Why doesn't the force eventually tend to zero when using CP2K for Slow-growth simulation

[ice ZQing]

Hello everyone,

I am currently learning how to perform slow-growth simulations in CP2K to obtain free-energy profiles. I followed the exercise “NaCl Free Energy Dissociation” from the CP2K website (exercises:2015_ethz_mmm:nacl_free_energy), which uses PMF to compute the free-energy surface.

Based on that, I tried to reproduce a similar NaCl dissociation process using the following constraint setup:

&CONSTRAINT

    &COLLECTIVE

      COLVAR 1

      INTERMOLECULAR

      TARGET [angstrom] 2.4

      TARGET_GROWTH [angstrom*fs^-1] 1E-4

      TARGET_LIMIT [angstrom] 6.0

    &END COLLECTIVE

    &LAGRANGE_MULTIPLIERS

      COMMON_ITERATION_LEVELS 1

    &END

 &END CONSTRAINT

This means that the Na–Cl distance is slowly increased from 2.4 Å to 6.0 Å at a rate of 1E–4 Å/fs.
The simulation itself runs smoothly, but the results are somewhat puzzling.

As shown in the figure below, as the distance increases, the recorded constraint force gradually approaches a small negative value close to zero, instead of approaching zero from either side. Because of this, when I integrate the force to obtain the free-energy profile, the resulting free energy continues to increase in the long-distance region rather than converging to a plateau — which does not seem physically reasonable for a dissociating ion pair.

For reference, my system contains 1 Na⁺, 1 Cl⁻, and 63 H₂O molecules, exactly the same as in the CP2K exercise mentioned above. My full input files are attached below.

I would greatly appreciate any suggestions or insights into why the constraint force at large separations does not decay to zero, and how to correctly obtain a converged free-energy profile.

Thank you very much!