Dynamical simulation methods velocity propagation

Usually refers to a method of solving Newton s equations of classical mechanics numerically, in order to propagate the positions and velocities of a system of molecules forward in time and thus to explore the phase space of the system. See Molecular Dynamics and Hybrid Monte Carlo in Systems with Multiple Time Scales and Long-range Forces Reference System Propagator Algorithms Molecular Dynamics DMA Molecular Dynamics Simulations of Nucleic Acids Molecular Dynamics Studies of Lipid Bilayers and Molecular Dynamics Techniques and Applications to Proteins. 

An important advance in making explicit polarizable force fields computationally feasible for MD simulation was the development of the extended Lagrangian methods. This extended dynamics approach was first proposed by Sprik and Klein [91], in the sipirit of the work of Car and Parrinello for ab initio MD dynamics [168], A similar extended system was proposed by van Belle et al. for inducible point dipoles [90, 169], In this approach each dipole is treated as a dynamical variable in the MD simulation and given a mass, Mm, and velocity, p.. The dipoles thus have a kinetic energy, JT (A)2/2, and are propagated using the equations of motion just like the atomic coordinates [90, 91, 170, 171]. The equation of motion for the dipoles is... 

Molecular dynamics (MD) simulations provide a detailed description of complex systems in a wide range of time and spatial scales.138 Simulations involve a statistical uncertainty component as the result of the finite length of the simulation.139 143 MD methods generate a series of time-correlated points in phase space by propagating a suitable starting set of coordinates and velocities according to Newton s second equation. This kind of computational simulations are useful in studies of time evolution of a variety of systems biological molecules, polymers, or catalytic materials, and in a variety of states crystal, aqueous solutions, or in the gas phase. 

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