We present a new multiple time stepping (MTS) integrator for
constant temperature molecular dynamics
simulations, the Targeted Mollified Impulse method (TM),
which combines a stabler version of Verlet-I/r-RESPA (
reversible
REference
System
Propagator
Algorithm), called Mollified Impulse (MOLLY) and a self-consistent
dissipative leapfrog integrator commonly used in dissipative particle
dynamics (Hoogerbrugge,
et al., Europhys. Lett. 19 (1992) 155).
TM introduces the Langevin coupling in a targeted manner to stabilize
the MTS integrator such that the total linear momentum is conserved
and less randomness in slower modes is imposed.
Numerical analysis of simple model problems confirms that TM samples from
the canonical ensemble. The method might be helpful in exploring large
volumes of configuration space. Possible applications include kinetics
calculations such as conformational transition rates, computation of
structural quantities from a canonical ensemble, and approximation of
dynamical quantities from a canonical ensemble. We present evidence of
the last two by showing that both the radial distribution functions
and the self-diffusion coefficient are correctly computed from the
simulations of flexible TIP3P waters (Jorgensen et al.,
J. Chem. Phys. 79(1983):296) using TM with outermost time
step of upto
fs and the innermost time step of
fs. Compared to
leapfrog with time step of
fs, the implementation of TM achieves
a six-fold computational speedup, whereas
impulse with outer time
step of
fs and inner time step of
fs only achieves a
three-fold speedup. The overhead associated with
mollification is low. Extension of TM to handle larger molecules is
straightforward.
