The finite difference thermodynamic integration, tested on calculating the hydration free energy difference between acetone and dimethyl amine in water Abstract: A new technique is proposed to compute by Monte Carlo (or molecular dynamics) computer simulation the hydration free energy differences. The method, called finite difference thermodynamic integration, is a combination of the thermodynamic integration and the perturbation method. It was compared with thermodynamic integration over two different paths and the perturbation method on computing the solvation free-energy difference between the dilute aqueous solution of acetone and dimethyl amine. Finite difference thermodynamic integration was found to have the best convergence characteristics among the methods tested.