Cluster pair correlation function of simple fluids: Energetic connectivity criteria

Abstract

We consider the clustering of Lennard-Jones particles by using an energetic connectivity criterion proposed long ago by T.L. Hill [J. Chem. Phys. 32, 617 (1955)] for the bond between pairs of particles. The criterion establishes that two particles are bonded (directly connected) if their relative kinetic energy is less than minus their relative potential energy. Thus, in general, it depends on the direction as well as on the magnitude of the velocities and positions of the particles. An integral equation for the pair connectedness function, proposed by two of the authors [Phys Rev. E 61, R6067 (2000)], is solved for this criterion and the results are compared with those obtained from molecular dynamics simulations and from a connectedness Percus-Yevick like integral equation for a velocity-averaged version of Hill's energetic criterion.

Thermodynamics of Small Alkali Metal Halide Cluster Ions: Comparison of Classical Molecular Simulations with Experiment and Quantum Chemistry

“…Though simple in specific cases, geometrical criteria are difficult to generalize for more complex systems containing mixtures of molecular particles, such as in the present study, which requires consistent treatment of cluster ions and pure water clusters. Instead, here we opt for two energy-based stability criteria, A and B, similar to those proposed by Hill , and used for simple and fast identification of clusters. , Neither of our criteria will result in the selection of indefinitely stable clusters, with the exception of a dimer of structureless atomic particles. According to criterion A, a stable dimer is formed when the pair interaction energy is lower than the mutual kinetic energy, i.e., u i j ( r i , r j ) ≤ prefix− false( boldp i − boldp j false) 2 / 4 μ Here i and j represent two particles or groups of particles whose mutual interaction energy is u ij , r i and p i are the vector position and linear momentum of i , respectively, and μ is the reduced mass of the binary system.…”

“…Instead, here we opt for two energy-based stability criteria, A and B, similar to those proposed by Hill 52,53 and used for simple and fast identification of clusters. 54,55 Neither of our criteria will result in the selection of indefinitely stable clusters, with the exception of a dimer of structureless atomic particles. According to criterion A, a stable dimer is formed when the pair interaction energy is lower than the mutual kinetic energy, i.e.,…”

Highlighting the difference in nanostructure between domain-forming and domainless protic ionic liquids

“…The clustering criteria can be based on the distance between single atoms or centers of mass of the groups of atoms, choice of the nearest neighbors, or energetic properties. 67 A broadly applicable approach is Voronoi tessellation, in which polyhedral Voronoi cells corresponding to each of the atoms are generated. 30,68,69 These cells consist of all points of space lying closer to the given atom than to any other atom.…”

Percolation line and response functions in simple supercritical fluids

“…Theoretical arguments suggest that it should terminate at the critical point [12] but vast majority of simulation results have not indicated any such tendency. Surprisingly, this important issue has in fact gained only little attention and we are aware of only two papers confirming the theoretical arguments for continuous models, for supercritical Lennard-Jonesium (LJ) [14,15]. With respect to the above mentioned ambiguities one reason may be an inappropriate choice for the bond definition or/and estimation of the percolation threshold.…”

“…For example, it has been already well-known that application of a simple geometric definition of cluster tends to produce a percolation line ending below the critical temperature in the low-density region (e.g., [13]). On the other hand, we are aware of two papers which, using a 'proper' definition of cluster for a continuous model, supercritical Lennard-Jonesium (LJ), confirm that the percolation line terminates at the critical point [14,15]. It is also known that the percolation line can be moved to the left or right side from the critical point by using different (more sophisticated) criteria (see, e.g., [16,17]).…”