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Dipolar Poisson models in a dual view.

Hélène Berthoumieux1, Geoffrey Monet1, Ralf Blossey2

  • 1Sorbonne Université, CNRS, Laboratoire de Physique Théorique de la Matière Condensée (LPTMC, UMR 7600), F-75005 Paris, France.

The Journal of Chemical Physics
|July 16, 2021
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Summary
This summary is machine-generated.

We present convex formulations of dipolar-Poisson models for electrostatic potential, enabling nonlinear generalizations for solvation and electron transfer theories. These models are validated using molecular dynamics simulations.

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Area of Science:

  • Continuum electrostatics
  • Theoretical chemistry
  • Computational physics

Background:

  • Dipolar-Poisson models describe electrostatic interactions but are non-convex.
  • Existing models lack proper treatment of polarization saturation.
  • Non-convexity poses challenges for theoretical analysis and computation.

Purpose of the Study:

  • To derive convex dual functionals for dipolar-Poisson models using Legendre transforms.
  • To compare convex functionals in polarization (P) space with non-convex functionals in electric field (E) space.
  • To apply these models to ion solvation and nonlinear electron transfer theories.

Main Methods:

  • Application of the Legendre transform approach.
  • Derivation of convex vector-field functionals for dielectric displacement (D) and polarization (P).
  • Comparison of P-space and E-space functionals.
  • Parameterization using molecular dynamics simulations.

Main Results:

  • Convex dual functionals were successfully derived for dipolar-Poisson models.
  • The dipolar-Poisson-Langevin model provides a nonlinear generalization of Marcus theory.
  • The model is quantitatively parameterizable via molecular dynamics.

Conclusions:

  • Convex formulations offer a robust framework for studying electrostatic phenomena.
  • The dipolar-Poisson-Langevin model is suitable for nonlinear regimes in electron transfer.
  • Molecular dynamics simulations are crucial for parameterizing these continuum models.