Symplectic quaternion scheme for biophysical molecular dynamics

Abstract

Massively parallel biophysical molecular dynamics simulations, coupled with efficient methods, promise to open biologically significant time scales for study. In order to promote efficient fine-grained parallel algorithms with low communication overhead, the fast degrees of freedom in these complex systems can be divided into sets of rigid bodies. Here, a novel Hamiltonian form of a minimal, nonsingular representation of rigid body rotations, the unit quaternion, is derived, and a corresponding reversible, symplectic integrator is presented. The novel technique performs very well on both model and biophysical problems in accord with a formal theoretical analysis given within, which gives an explicit condition for an integrator to possess a conserved quantity, an explicit expression for the conserved quantity of a symplectic integrator, the latter following and in accord with Calvo and Sanz-Sarna, Numerical Hamiltonian Problems ͑1994͒, and extension of the explicit expression to general systems with a flat phase space.

RASPA: molecular simulation software for adsorption and diffusion in flexible nanoporous materials

“…[68,70,71] Figure 9 shows that this type of scheme has excellent energy conservation over many nanoseconds. The CO 2 is modelled as rigid and integrated using the quaternion integration scheme of Miller et al [67]. Separate thermostats are used to thermostat the translation and the rotation of the molecules.…”

“…Since symplectic integrators preserve the topological structure of trajectories in phase space, they are more reliable for longterm integration than non-symplectic integrators. The implemented NVE integrator is the symplectic and time reversible integrator for molecules with an arbitrary level of rigidity, developed by Miller et al [67] based on a novel quaternion scheme. Thermo-and barostats can be combined with the Miller scheme to control the temperature and pressure.…”

Diffusive hydrogen inter-cage migration in hydrogen and hydrogen-tetrahydrofuran clathrate hydrates

“…In the SPME method, the screening parameter, α, and the number of wave-vectors were arranged so that the relative error was less than 1×10 -5 ; the Ewald electrostatic energy and forces changed little with α. Rigid molecule models were employed for H 2 , THF and H 2 O with the NOSQUISH algorithm of Miller et al [38], using velocity-Verlet [39] integration. 100 ps of Nosé-Hoover [40] NVT simulations were run at 200, 220, 230, 240, 250, 260 K for each system with 2 fs time step at 0.05 kbar, and a rather mild 0.5 ps thermostat relaxation time; these were followed by 250 ps of NPT runs [41,42] at 0.05 kbar at each temperature, with thermostat and barostat periods of 0.5 and 2 ps respectively, to allow each system volume to settle.…”

Understanding interactions between capped nanocrystals: Three-body and chain packing effects

“…The rotation of rigid NCs about their centers of mass is realized using quaternion rigid body dynamics. 48 The temperature is kept constant using the Andersen thermostat. 49 …”