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A generalized Poisson and Poisson-Boltzmann solver for electrostatic environments

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 equation 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 to the generalized Poisson equation and the linear regime of the Poisson-Boltzmann, allowing to solve iteratively the minimization problem with some ten iterations of a 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 different boundary conditions, as for example surface systems. 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.