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Function-Space-Based Solution Scheme for the Size-Modified Poisson–Boltzmann Equation in Full-Potential DFT

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Chair for Theoretical Chemistry and Catalysis Research Center, Technische Universität München, Lichtenbergstr. 4, D-85747 Garching, Germany
Fachbereich f. Mathematik u. Informatik, Freie Universität Berlin, Otto-von-Simson-Str. 19, D-14195 Berlin, Germany
Cite this: J. Chem. Theory Comput. 2016, 12, 8, 4052–4066
Publication Date (Web):June 20, 2016
Copyright © 2016 American Chemical Society

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The size-modified Poisson–Boltzmann (MPB) equation is an efficient implicit solvation model which also captures electrolytic solvent effects. It combines an account of the dielectric solvent response with a mean-field description of solvated finite-sized ions. We present a general solution scheme for the MPB equation based on a fast function-space-oriented Newton method and a Green’s function preconditioned iterative linear solver. In contrast to popular multigrid solvers, this approach allows us to fully exploit specialized integration grids and optimized integration schemes. We describe a corresponding numerically efficient implementation for the full-potential density-functional theory (DFT) code FHI-aims. We show that together with an additional Stern layer correction the DFT+MPB approach can describe the mean activity coefficient of a KCl aqueous solution over a wide range of concentrations. The high sensitivity of the calculated activity coefficient on the employed ionic parameters thereby suggests to use extensively tabulated experimental activity coefficients of salt solutions for a systematic parametrization protocol.

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The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jctc.6b00435.

  • Derivations of the free energy formulas and Kohn–Sham Hamiltonian correction terms both for the MPBE and the LPBE case. Detailed description of the applied Newton method appended along with extensive accuracy and convergence tests of the implemented method. (PDF)

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