A new method for the calculation of free energy differences by molecular dynamics simulations of molecular systems is presented. The main characteristic of the method is that the three-dimensional physical space is augmented by a further dimension. This allows the system to circumvent energy barriers in three-dimensional space. When simulating physical (three-dimensional) states, the dynamics along the 4th coordinate is uncoupled from the dynamics described with the original three coordinates. In the method presented here, free energy differences between physical states are determined using pathways leading over states where the dynamics along all four dimensions are coupled. Due to the barrier lowering in four dimensions, an increase of efficiency can be expected when low free energy physical states are separated by high barriers. The method is tested by application to an atomic liquid.