Cutoff Effect in the Nosé–Poincaré and Nosé–Hoover Thermostats

Abstract

We performed molecular dynamics (MD) simulations of a Lennard-Jones system and investigated the effect of potential cutoff in the Nose–Poincare and Nose–Hoover thermostats. The Nose–Poincare thermostat is the symplectic algorithm of the Nose thermostat, while the Nose–Hoover thermostat is not a symplectic algorithm. If the potential energy is twice or more differentiable, the Hamiltonian was conserved well in the Nose–Poincare thermostat. If the potential energy is once or less differentiable, however, the Hamiltonian was not conserved, but increased because the continuity of potential energy is required in a symplectic MD simulation. The increase in the Hamiltonian caused the increase in instantaneous temperature, and physical quantities cannot be obtained correctly. It is because the difference in the Hamiltonian effectively increases the set temperature in the equations of motion. On the other hand, the Hamiltonian was not conserved for any cutoff method in the Nose–Hoover thermostat because it is not ...