A new dipolar potential for numerical simulations of polar fluids on the $4\mathrm{D}$ hypersphere

TL;DR

This paper introduces a novel Monte Carlo simulation method for polar fluids using a 4D hypersphere geometry, deriving new electrostatic potentials and boundary conditions to improve accuracy and analyze thermodynamic properties.

Contribution

It presents a new dipolar potential and boundary conditions for simulating polar fluids on a 4D hypersphere, enhancing the modeling of electrostatic interactions.

Findings

Derived expressions for thermodynamic and structural properties.

Validated the method with simulations of dipolar hard spheres.

Compared results with previous methods, highlighting finite size effects.

Abstract

We present a new method for Monte Carlo or Molecular Dynamics numerical simulations of three dimensional polar fluids. The simulation cell is defined to be the surface of the northern hemisphere of a four-dimensional (hyper)sphere. The point dipoles are constrained to remain tangent to the sphere and their interactions are derived from the basic laws of electrostatics in this geometry. The dipole-dipole potential has two singularities which correspond to the following boundary conditions : when a dipole leaves the northern hemisphere at some point of the equator, it reappears at the antipodal point bearing the same dipole moment. We derive all the formal expressions needed to obtain the thermodynamic and structural properties of a polar liquid at thermal equilibrium in actual numerical simulation. We notably establish the expression of the static dielectric constant of the fluid as well as the behavior of the pair correlation at large distances. We report and discuss the results of extensive numerical Monte Carlo simulations for two reference states of a fluid of dipolar hard spheres and compare these results with previous methods with a special emphasis on finite size effects.