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Density functional calculations of atomic structure, charging effect, and static dielectric constant of two-dimensional systems based on B-splines

We implement a total-energy minimization scheme to allow for relaxation of atomic positions in density functional calculations for two-dimensional (2D) systems using a mixed basis set. The basis functions consist of products of 2D plane waves in the plane of the material and localized B-splines along the perpendicular direction. By using this mixed basis approach (MBA), we studied the atomic relaxation and charge polarization of 2D systems under an applied electric field. Compared to the conventional supercell approach (SCA) which adopts repeated slabs sandwiched between vacuum regions, MBA makes no requirement of compensating background charge for treating electrically charged 2D systems due to carrier injection. Furthermore, with MBA, the sawtooth potentials for systems under the applied field to maintain periodicity as needed in SCA is automatically avoided. From the linear response of charge polarization to the applied field, we introduced a simple method to determine the out-of-plane dielectric constants of 2D materials without the ambiguity of defining their effective thickness. Selected 2D systems including graphene and transition-metal dichalcogenides are tested. Our MBA results are consistent with previous SCA calculations when both approaches are equally applicable. However, for the charged system with high carrier density, we found significant deviation from SCA results obtained by imposing artificial charge neutrality condition. PACS: 71.15.