In molecular dynamics, Hamiltonian systems of differential equations are numerically integrated using some symplectic method. Symplectic integrators are simple algorithms that appear to be wellsuited for large scale simulations. One feature of these simulations is that there is an unphysical drift in the energy of the system over long integration periods. A drift in the energy is more obvious when a relatively long time step is used. In this article, a special approach, based on symplectic discretization and momenta corrections, is presented. The proposed method conserves the total energy of the system over the interval of simulation for any acceptable time step. A new approach to perform a constanttemperature molecular dynamics simulation is also presented. Numerical experiments illustrating these approaches are described.