AIMD - RDF - PMF - pKa calculation?

[jinylee]

I think I'm in a deep mis-understanding now.
As a result of NVT calculations, we can easily draw RDF(radial distribution function),
PMF(potential of mean-force) = -kB(boltzman-constant)*T*ln(RDF). Is this formula true?
If it is, easily find PMF with a simple operation,
and then, can I think of the difference between the two energy valleys as Gibbs free energy difference(ΔG)?

When Gibbs free energy is approximated by Helmholtz energy, ΔA, can I easily get the pKa through pKa = ΔG/2.303RT ?
If my assumptions are correct, why are you doing Umbrella sampling and special(difficulty) processing?

[support_vasp]

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