NVE Dynamics Research Articles

Driving forces in MD simulations of transition and ‘Free’ flows

Simulations of porous gaseous flows are routinely used to investigate membrane permeation in catalytic adsorption and separation problems. Although basic continuum equations are supposed to breakdown in these nanoscale pores, many studies of force/flow relations assume flow to be linear in chemical potential or pressure differences. This work tests common assumptions using simulations of an atomistic, Lennard–Jones pore flow with distant, Langevin forcing at densities stretching through the transition and free flow regimes. Using NVE dynamics in very large boundary reservoirs, we find local equilibrium is established in the steady-state, but also identify two new finite-size effects. First, there is a steady flow of heat from the high-pressure reservoir backward to the thermostat region, and second, a significant proportion of the channel flow originates from the monolayer adsorbed to the flat outer wall. All walls are shown to obey a simple Langmuir adsorption isotherm at these low ( kPa) pressures, even in the presence of flow. Despite multi-layer formation on the inner pore walls as density increases, the current carried by atoms at the wall has the same proportion to current carried through the channel center under nearly all conditions tested (with constant pore diameter). Comparing our flow rates to Fickian and Knudsen linear relations shows that the difference in reservoir pressure is significantly more predictive than the difference in chemical potential for this size regime.

NVU dynamics. III. Simulating molecules at constant potential energy

This is the final paper in a series that introduces geodesic molecular dynamics at constant potential energy. This dynamics is entitled NVU dynamics in analogy to standard energy-conserving Newtonian NVE dynamics. In the first two papers [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, J. Chem. Phys. 135, 104101 (2011)10.1063/1.3623585; T. S. Ingebrigtsen, S. Toxvaerd, T. B. Schrøder, and J. C. Dyre, J. Chem. Phys. 135, 104102 (2011)10.1063/1.3623586], a numerical algorithm for simulating geodesic motion of atomic systems was developed and tested against standard algorithms. The conclusion was that the NVU algorithm has the same desirable properties as the Verlet algorithm for Newtonian NVE dynamics, i.e., it is time-reversible and symplectic. Additionally, it was concluded that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit. In this paper, the NVU algorithm for atomic systems is extended to be able to simulate the geodesic motion of molecules at constant potential energy. We derive an algorithm for simulating rigid bonds and test this algorithm on three different systems: an asymmetric dumbbell model, Lewis-Wahnström o-terphenyl (OTP) and rigid SPC/E water. The rigid bonds introduce additional constraints beyond that of constant potential energy for atomic systems. The rigid-bond NVU algorithm conserves potential energy, bond lengths, and step length for indefinitely long runs. The quantities probed in simulations give results identical to those of Nosé-Hoover NVT dynamics. Since Nosé-Hoover NVT dynamics is known to give results equivalent to those of NVE dynamics, the latter results show that NVU dynamics becomes equivalent to NVE dynamics in the thermodynamic limit also for molecular systems.

Effects of Molecular Dynamics Thermostats on Descriptions of Chemical Nonequilibrium.

The performance of popular molecular dynamics (MD) thermostat algorithms in constant temperature simulations of equilibrium systems is well-known. This is not the case, however, in the context of nonequilibrium chemical systems, such as chemical reactions or nanoscale self-assembly processes. In this work, we investigate the effect of popular thermostat algorithms on the "natural" (i.e., Hamiltonian) dynamics of a nonequilibrium, chemically reacting system. By comparing constant-temperature quantum mechanical MD (QM/MD) simulations of carbon vapor condensation using velocity scaling, Berendsen, Andersen, Langevin, and Nosé-Hoover chain thermostat algorithms with natural NVE simulations, we show that efficient temperature control and reliable reaction dynamics are mutually exclusive in such a system. This problem may be circumvented, however, by placing the reactive system in an inert He atmosphere, which is itself described using NVT MD. We demonstrate that both realistic temperature control and dynamics consistent with natural NVE dynamics can then be obtained simultaneously. In essence, the thermal energy created by the natural dynamics of the NVE subsystem is drained by the thermostat acting on the NVT atmosphere, without adversely affecting the dynamics of the reactive system itself.

A Multibox Splitting Scheme: Robust Approximation For ab Initio Molecular Dynamics.

In this work, the multibox (M-box) simulation scheme is introduced, which can be considered as a generalization of the QM/MM scheme for multifragment (molecular) systems. This scheme exploits the natural locality of multifragment molecular-based systems by mapping the system into force-coupled block subspaces. Where defined in this way, the entire system can be fully modeled under a quantum mechanical force field. This allows the description of each subspace explicitly by means of a robust electronic structure theory without the requirement for large computational resources. An adequate block-to-block coupling by means of shared subsystem fragments is applied to preserve the long-distance structural correlation in the system during a molecular dynamic (MD) simulation. Since electronic structure descriptions play a central role in the formulation of several parametric models for charge or energy transport, we expect that this space-time correlated scheme can become a reliable computational tool for charge/energy transport/transfer applications. The efficiency of the method is demonstrated by performing statistical and time-resolved analysis using both the multifragment box and full ab initio approaches. We illustrate the method using as examples the melting process of a one-dimensional benzene chain (weak interaction situation) and NVE dynamics for the CnHn polymeric chain (strong interaction situation). We also have extended the threshold of applicability of our model, demonstrating how it can cope with MD simulation with more complex systems and processes.

NVU dynamics. II. Comparing to four other dynamics

In the companion paper [T. S. Ingebrigtsen, S. Toxvaerd, O. J. Heilmann, T. B. Schrøder, and J. C. Dyre, "NVU dynamics. I. Geodesic motion on the constant-potential-energy hypersurface," J. Chem. Phys. (in press)] an algorithm was developed for tracing out a geodesic curve on the constant-potential-energy hypersurface. Here, simulations of NVU dynamics are compared to results for four other dynamics, both deterministic and stochastic. First, NVU dynamics is compared to the standard energy-conserving Newtonian NVE dynamics by simulations of the Kob-Andersen binary Lennard-Jones liquid, its WCA version (i.e., with cut-off's at the pair potential minima), and the Lennard-Jones Gaussian liquid. We find identical results for all quantities probed: radial distribution functions, incoherent intermediate scattering functions, and mean-square displacement as function of time. Arguments are presented for the equivalence of NVU and NVE dynamics in the thermodynamic limit; in particular, to leading order in 1∕N these two dynamics give identical time-autocorrelation functions. In the final part of the paper, NVU dynamics is compared to Monte Carlo dynamics, to a diffusive dynamics of small-step random walks on the constant-potential-energy hypersurface, and to Nosé-Hoover NVT dynamics. If time is scaled for the two stochastic dynamics to make single-particle diffusion constants identical to that of NVE dynamics, the simulations show that all five dynamics are equivalent at low temperatures except at short times.