibrational frequencies - and many vibrations have at least some anharmonic character.

There are many more recent vibrational scaling papers. Basically, authors will compile high-quality experimental vibrational spectra, then compare individual experimental frequencies against computed frequencies from the various methods via linear least-squares regression for one scaling factor.

A somewhat more recent compilation by Leo Radom can be found in "An Evaluation of Harmonic Vibrational Frequency Scale Factors" J. Phys. Chem. A 2007, 111, 45, 11683–11700

There are a bunch of other methods for "correcting" computed vibrational frequencies. There's a review in Molecular Spectroscopy—Experiment and Theory and undoubtedly by other authors as well.

For example Grimme argues on scaling atomic masses instead of one-parameter scaling factors in a recent paper. I still expect the single scale factor to remain popular for simplicity, though.

At some point, perhaps anharmonic vibrational calculations will be more tractable, though the NIST group indicated in 2013 that anharmonic calculations may not be more accurate than scaled harmonic.

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