The Nosé-Poincaré Method for Constant Temperature Molecular Dynamics

Molecular-dynamics computer simulation [1, 2] has become a standard tool in computational biophysics and chemistry. Traditional molecular dynamics samples configurations from a constant energy or microcanonical distribution. This is often inappropriate since experiments are usually performed at constant temperature (canonical ensemble). While Monte Carlo methods can be used for the canonical ensemble, these methods cannot be used to recover dynamical quantities and time-correlated functions. Hybrid methods using stochastics with molecular dynamics [3] can be used to generate the correct distributions, but they fail to provide correct dynamical quantities due to the discontinuous, stochastic changes in the flow. Methods using ad hoc non-reversible temperature controls [4], and isokinetic constraints [5–7] have also been proposed in the literature. These methods succeed in producing smooth trajectories, but they fail to yield the correct canonical fluctuations in the kinetic energy [1]. This paper will focus on the newer dynamical methods derived from the extended Hamiltonian proposed by Nosé [8, 9]: