Thermodynamic equivalence between the Lennard–Jones and hard-core attractive Yukawa systems

The generalized continuous multiple step (GCMS) potential: model systems and benchmarks

The generalized continuous multiple step (GCMS) potential is presented in this work. Its flexible form allows forrepulsiveand/orattractivecontributions to be encoded through adjustable energy and length scales. The GCMS interaction provides a continuous representation of square-well, square-shoulder potentials and their variants for implementation in computer simulations. A continuous and differentiable energy representation is required to derive forces in conventional simulation algorithms. Molecular dynamics simulations are of particular interest when considering the dynamic properties of a system. The GCMS potential can mimic other interactions with a judicious choice of parameters due to the versatile sigmoid form. In this study, our benchmarks for the GCMS representation include triangular, Yukawa, Franzese, and Lennard-Jones potentials. Comparisons made with published data on volumetric phase diagrams, liquid structure, and diffusivity from model systems are in excellent agreement.

Application of Schrödinger equation in quantum well of Cu2ZnSnS4 quaternary semiconductor alloy

An approximate solution of the radial Schrödinger equation is obtained with a generalized group of potentials in the presence of both magnetic field and potential effect using supersymmetric quantum mechanics and shape invariance methodology. The energy bandgap of the generalized group of potentials was calculated for s−wave cases at the ground state. By varying the numerical values of the potential strengths, the energy band gap of Hellmann's potential and Coulomb-Hulthẻn potential respectively were obtained. It is noted that the inclusion of the potential effect greatly affects the accuracy of the results. Our calculated results are in agreement and better than the existing calculated results. The present results approximately coincide with the standard bandgap of Cu₂ZnSnS₄ (CZTS).

Theoretical equations of state for a charged fluid

In this article, we present a molecular thermodynamic study of a system of N particles contained within a volume V and interacting via a hard-core pair potential with an attractive interaction according to the Wolf model for charged systems. This variable-range potential is characterized by three parameters: the repulsive hard-core diameter σ, the energy-well depth ϵ, and the inverse range α; a fourth parameter of the model is a cut-off distance x_c that depends on α according to the relation x_c = 2/α. Two equations of state (EOSs) are presented and derived from thermodynamic perturbation theory and Monte Carlo (MC) simulation data. The first EOS is given by the standard Zwanzig's high-temperature expansion of the Helmholtz free energy, where the first three perturbation terms a₁, a₂, and a₃ were obtained from MC simulations in the canonical ensemble (NVT) and parameterized as functions of α and the reduced density of particles ρ^* = Nσ³/V. The second EOS was obtained from the discrete perturbation theory applied to a discrete representation of the Wolf potential. Results for pressures, internal energies, and isochoric heat capacities are compared to the MC computer simulation data of the Wolf system, including vapor-liquid coexistence curves, for different values of α. Overall, both EOSs give a very good representation of the thermodynamic properties of the Wolf fluid when 0.3 ≤ α ≤ 1.0 and 0.05 ≤ ρ^* ≤ 0.8. Since the Yukawa fluid can reproduce information of screened ionic interactions, we discuss the equivalence between the Wolf and Yukawa fluids in the context of equivalent systems in liquid theory.