A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

Abstract

The computational study of chemical reactions in complex, wet environments is critical for applications in many fields. It is often essential to study chemical reactions in the presence of applied electrochemical potentials, taking into account the non-trivial electrostatic screening coming from the solvent and the electrolytes. As a consequence, the electrostatic potential has to be found by solving the generalized Poisson and the Poisson-Boltzmann equations for neutral and ionic solutions, respectively. In the present work, solvers for both problems have been developed. A preconditioned conjugate gradient method has been implemented for the solution of the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of the ordinary Poisson equation solver. In addition, a self-consistent procedure enables us to solve the non-linear Poisson-Boltzmann problem. Both solvers exhibit very high accuracy and parallel efficiency and allow for the treatment of periodic, free, and slab boundary conditions. The solver has been integrated into the BigDFT and Quantum-ESPRESSO electronic-structure packages and will be released as an independent program, suitable for integration in other codes. C 2016 AIP Publishing LLC. [http://dx

Surface reconstruction of fluorites in vacuum and aqueous environment

“…We employed the soft-sphere continuum solvation model [45,46] to explore the solvent-surface interaction by including the solvent as a continuum at the DFT level. Within this approach, the interface between the quantum-mechanical solute and surrounding environment is described by a fully continuum and differentiable permittivity (r) function of the atomic coordinates.…”

“…Different coverages were modeled by adding an increasing number of water molecules. In the second approach, the aqueous environment was modeled at the DFT level by means of a recently developed implicit solvation model [45,46] which replaces the explicit water molecules by a continuum body surrounding the quantum-mechanical system. This implicit approach allowed efficient minima hopping explorations of the potential energy surface for hydrated fluorite terminations.…”

“…This explicit inclusion of water should be in principle the most accurate to account for solvent effects, albeit fully explicit ab-initio approaches result in well-known limitations in describing an aqueous environment, in particular regarding its structural and dielectric properties [42][43][44]. In order to reduce the large number of degrees of freedom of the explicit solvent model, which gives many different configurations of the water molecules for identical surface reconstructions, we employ in addition a recently developed implicit solvation model [45,46]. Using this method, we explore the potential energy surface of the hydrated surface reconstructions.…”

Evaluating continuum solvation models for the electrode-electrolyte interface: Challenges and strategies for improvement

“…In the LinearPCM / VASPsol and NonlinearPCM models, the distance from the solute at which the continuum solvent appears is controlled by an electron density threshold parameter n c . 17 (The SCCS model 33,34 uses two electron density parameters ρ min and ρ max in a formally different but functionally equivalent parameterization.) To correct the surface charging behavior of Ag(100), we adjust the value of n c for the nonlinear model to match the surface charge at the highest potential reported experimentally in Ref.…”

A domain decomposition method for the polarizable continuum model based on the solvent excluded surface

“…First, one can obtain a generalized Poisson (GP) equation if ρ is independent on ψ as for the non-ionic solvent and second, a Poisson-Boltzmann equation [16] is obtained if the solvent contains ions whose movement is accounted for by Boltzmann statistics. Since the end of 1980s, many codes have been proposed for solving the Poisson-Boltzmann (or Poisson) equation for example using the boundary element method [7,35], the finite element method [2,24] or the finite difference method including UHBD [15], DelPhi [30], APBS [3,17,27] and the other work [18]. In particular, the APBS software is popular and widely used which can calculate the biomolecular electrostatics for large molecules.…”