Multidimensional geometric aspects of the solid–liquid transition in simple substances

Abstract

Any molecular system explores significantly different regions of the potential-energy hypersurface as the system is found, respectively, in the solid and liquid phases. We study in detail the multidimensional geometry of these different regions with molecular-dynamics calculations for 256 simple atoms in a fixed volume. The atomic interactions are chosen to represent the noble gases. The stable crystal for this model displays a face-centered cubic structure. We evaluate the local gradient and curvatures of the regions of the hypersurface sampled by the system for a wide range of temperatures. We observe that a significant fraction of the curvatures become negative in the region sampled by the system at temperatures even as low as one-fourth the melting temperature. Further, the curvature distribution changes dramatically with respect to temperature at the melting point. We also construct and evaluate a new distribution for the distance between the atoms in their instantaneous dynamical configurations and those in their corresponding "quenched" configuration (i.e., the configuration found at the corresponding potential-energy minimum). With the help of this new distribution, we conclude that the quenched configurations which are encountered during the melting process are structures which contain vacancy-interstitial defect pairs.

Cages of Water Coordinating Kr in Aqueous Solution

“…We recall that in Stillinger's prescription 30,31 for the inherent structure, one follows the steepest descent path connecting the initial configuration (the cluster) to the nearest minimum on the potential-energy hypersurface (which almost always turns out to be a local minimum). This prescription instantaneously removes temperature from the configuration (hence the term "quench"), and most importantly, it removes the vibrational distortions due to thermal fluctuations.…”

Inherent-structure dynamics and diffusion in liquids

“…Since the magnitude of the [5] return distance u(t) = r(t) − R(t) is bounded by the size of a single basin while the MSD increases without limit the IS-MSD also serves, < (∆R(t)) 2 > /6N = Dt, t → ∞, where ∆R(t) = R(t)− R(0). The IS-MSD is the sum of the IST vectors, the separations of successive IS, ∆R(t) = n(t) α=1 δR α after n transitions.…”

Evolution of off-lattice model proteins under ligand binding constraints

“…A monomer is considered ordered when λ j ≤ λ † , analogous to the Lindemann melting criterion [24][25][26], where λ † ∼ 0.15 l, and l = 3.8…”