Hi everyone,
When doing optimization and frequency computation on molecules, it's common to have imaginary frequencies, sometimes more than one, many times undesired.
Sometimes tight requirements on the optimization and scf convergence help, especially with fine integration grid.
However... I've witnessed some examples when all that is simply not enough. You end with one or two spurious frequencies you can't supress.
After asking many times, the usual answer I get is 'just ignore them, it's numerical noise'.
So my questions are: What's this numerical noise? What is its origin and its meaning? Is it really safe to ignore it? How to tell when it's nois and when is an unwanted mode?
I may be naïve, but if I get two undesired imaginary frequencies, that is two degrees of freedom I'm not correctly accounting for in the calculation of entropy, and thus the free energies I get from this computation are meaningless...
Can someone give some guidance on this?
Thanks in advance.
In general, "numerical noise" refers to the errors inherent in calculating numerical derivatives on a grid which, of course, translates into errors in the frequencies. I suppose they are more readily recognizable in the low or imaginary frequency cases you mention. Some low frequency modes could be hindered rotations. If you animate the modes, you may be able to see the behavior. If the frequencies are small, their effect on thermodynamic properties cannot be significant.
Numerical computation generally involves errors due to rounding, truncation, and in bad cases, saturation or wrap around. These errors are deterministic --- they are completely determined by the input, but for analysis purposes these errors can be modeled as additive random noise, which is termed "numerical noise". Each step in the computation is viewed as a source of additive random noise which is also white if saturation and wrap around are not involved. Numerical noise causing spurious frequencies could be the result of two things: (1) There is saturation or wrap-around in the computation. (2) white numerical noise from early stages of the computation was shaped by later stages into having some prominent frequency components.
I do not know if the spurious frequencies that you get are really due to numerical noise, but you can determine what numerical noise you have by carefully analyzing the numerical processing scheme.
I think the easiest way to test would be to displace the atoms along the displacement vectors associated with a mode and see if it converges to a solution with no imaginary frequencies.
Dear B.R. Ramachandran:
Definitely some low frequency modes can be considered hindered rotations. And if treated as such, then it is true that their contribution to free energy is small as stated by S. Grimme (Chem. Eur. J. 2012, 18, 9955). But if you consider vibrational entropy, the term -ln(1-e(-hv/kT)) becomes increasingly important as modes become lower in frequency. Of course, this applies to real frequencies, not imaginary modes.
Entropy: A concept that is not a physical quantity
https://www.researchgate.net/publication/230554936_Entropy_A_concept_that_is_not_a_physical_quantity
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