Employing Frozen-Density Embedding to Tackle Local Perturbations in Two-Dimensional Periodic Molecular Environments

We report an approach to treat polarization effects in a two-dimensional (2D) environment using frozen-density embedding (FDE), suitable for computing response to electron loss or attachment as occurring in organic semiconductors during charge migration. FDE enables us to avoid an infinite repetition of the occurring charge. The procedure is carried out in two subsequent steps. First, the density of an unperturbed 2D molecular slab is relaxed self-consistently using FDE. Supermolecular quantities are avoided by translating the subsystem density along two translation vectors to compute long-range Coulomb potentials. The resulting large summation is tackled using the Van Wijngaarden transformation. Second, long-range contributions are frozen, and a local perturbation is introduced in the center subsystem. Freeze-thaw iterations are used to relax the electronic wave function of both the center subsystem and the subsystems in an active region around it. The proposed scheme can be applied to purely electronic perturbations as well as perturbations of the geometry. Application to systems with a molecule size of dozens of atoms leads quickly to systems consisting of thousands of atoms due to the 2D slab, which can be treated with the reported approach. As a sample application with regard to organic semiconductors, we report FDE calculations on a charged bay-CF₃-TAPP-H₄Cl₄ dimer (84 atoms) polarizing 20 dimers (1680 atoms) in its surrounding, altogether enclosed by 24 dimers (2016 atoms) with frozen density, resulting in total 3780 atoms, all embedded in a long-range 2D Coulomb field.