Potential energy landscape and inherent dynamics of a hard-sphere fluid

Abstract

Hard-sphere models exhibit many of the same kinds of supercooled-liquid behavior as more realistic models of liquids, but the highly nonanalytic character of their potentials makes it a challenge to think of that behavior in potential energy landscape terms. We show here that it is possible to calculate an important topological property of hard-sphere landscapes, the geodesic pathways through those landscapes, and to do so without artificially coarse-graining or softening the potential. We show, moreover, that the rapid growth of the lengths of those pathways with increasing packing fraction quantitatively predicts the precipitous decline in diffusion constants in a glass-forming hard-sphere mixture model. The geodesic paths themselves can be considered as defining the intrinsic dynamics of hard spheres, so it is also revealing to find that they (and therefore the features of the underlying potential energy landscape) correctly predict the occurrence of dynamic heterogeneity and nonzero values of the non-Gaussian parameter. The success of these landscape predictions for the dynamics of such a singular model emphasizes that there is more to potential energy landscapes than is revealed by looking at the minima and saddle points.

What is special about how roaming chemical reactions traverse their potential surfaces? Differences in geodesic paths between roaming and non-roaming events

“…In condensed matter contexts, geodesic path lengths have been shown to have quantitative connections with diffusion constants. 29,32 It would be interesting to see if one could ever use geodesic features in small molecule systems in an analogous fashion, as probes of the times needed to accomplish the requisite energy transfer.…”

“…What distinguishes the tendency towards one kind of pathway or another is buried under the noise of the vibrational dynamics-which is why we need to compare the geodesic (inherent) pathways. [31][32][33]…”

“…The suggestion then is that it is worth examining what is special about the prototypical coordinate-space pathways taken on (what may be) high-dimensional potential surfaces of systems that roam. A potential-landscape approach that has had some recent success in looking at such inherent paths in the context of slow liquid-state dynamics [28][29][30][31][32][33] offers a novel possibility for understanding some features of roaming. Instead of looking for transition-state surfaces through which some classical-trajectory flux is a maximum, this approach looks instead for paths through the potential landscape that are, in some sense, the most efficient.…”

“…II and discuss why it might be especially appropriate to apply in the context of small-molecule roaming. But two examples of recent applications to liquid dynamics might help illustrate the possibilities offered by the method: In one instance, that of a mixture of infinitely hard spheres of two different sizes, 32 the question was how to understand the sharp drop in the diffusion constant with increasing density. There was clearly no benefit to looking to create a transition-state theory of diffusion centered on the passage over potential saddle points-the entire potential energy was horribly non-analytic; it had no stationary points to find.…”

The role of local structure in dynamical arrest

“…Such analysis yields the minimum energy structure, which, in the case of the Kob-Andersen system is crystalline [352] with a striking structural similarity to the bicapped square antiprisms which the locally favoured structure for this model [108,327]. Another means to evaluate the energy landscape, emphasising the dynamics, has been advanced by Ma and Stratt [321] through their geodesic approach to hard spheres. This approach emphasises dynamical aspects of the energy landscape.…”