A novel method for the calculation of the free energy difference between two states of a molecular system is presented. The method, an extension of thermodynamic integration, treats the coupling parameter lambda as a variable in an extended Hamiltonian formulation and propagates it with the physical coordinates. In the resulting generalized ensemble, the crossing of barriers in the physical space is enhanced. The free energy difference is determined by integrating the reversible work required to move lambda from zero (corresponding to the initial state) to one (corresponding to the final state). Examples are presented to illustrate the method. (C) 2003 Elsevier B.V. All rights reserved.