Momentum conservation law in the Car-Parrinello method

Momentum conservation law in the Car-Parrinello (CP) method is investigated. In classical molecular dynamics (MD), a total ionic momentum is a conserved quantity when a Lagrangian is invariant by a uniform spatial displacement. The total ionic momentum is no longer a conserved quantity in the original CP case, in which no thermostat and no pressure piston are considered. But in the same manner as classical MD, another conserved quantity can be derived, which is a sum of the total ionic momentum and corresponds to electronic wave functions. In this situation, the nonconservation of the total ionic momentum produces no serious problem. However, when multiple thermostats are introduced in the constant-temperature CP case, a conserved quantity corresponding to momentum does not exist. The fluctuation of the total ionic momentum is amplified strongly in some situations, especially in metallic state. We have analyzed this problem and concluded that it is necessary to add the resetting procedures of the total ionic momentum in this type of simulation.