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I'm having some trouble with my POTIM value.

I'm trying to calculate the vibrational frequency of an absorbed/adsorbed species.

What I've been doing is as follows
(1) Optimize structure with EDIFFG = 1E-4 and EDIFF = 1E-5
(2) Set all degrees of freedom as F in structure and T for adsorbate/absorbate
(3) Submit vibration calculation with IBRION = 5 and NFREE = 2

I've been varying POTIM to see how my frequency values change and what a good POTIM is.

What I'm seeing in a frequency vs POTIM plot is something that looks like a deformed parabola with a flat (minima) region between POTIM=0.03 and 0.10 and the correspondingly appropriate positive upswings below 0.03 and above 0.10.

I'm comfortable with the upswing above 0.10 as I realize this is the breakdown of the simple harmonic oscillator approximation, but what I don't understand is why there's this big spike below 0.03. The spike below 0.03 has been between 20 and 30 wavenumbers (cm^-1) is in the incidences that I've calculated and thus corresponds to an energy differential larger that which might be expected from a miscalculation of the local energy minimum from EDIFFG and EDIFF.

Can someone tell me why there is this large jump in calculated frequency for small POTIM values?

POTIM has to be chosen small (about 0.015) to make sure that the harmonic approximation is valid for the calculation of the frequency.
(of course the maximum POTIM which gives good results depends on the system under investigation)