A Systematic Way to Extend the Debye–Hückel Theory beyond Dilute Electrolyte Solutions

An extended Debye–Hückel theory with fourth order gradient term is developed for electrolyte solutions; namely, the electric potential φ(r) of bulk solution can be described by ∇2φ(r) = κ2φ(r) + LQ2∇4φ(r), where parameters κ and LQ are chosen to reproduce first two roots dielectric response function solution. Three boundary conditions solving problem proposed based upon continuity involving functions at boundary, which a element method solute general geometrical shape charge distribution derived. Solutions spherical ion diatomic molecule found used calculate their electrostatic solvation energies. The validity successfully demonstrated when applied binary as well multicomponent primitive models solutions.