Dear Xiaoquan,

your question is by far not 'stupid' ! Please consult this most recent work:

Kin-Yiu Wong and Darrin M. York, "Exact Relation between Potential of Mean Force and Free-Energy Profile", J. Chem. Theory Comput., 2012, 8 (11), pp 3998–4003.

And, as for the general notion of the so-called "free energy", you might wish to cast a look at my most recent work:

https://www.researchgate.net/publication/259080040_Valid_Entropy-Enthalpy_Compensation_Its_True_Physical-Chemical_Meaning

If you have more questions, please do not hesitate to ask them !

Respectfully yours,

Evgeni

Article Valid Entropy-Enthalpy Compensation: Its True Physical-Chemi...

See also this article (Wouter K. den Otter, "Revisiting the Exact Relation between Potential of Mean Force and Free-Energy Profile" J. Chem. Theory Comput., 2013, 9 (9), pp 3861–3865) which  refutes  suggestions made in:

Kin-Yiu Wong and Darrin M. York, "Exact Relation between Potential of Mean Force and Free-Energy Profile", J. Chem. Theory Comput., 2012, 8 (11), pp 3998–4003.

I sense that this is a profound question. The three papers are all difficult to understand. I am finding a way to improve my math.

Dear Evgeni B. Stariko, Cédric Leyrat

As Sun mentioned,  "I sense that this is a profound question. " I think the same way, could you please elaborate or summaries your thoughts about this question.

Xiaoquan and Abishek,

Though this question was posed two years ago, I find myself browsing several sources for my studies regarding SMD and free energy calculations. I do not know about the relationship between PMF and FEP. However, I may be able to direct you to some useful resources regarding SMD and PMF calculation...

The creators of NAMD and VMD at the University of Illinois Urbana-Champaign provide some very useful tutorials which can be found at the following links:

NAMD Free Energy Methods http://www.ks.uiuc.edu/Training/Tutorials/#freeenergymethods 

In the "Stretching Deca-Alanine" tutorial, it is explained that when the SMD simulation is run slowly enough (in their example it is at 0.01A/ps), then the process is reversible. So "the work done during the pulling is equal to the free energy difference of your system between the initial and final states." and the "'reversible work curve' can be considered as an exact PMF."

**The Tcl scripts provided in the tutorial files may be of some use to you as well. Some of them you can use directly (change filenames, etc. as needed), and others should be a guideline for writing your own scripts.

NAMD Tutorial - Part 3 is another SMD simulation, though the PMF is not calculated here.

http://www.ks.uiuc.edu/Training/Tutorials/#namd

Other articles:

• Park, S., F. Khalili-Araghi, E. Tajkhorshid, and K. Schulten. 2003. Free energy

calculation from steered molecular dynamics simulations using Jarzynski's

equality. J. Chem. Phys. 119:3559-3566.

• Park, S. and K. Schulten. 2004. Calculating potentials of mean force from

steered molecular dynamics simulations. J. Chem. Phys. 120:5946-5961.

• Jarzynski, C. 1997. Equilibrium free-energy dierences from nonequilibrium

measurements: A master equation approach. Phys. Rev. E. 56:5018-

5035.

I hope this is helpful somehow.

Best, 

Amy

Dear Colleagues,

...Years go and go, but the story seems to get stuck somehow...

Here is the interesting report of a colleague who could fetch the nerve of the story truly longer time ago, I guess:

http://w3.iams.sinica.edu.tw/lab/jlli/thesis_andy/node15.html

Our Taiwan colleague notes a basic deficiency of our computer simulation approaches:

"The standard Monte Carlo or molecular dynamics simulation methods do not adequately sample regions where the radial distribution function differs drastically from the most likely value, leading to inaccurate values for the PMF. We shall describe two calculation schemes in the following to circumvent this problem."

And here are the collegial suggestions:

1: http://w3.iams.sinica.edu.tw/lab/jlli/thesis_andy/node17.html

2: http://w3.iams.sinica.edu.tw/lab/jlli/thesis_andy/node18.html

Very nice!

The results of the approaches and their discussion might be fetched here:

http://w3.iams.sinica.edu.tw/lab/jlli/thesis_andy/node19.html

Of tremendows importance ought to be the problem of how to simulate the intermolecular interaction correctly and efficiently.

The basic point is the intermolecular interactions do deliver the Potential Energy of the system under study.

Potential Energy is nothing more and nothing less than the System's Energy Stock.

Further, the actual value of the Energy Stock is inevitable, when analyzing the capabilities of the System in question, for it is the Potential Energy, which is converted to the Kinetic Energy, that is, to the Livening/Driving Force of any realistic process.

In the Molecular Modelling, by using the relevant force fields, we might simulate realistic atomic trajectories. In properly analyzing them, we could have ideas about the mechanisms of diverse realistic processes, in which the simulated molecules are participating.

This is why, skillful estimates of PMF anf FE are of great interest and importance.

See the following papers

1. Exact Relation between Potential of Mean Force and Free-Energy Profile

Wong, Kin-Yiu, York, Darrin M. DOWNLOADMagazine:Journal of Chemical Theory and Computation

https://booksc.xyz/book/18728301/8f3b3a

2. Revisiting the Exact Relation between Potential of Mean Force and Free-Energy Profile

den Otter, Wouter K.

Magazine:Journal of Chemical Theory and Computation

https://booksc.xyz/book/22195885/fbfc10