Small but modest displacements at negligible forces from DFT

When looking at a Gaussian log file today, I noticed the following information in the convergence criterion section after an analytical frequency calculation was performed:


`Item Value Threshold Converged?
 Maximum Force 0.000001 0.000450 YES
 RMS Force 0.000000 0.000300 YES
 Maximum Displacement 0.000190 0.001800 YES
 RMS Displacement 0.000030 0.001200 YES`


This struck me as odd. How could the forces be *so low* but the maximum displacement still be non-negligible? Does anyone have any hypothesis about why this phenomenon would occur? This makes me wonder if the convergence condition for the maximum displacement is unreasonably low if essentially no acting forces can result in a maximum displacement that's merely 1 order of magnitude lower than the default threshold. I believe the force units are Hartrees/Bohr and the distance units are angstroms.




For clarity I will assume Gaussian performs a generic Newton-Raphson minimization (NR), which should suffice to explain the phenomenon.
In NR, the linear problem
$$
\nabla\nabla^\ast E \Delta + \nabla E = 0
$$
is solved, where $\Delta$ is the displacement. In order to arrive at "large" displacements despite "small" (but non-zero) forces ($-\nabla E$), it suffices for the Hessian ($\nabla\nabla^\ast E$) to have eigenvalues close to 0 itself, because a small number is divided by an even smaller number. This happens when the potential energy surface is very flat.


 3