Can anyone help me by explaining how the normal mode coordinates are written in Gaussian16 frequency calculations?
I understand that they are normalized and hence can be considered "unitless" but I am more concerned if they are the normalized, mass-weighted cartesian coordinates or just the normalized cartesian coordinates? If they are mass-weighted, how can I extract just the cartesian coordinates from them? Any help is much appreciated.
Gaussian prints out harmonic force constants that have been mass-weighted (you can check this by re-running frequency calculations and changing isotopic masses with e.g., H(iso=2) in the molecule specification.
The coordinates are Cartesian displacements from the equilibrium geometry - AFAIK, you don't need to do any further transformation to these displacements to e.g. animate or project along the normal mode from a stationary point.
'Normal' means a vector space in normal coordinates that provides a set of n independent harmonic oscillators associated with n eigenvalues from which we can determine the vibrational spectrum of a polyatomic molecule. Normal coordinates can be shown to be linear combinations of internal and Cartesian coordinates. There is a very annoying mix-up over notation in the literature, but please check these references out:
E. B. Wilson. Some Mathematical Methods for the Study of Molecular Vibrations. J. Chem. Phys., 9:76–84, 1941.
https://gaussian.com/wp-content/uploads/dl/vib.pdf
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