Molecular Dynamics Simulations: Energy Conservation

This lecture covers the concept of energy conservation in Hamiltonian systems with time-independent potentials, focusing on the conservation of total energy in Newton, Lagrange, and Hamilton equations of motion. It also discusses the importance of conserving energy during numerical integration, the choice of time step based on the fastest motion in the system, and the use of multiple time step integrators with constraint algorithms to keep bonds fixed. The lecture emphasizes the properties of an ideal propagator, such as accuracy, conservation of energy and momentum, low CPU and memory cost, error bounds, time reversibility, and symplectic nature. Various integrators and constraint algorithms are explored, including Velocity Verlet and Lagrange multipliers.