Another class of methods are the alchemical methods, where the thermodynamic path between two end states is defined and the free energy change is calculated based on statistical mechanical analysis of the simulations. Based on the theoretical foundation of Kirkwood, Zwanzig and Bennett among others, three widely used alchemical methods are Thermodynamic Integration (TI), Free Energy Perturbation (FEP), and Bennett Acceptance Ratio (BAR). In these approaches, the alchemical transformation from the initial state to the final state usually is characterized by a coupling parameter l varying from 0 to 1 and the free energy difference is calculated as the summation of alchemical transformation between fixed-l states.