FEP Basic Theory Overview

For two systems with the same number of particles and different potential energies U₀(x) and U₁(x), the free energy difference between them can be calculated through the following FEP formula [10]:

where b = 1/kT, ΔU = U₁(x) −U₀(x) is the difference in potential, and the average is over the ensemble of the initial state corresponding to a system with potential energy U₀(x). Q is the partition function,

The result above follows from writing the partition function Q₁ as

The ratio of the partition functions is then just the ensemble average of the initial state. Similarly, the free energy difference can also be written in terms of an average over the ensemble of the final state: