Overlapping distribution method

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The Overlapping distribution method was introduced by Charles H. Bennett [1] for estimating chemical potential.

Theory

For two N particle systems 0 and 1 with partition function and ,

from

get the thermodynamic free energy difference is

For every configuration visited during this sampling of system 1 we can compute the potential energy U as a function of the configuration space, and the potential energy difference is

Now construct a probability density of the potential energy from the above equation:

where in is a configurational part of a partition function

since



now define two functions:

thus that

and can be obtained by fitting and

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References

  1. Bennett, C.H. (1976). "Efficient Estimation of Free Energy Differences from Monte Carlo Data". Journal of Computational Physics. 22 (2): 245–268. Bibcode:1976JCoPh..22..245B. doi:10.1016/0021-9991(76)90078-4.