A method for carrying out molecular dynamics simulations in which the potential energy U of the molecular system is constrained at its initial value is developed and thoroughly tested. The constraint is not introduced within the framework of the Lagrange multipliers technique, rather it is fulfilled in a natural way by carrying out the simulations in terms of suitable sets of delocalized coordinates. Such coordinates are defined by an appropriate tuning of the Baker, Kessi, and Delley internal delocalized nonredundant coordinates technique [J. Chem. Phys. 105, 192 (1996)]. The proposed method requires multiple evaluations of energy and gradients in each step of the molecular dynamics simulation, so that constant U simulations suffer some overhead compared to ordinary simulations. But the particular formulation of the delocalized coordinates and of the equations of motion greatly simplifies all the various steps required by the Baker's technique, thus allowing for the efficient implementation of the method itself. The technique is reliable and allows for very high accuracy in the potential energy: conservation during the whole simulation. Moreover, it proved to be free of drift troubles which can occur when standard constraint methods are straightforwardly implemented without the application of appropriate correcting techniques. (C) 2004 American Institute of Physics.