Applications of Radial Distribution Function (RDFg(r)) Tool in Statistical Analyses of Microcanonical Ensembles

Abstract

In the domains of quantum mechanics enriched mathematical formulations implementing theoretical/computational sciences and their efficient yet versatile parametrizations state-of-art iterative schemes, the large scale MD simulations of the microcanonical ensemble characterized with the constancy on number of particles , volume , and total energy , and the comprehensive big data concept act as the mainstream paradigms. However, effective integrations of the MD produced massive datasets and the genuine assessments of its explicit trajectories by retrieving all the needy microscopic and macroscopic physicochemical properties are still considered as a challenging task. Towards resolving these bottlenecks to a large extent, the advanced computer aided molecular graphics and the specific programmatic schemes scripted mainly for executing the complex mathematical formulae stand as the frontline means. The radial distribution function (RDF ) and its deterministic computational scheme is one of them which readily enables the users to describe probability density functions of each particle present in the simulating micro-canonical ensembles. In this study, the in-depth statistical analyses of the four different NVE ensembles set with the definite numbers of H₂O, H₃O⁺, SO₄^2-, HSO₄^-, SO₃^2-, and Vⁿ⁺ (n = +2, +3, +4, +5) are carried out by employing the RDF  scheme computationally, and the respective inter-particle interactions are quantitatively theorized. All the nanometer ranged radial distributions of every distinctive particles, their approximate pair distances, complex forming propensities, hydration abilities, dissolution phenomena, affinities towards acquiring free water molecules, etc. are found to be consistent with the pre-established experimental/theoretical datasets. The quantitative results conferred herewith are believed to be highly useful and directly applicable to understand the internal compositions of every particles in their own aqueous electrolyte systems of the batteries, humid weathers, acidic/alkaline solutions, marine ecosystems, soil and geological systems, micellar assemblies, medicinal solutions, biofluids, etc.