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# Free energy perturbation

Free energy perturbation (FEP) theory is a method based on statistical mechanics that is used in computational chemistry for computing free energy differences from molecular dynamics or Metropolis Monte Carlo simulations. The FEP method was introduced by R. W. Zwanzig in 1954.[1] According to free-energy perturbation theory, the free energy difference for going from state A to state B is obtained from the following equation, known as the Zwanzig equation:

$\Delta G(A \rightarrow B) = G_B - G_A = -k_B T \ln \left \langle \exp \left ( - \frac{E_B - E_A}{k_B T} \right ) \right \rangle _A$