The thermodynamic integration technique to evaluate free energy differences by molecular dynamics simulations is analyzed. The hydration of the ions Na+ , K+ , Ca++ , F−, Cl−, and Br− is used as the process to illustrate the potential utility of the method. A neon–water system is used as a reference system. The parameters that influence the performance and accuracy of the thermodynamic integration, in which the potential interaction parameters are gradually and continuously changed, are studied. These parameters include the total simulation time, the magnitude of the time step for the numerical integration of the equations of motion, the system size, and the cutoff radii for the intermolecular interactions. Fast convergence is found for the Gibbs free energy difference between Ne and Na+ with respect to total simulation time. The time step and system size are relatively unimportant. The use of cutoff radii, for the ion–water but especially unfortunately also the water–water intermolecular interactions, seriously influences the results obtained. A simple correction for the use of cutoff radii cannot be made. Results are compared to experimental values.