Achieving Linear Scaling in Computational Cost for a Fully Polarizable MM/Continuum Embedding

In this paper, we present a new, efficient implementation of a fully polarizable QM/MM/continuum model based on an induced-dipoles polarizable force field and on the Conductor-like Screening Model as a polarizable continuum in combination with a self-consistent field QM method. The paper focuses on the implementation of the MM/continuum embedding, where the two polarizable methods are fully coupled to take into account their mutual polarization. With respect to previous implementations, we achieve for the first time a linear scaling with respect to both the computational cost and the memory requirements without limitations on the molecular cavity shape. This is achieved thanks to the use of the recently developed ddCOSMO model for the continuum and the Fast Multipole Method for the force field, together with an efficient iterative procedure. Therefore, it becomes possible to include in the classical layer as much as several tens of thousands of atoms with a limited computational effort.