Manifold Correction Method for the Nosé–Hoover and Nosé–Poincaré Molecular Dynamics Simulations

We introduce the manifold correction method to molecular dynamics (MD) simulations with the Nose–Hoover and Nose–Poincare thermostats. The manifold correction method was originally developed in astronomy, as an accurate numerical method for many body systems. Because the Nose–Hoover thermostat is not a symplectic algorithm, the quantity which is conserved analytically is not conserved but increases in actual MD simulations. Using the manifold correction method, this quantity is completely conserved, and it makes the MD simulation stable. Because the conservation of this quantity is required in the proof that the Nose–Hoover thermostat gives the canonical ensemble, the manifold correction method guarantees to provide the correct statistical ensemble. Although the time development of the Nose–Poincare thermostat is described as a symplectic algorithm, if the interatomic potential energy is truncated, the Nose–Poincare thermostat is no longer symplectic. In this case, the Hamiltonian increases, and temperatu...

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