I'd say yes. The separation energy depends a lot on the path taken. That's why constant velocity pulling is considered inaccurate, compared to e.g. umbrella sampling. You need to cover the energy changes due changes in confirmation while detaching - the entropie contribution.

Dear Ehsan Shahini

I am not an expert, so take my opinion as it is, and I am open to any discussion.

My understanding is that people refer to the potential of the mean force as the free energy profile along a well defined reaction coordinate (such as angles, axis and so on).

From a pure theoretical perspective, the free energies are thermodynamic functions of your system, which are exact differentials (https://chem.libretexts.org/Bookshelves/Physical_and_Theoretical_Chemistry_Textbook_Maps/Book%3A_Mathematical_Methods_in_Chemistry_(Levitus)/09%3A_Exact_and_Inexact_Differentials/9.03%3A_Differentials_in_Thermodynamics_-_State_and_Path_Functions).

This means that, if you are in state A at therm equil, and in state B in therm equil, the free energy difference is uniquely defined by the states (so p, T, V etc) of your system and therefore the difference cannot depend on how you arrived from state A to B. From your image, it would seem something like: interaction among graphene sheets (state A) and graphene sheets far enough to be non interacting (state B). Therefore you have different paths (reaction coordinates) but the same start and end points A and B.

So I think that the point is to what degree does the PMF correspond to the exact free energy difference? Which is a honest and absolutely non-trivial question, and has been asked before also (https://www.researchgate.net/post/Difference-between-Potential-of-Mean-Force-and-Free-Energy-Profile).

I know that this answer is not really an answer, but I think that what you are asking is not a stupid question at all.

Best,

Nicola

P.S. I just saw that you ask if the CALCULATION depends on the reaction coordinate, and in that case I would say yes. As you see in the cited papers in the other answer that I linked, you should correct your calculations with terms like jacobians that depend on the type of reaction coordinate that you are using, so in general the RC is an (if not the most) important factor in PMF predictions.

Heyyy,

This is a PMF profile of 5 layer graphene which I calculated in the past for fun :). I performed it with constant velocity pulling. It looks like an AFM result, isn't it? :)

Since this is the response of the nature, you should observe the same thing either you choose a theoretical or experimental approach. Physicists love such fancy phrases.(I'm also a physicist :D :D)

As Zhaoxi Sun said, since the free energy is a state function, it doesn't depend on how you calculate it. There are path dependent/independent methods to calculate these free energy profiles.

As Norman Geist mentioned, constant velocity pulling gives inaccurate results (e.g. due to the dissipative forces) depending on the choice of simulation parameters (e.g. low and high pulling velocities) compared to equilibrium methods.

Thank you all for your thorough answers. I asked the same question in GROMACS forum and here's Justin Lemkul's quote which seems to be in a little contrast with previous answers.

"You’ll get different results as you’re illustrating two different movements; overall COM separation might be the same but there’s no real reason to think these will produce similar results. The PMF you calculate does depend on path; look into early work by Jarzynski for some related fundamental concepts."