I have a 1D histogram, I have binned the data, I got the frequencies corresponding to each bin. I have weighting factor/weights as well. How do I calculate free energies from weights?
P.S. The data is not from REMD or metadynamics simulations.
If I'm not wrong, the free energy surface should be equal to dG = -RT ln P, where P is the probability.
If you multiply the frequencies by the weights, you should bet probabilities. Check, if the integral of the weighted frequencies yields 1. Otherwise you have to normalize the histogram. Next, just scale the logarithm of the normalized weighted frequencies by the factor -RT.
You need to be more specific. Do you have an analog of the temperature or some energy to think about the free energy?
From what I understood, you merely have divided data into bins and you know their frequencies. From this information, you can only compute the entropy of the distribution.
It is necessary to use specific numerical method ( Mbar or thermodynamics integation melthod )
If I understood your question, with reweighting and energy histogram methods you can calculate the free energy barrier and interface tension in a simple way. Please see Phys. Rev. D 46 (1992) 3678, and references therein, mainly by J. Lee and J.M. Kosterlitz, for details.
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