# Calculate free energy for a canonical (NVT) ensemble [closed]

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I have an NVT ensemble of water molecules (liquid) and I want to calculate the Free energy (helmholtz or gibbs) whichever is equivalent to the following relation: $$\Delta F = -RTlnQ \tag{1}$$ I can't calculate the value of Q in a traditional way i.e. $$Q=\frac{[Products]}{[Reactants]}\tag{2}$$ Is there any other way to calculate frame-wise free energy? I have the following values at my disposal currently (can calculate more if given a way):

• N (starting number of molecules - NOT intermediate count of reactants and products)
• V (box dimensions)
• T (frame-wise temperature)
• Total Energy (frame wise)
• Potential Energy (frame wise)
• Pressure (framewise)

I have also looked at FEP (Free energy perturbation) but unsure if that is applicable to an existing trajectory and if yes, then how.

• When I read the question I understood that you had some liquid water at equilibrium. I think it would help if you clarified that you are interested in looking at the system through a transition state and perhaps explain what the initial and final states are; otherwise others may also misunderstand it like I did. – ProfM Jul 25 '20 at 12:09
• I agree, it would help to tell us what it is exactly that you are trying to calculate and how you are doing it, because the question is unclear as it stands. – Godzilla Jul 25 '20 at 12:15
• @ProfM please help me determine this. So my system starts off as water at 300K and then i run an unbiased simulation of the system with a force field that should help me capture some auto ionization. Since it is unbiased it's hard to say what the initial and final states are but there will be an unionized state, a completely ionized state and a tranition state in the middle – fireball.1 Jul 25 '20 at 12:16
• I am no expert in these simulations, so we should wait for someone to provide a proper answer. But I think that editing your question to add this information that you wrote in the comment (starting at 300K, using a force field, interested in describing auto ionization) would greatly help clarify what you need and therefore lead to a good answer. – ProfM Jul 25 '20 at 12:27
• You need to mathematically define a collective variable, so that you can set up biased simulations that explore the particular free energy profile along the collective variable that you are interested in. Unless you are going over the kinetic barriers of interest with the unbiased simulation, the data you have now won't be sufficient for what you want. Also, "frame-wise free energies" don't exist, free energy is a statistical concept of the macrostate, not a particular microstate. – Godzilla Jul 25 '20 at 12:28