Replica-Exchange Molecular Dynamics Simulations for Various Constant Temperature Algorithms

In the replica-exchange molecular dynamics method, where constant-temperature molecular dynamics simulations are performed in each replica, one usually rescales the momentum of each particle after replica exchange. This rescaling method had previously been worked out only for the Gaussian constraint method. In this letter, we present momentum rescaling formulae for four other commonly used constant-temperature algorithms, namely, Langevin dynamics, Andersen algorithm, Nos\'{e}-Hoover thermostat, and Nos\'{e}-Poincar\'{e} thermostat. The effectiveness of these rescaling methods is tested with a small biomolecular system, and it is shown that proper momentum rescaling is necessary to obtain correct results in the canonical ensemble.