  Discrete gradients (DG) or more exactly discrete gradient methods are time
integration schemes that are custom-built to preserve first integrals or
Lyapunov functions of a given ordinary differential equation (ODE). In
conservative molecular dynamics (MD) simulations, the energy of the system is
constant and therefore a first integral of motion. Hence, discrete gradient
methods seem to be a natural choice as an integration scheme in conservative
molecular dynamics simulations.
