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A third and fourth order perturbation theory for dipolar hard spheres
1Institute of Thermodynamics and Thermal Process Engineering, University of Stuttgart, Pfaffenwaldring 9, 70569 Stuttgart, Germany.
The Journal of Chemical Physics
|August 3, 2018
Summary
We developed new perturbation theories for dipolar hard spheres. The fourth-order theory significantly improves electrostatic energy predictions at higher densities and dipole moments compared to the third-order theory.
Area of Science:
- Statistical Mechanics
- Computational Chemistry
- Physical Chemistry
Background:
- Understanding electrostatic interactions in fluids is crucial for predicting their behavior.
- Existing theories often struggle to accurately capture these interactions, especially at higher densities.
- Perturbation theories offer a promising avenue for developing more accurate models.
Purpose of the Study:
- To develop and analyze third and fourth-order perturbation theories for non-polarizable dipolar hard spheres.
- To accurately model both short-ranged and long-ranged electrostatic potentials.
- To improve the prediction of electrostatic energy in dense fluids.
Main Methods:
- Splitting the electrostatic potential into short- and long-ranged components.
- Applying perturbation expansion with Padé approximations ([2,1] for third-order, [2,2] for fourth-order).
- Utilizing Local Molecular Field (LMF) theory for long-ranged contributions, incorporating a perturbation theory for relative permittivity.
Main Results:
- The fourth-order perturbation theory shows significantly improved agreement with molecular simulations for electrostatic energy at higher densities (up to μ*² ≤ 4 for ρ* ≲ 1).
- Both third and fourth-order theories agree well with simulations for lower densities (ρ* ≤ 1) and dipole moments (μ*² ≤ 1).
- The LMF theory, when combined with perturbation theory for relative permittivity, accurately predicts long-ranged electrostatic energy.
Conclusions:
- The developed fourth-order perturbation theory offers a substantial advancement in accurately modeling electrostatic interactions in dipolar hard sphere systems.
- This improved theoretical framework is valuable for simulations and understanding fluid behavior under various conditions.
- The study highlights the effectiveness of combining perturbation theories and advanced approximations for electrostatic energy calculations.
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