# Optimization completed on the basis of negligible forces

I am performing relaxed scan in Gaussian (B3LYP/6-31G(d,p)). There are two small organic molecules, one of which is a radical, the other has a benzene ring.

I'm trying to understand the optimization output. Specifically, the line Optimization completed on the basis of negligible forces. I understand that these forces are the maximum and RMS forces above.

Some examples of "negligible forces" from my output file:

        Item               Value
Maximum Force            0.000004
RMS     Force            0.000001
Maximum Displacement     0.019917
RMS     Displacement     0.004747

Item               Value
Maximum Force            0.000002
RMS     Force            0.000000
Maximum Displacement     0.002231
RMS     Displacement     0.000490

Item               Value
Maximum Force            0.000002
RMS     Force            0.000001
Maximum Displacement     0.003132
RMS     Displacement     0.000805


However, some small values like

        Item               Value
Maximum Force            0.000002
RMS     Force            0.000001
Maximum Displacement     0.000666
RMS     Displacement     0.000149


are followed only by Optimization completed. So what does "negligible" mean? How small do they need to be to say they are negligible? Or is this connected to at least one NO in convergence criterion section?

Next question, how reliable is optimization when such message pops up? If it's unreliable, what do I do about this? Would altering the initial geometry fix it when in only happens in a couple of scan steps?

• Please list the displacements (Max and RMS) for each set of forces you've reported. Also, the forces you've reported are very small. You should look at the convergence criteria for Gaussian (under opt in the manual). – LordStryker Jan 9 at 21:03
• @Anna Your energies should be fine but your frequencies could be affected. I've seen responses to specific cases and situations but never a comprehensive answer. Time to bounty up. – LordStryker Jan 21 at 16:15
• Related and at least explains the basic distinction between "optimization completed" and "Optimization completed on the basis of negligible forces": gaussian.com/faq3 Essentially, the negligible forces occurs when the displacement criteria aren't below Gaussians thresholds, but the force criteria are both two orders of magnitude smaller than the threshold. – Tyberius Jan 21 at 16:52
• @LordStryker it's kind of tucked in there, but in the convergence disagreements section, the two bullet points state how define convergence in Gaussian – Tyberius Jan 21 at 17:09
• @LordStryker I see, I misinterpreted your last comment. I'm not certain, I'd be interested to see if the there are known cases where the approximate Hessian used in a typical geom opt is bad and how the quality of the stationary point is related to convergence criteria used. – Tyberius Jan 21 at 17:22

According to the Gaussian Frequently Asked Questions:

In general, a stationary point is found when one of two criteria is met for a point in an optimization calculation:

• All four values listed in the output are smaller than the indicated thresholds.
• The Maximum Force and RMS Force are two orders of magnitude smaller than the thresholds shown, regardless of the values of the displacements.

You indicate three molecules where the second criteria activate - the forces are really, really small. So the optimization gives up.

In your final case, you can see that the displacements are also small, so the first criteria activate.

You then want to know how "reliable" the geometries are when the forces are small, but the displacements are not. That depends a lot on your needs. The optimization quits because such small forces imply a very flat potential energy surface and it may take a long time before "complete" convergence. My guess is that you still have some imaginary frequencies, but that might not matter depending on your needs.

It's worth pointing out that many quantum chemical programs have different criteria for declaring an optimization "finished." (In other words, your calculation in a different program might be declared done because of negligible energy and force/gradient change.)

If you want to push for a true minima, you should take that optimized geometry, run a force / frequency calculation to get an accurate Hessian, and save the result to a checkpoint, then re-start the optimization using the saved Hessian:

%Chk=myfile

One other very important point. If you're doing a scan of intermolecular interactions with B3LYP, you really should be using a dispersion correction such as EmpiricalDispersion=GD3BJ. I often see incorrect repulsive potential energy curves from B3LYP without dispersion corrections.