NVU dynamics. II. Comparing to four other dynamics

Abstract

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 constantpotential-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 LennardJones 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 NV T 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.

Simple liquids’ quasiuniversality and the hard-sphere paradigm

“…For most quantities, including spatial and time autocorrelation functions, this method gives the same results as for NVE simulations. It is also possible to use NVU dynamics, which traces out a geodesic curve on the constant-potential-energy hypersurface [53], leading to the same results as NVE or NVT dynamics [54]. Constant-pressure (NPT) dynamics is an option that is popular, in particular, among chemists and material scientists because experiments usually take place at ambient pressure.…”

“…An alternative is the so-called Brownian or Langevin stochastic dynamics. For details about such dynamics the reader is referred to the literature [48]; we here just note that deterministic and stochastic dynamics give the same static-and in most cases also very similar dynamic-properties [54][55][56].…”

Isomorphs, hidden scale invariance, and quasiuniversality

“…(21)) and φ(ρ) = −γ(ρ)g(ρ) + dg/d ln ρ. Equation (23) implies that at any fixed density virial and potential energy are strongly correlated. In particular, for constant-density equilibrium fluctuations at one state point one has ∆W (R) ∼ = γ ∆U (R) [16,35] in which γ depends only on the density [21].…”

“…Moreover, this happens if and only if the system has curves in the phase diagram (the isomorphs) along which the reduced-coordinate constant-potential-energy hypersurfaces are invariant. The latter property led to the introduction of N V U dynamics [22][23][24] -geodesic motion on the constant-potential-energy hypersurface. This is a novel molecular dynamics that in the thermodynamic limit for virtually all structural and dynamic properties gives results identical to those of conventional Newtonian dynamics.…”

Computer simulations of glasses: the potential energy landscape

“…Physically, NVU dynamics is a manifestation of Newton's second law: it models a system moving at constant velocity with zero friction, such that the force is always normal to the surface and thus does no work, conserving kinetic energy. It has been shown that NVU dynamics is equivalent to microcanonical (NVE) in the limit of large N [200], and its results are as good as for canonical (NVT) and stochastic dynamics (such as Monte Carlo) [201].…”