量子化学第3章计算方法.ppt

Other integrators for MD simulations Although the Verlet leapfrog method is not particularly fast, this is relatively unimportant because the time required for integration is usually trivial in comparison to the time required for the force calculations. The most important concern for an integrator is that it exhibits low drift, i.e. that the total energy fluctuates about some constant value. A necessary (but not sufficient) condition for this is that it is symplectic. Crudely speaking, this means that it should be time reversible (like Newton’s equations), i.e. if we reverse the momenta of all particles at a given instant, the system should trace back along its previous trajectory. Other integrators for MD simulations The Verlet method is symplectic, but methods such as predictor-corrector schemes are not. Non-symplectic methods generally have problems with long term energy conservation. Having achieved low drift, would also like the energy fluctuations for a given time step to be as low as possible. Always desirable to use the largest time step possible. In general, the trajectories produced by integration will diverge exponentially from their true continuous paths due to the Lyapunov instability. However, this does not concern us greatly, as the thermal sampling is unaffected ? expectation values unchanged. Choosing the correct time step… 1. The choice of time step is crucial: too short and phase space is sampled inefficiently, too long and the energy will fluctuate wildly and the simulation may become catastrophically unstable (“blow up”). 2. The instabilities are caused by the motion of atoms being extrapolated into regions where the potential energy is prohibitively high (e.g. atoms overlapping). 3. A good rule of thumb is that when simulating an atomic fluid, the time step should be comparable to the mean time between collisions (about 5 fs for Ar at 298K). 4. For flexible molecules, the time step should be an order