Effective multipoles and Yukawa electrostatics in dressed molecule theory

Area of Science:

• Physical Chemistry
• Theoretical Chemistry
• Statistical Mechanics

Background:

• Electrolyte solutions exhibit complex electrostatic interactions.
• Screened Coulomb potential is crucial for understanding these interactions.
• Molecular solvent effects and charge distributions require advanced theoretical treatment.

Purpose of the Study:

• To derive the multipolar expansion of the screened Coulomb potential in electrolyte solutions with molecular solvents.
• To determine effective molecular multipoles using dressed molecule theory.
• To analyze deviations from ordinary electrostatics and Coulomb potential behavior.

Main Methods:

• Derivation of multipolar expansion for screened Coulomb potential.
• Application of dressed molecule theory for renormalized charge distributions.
• Analysis of dilute solutions where potential decays as a Yukawa function.
• Inclusion of many-body correlations via a formally exact theory.

Main Results:

• The screened Coulomb potential in electrolyte solutions follows Yukawa decay, differing from Debye-Hückel theory.
• "Yukawa charge" of a molecule is not necessarily its Coulombic charge or the integral of its renormalized charge distribution.
• The multipolar expansion of the Yukawa potential does not match its asymptotic expansion, with all multipoles contributing to the leading term.

Conclusions:

• Electrostatic potential range in electrolytes is determined by molecular multipoles of all orders, not solely the charge term.
• This framework redefines electrostatic interactions in electrolyte solutions, applicable to both charged and neutral molecules.
• The multipole expansion formalism can be extended to the Poisson-Boltzmann approximation for primitive model electrolytes.