Overlapping distribution method
- Overlapping distribution method
-
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 Q0 and Q1 ,
from F(N,V,T) = − kBTlnQ
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
ΔU = U1(sN) − U0(sN)
Now construct a probability density of the potential energy from the above equation:
where in p1 is a configurational part of a partition function
since
ΔF = − kBTln(q1 / q0)
lnp1(ΔU) = β(ΔF − ΔU) + lnp0(ΔU)
now define two functions:
thus that
f1(ΔU) = f0(ΔU) + βΔF
andΔF can be obtained by fitting f1 and f0
Notes
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