Ruslan L. Davidchack

Ruslan L. Davidchack, Richard Handel, M. V. Tretyakov

We present a new method for isothermal rigid body simulations using the quaternion representation and Langevin dynamics. It can be combined with the traditional Langevin or gradient (Brownian) dynamics for the translational degrees of freedom to correctly sample the NVT distribution in a simulation of rigid molecules. We propose simple, quasi-symplectic second-order numerical integrators and test their performance on the TIP4P model of water. We also investigate the optimal choice of thermostat parameters.

Ruslan L. Davidchack, Thomas E. Ouldridge, Michael V. Tretyakov

We introduce new Langevin-type equations describing the rotational and translational motion of rigid bodies interacting through conservative and non-conservative forces, and hydrodynamic coupling. In the absence of non-conservative forces the Langevin-type equations sample from the canonical ensemble. The rotational degrees of freedom are described using quaternions, the lengths of which are exactly preserved by the stochastic dynamics. For the proposed Langevin-type equations, we construct a weak 2nd order geometric integrator which preserves the main geometric features of the continuous dynamics. The integrator uses Verlet-type splitting for the deterministic part of Langevin equations appropriately combined with an exactly integrated Ornstein-Uhlenbeck process. Numerical experiments are presented to illustrate both the new Langevin model and the numerical method for it, as well as to demonstrate how inertia and the coupling of rotational and translational motion can introduce qualitatively distinct behaviours.

Ruslan L. Davidchack

We investigate the influence of numerical discretization errors on computed averages in a molecular dynamics simulation of TIP4P liquid water at 300 K coupled to different deterministic (Nosé-Hoover and Nosé-Poincaré) and stochastic (Langevin) thermostats. We propose a couple of simple practical approaches to estimating such errors and taking them into account when computing the averages. We show that it is possible to obtain accurate measurements of various system quantities using step sizes of up to 70% of the stability threshold of the integrator, which for the system of TIP4P liquid water at 300 K corresponds to the step size of about 7 fs.