General Motivation

The atomistic simulation of the diffuse electrochemical double layer for an electrolyte of water with solvated ions is currently an important topic in solvation science. The structuring of ions and water at charged surfaces plays a significant role for a multitude of processes, such as precipitation of proteins, molecular friction or dispersion of colloid particles. Recent results suggest that intermolecular charge transfer has to be considered for the simulation of ion solvation. This can be achieved through the EEM method proposed by Mortier et al. [1], which re-assesses the atomic charges after every simulation step by minimizing the energy expression. However, this method allows charge transfer between any atomic side and is thus prone to an overestimation of charge transfer and overpolarization.

ACKS2 Energy Expression

The tendency to show long-range charge transfer and thus conductor-like behavior stems from two fundamental problems with the EEM method. Firstly, EEM does not show the expected linear scaling for dipole polarizabilities in the macroscopic limit but instead suggests cubic scaling. Secondly, EEM shows fractional instead of integer charges even for separated molecules.

The “Atom-condensed Kohn-Sham DFT approximation to second order” (ACKS2) model developed by Verstraelen [2] tackles this problem by expanding the energy expression to include kinetic energy terms instead of just focusing on the electrostatic contributions:

The inclusion of the additional energy term and an sp-basis solves the inherent problems of the EEM method by preventing artificial long-range charge transfer and allowing polarization perpendicular to the molecular plane.

Current Progress

  • EEM method implemented into the MOF-FF
  • Propagation of the charges via an Extended Lagrangian
  • Implementation of the sp-basis in progress

Long term goals

  • Full implementation and optimization of ACKS2
  • Validation of the results via measurements from the Valtiner group at the MPIE [3]
  • Addition of the polarizable FF to the RSDFT code in a QM/MM fashion


  • [1] Wilfried M., et al. Electronegativity equalization: application and parameterization, Journal of American Chemical Society 107(4):829-935 (1985).
  • [2] Verstraelen T., et al. ACKS2: atom-condensed Kohn-Sham DFT approximated to second order, J. Chem. Phys. 138(7):074108 (2013).
  • [3] Baimpos T., Shrestha BR., Raman S., Valtiner M., Effect of Interfacial Ion Structuring on Range and Magnitude of Electric Double Layer, Hydration, and Adhesive Interactions between Mica Surfaces in 0.05–3 M Li+ and Cs+ Electrolyte Solutions, Langmuir 30.15:4322-4332 (2014).