A Mixed Basis Density Functional Approach for Low Dimensional Systems with B-splines

TL;DR

This paper introduces a mixed basis density functional approach combining plane waves and B-splines for low dimensional systems, enabling efficient and accurate calculations of electronic structures without supercell models.

Contribution

It develops a novel mixed basis method using B-splines and plane waves, simplifying geometry optimization and reducing computational cost in low dimensional systems.

Findings

Accurate electronic structures for surfaces and graphene systems.

Reduced basis set size compared to traditional methods.

Good agreement with established computational codes.

Abstract

A mixed basis approach based on density functional theory is employed for low dimensional systems. The basis functions are taken to be plane waves for the periodic direction multiplied by B-spline polynomials in the non-periodic direction. B-splines have the following advantages:(1) the associated matrix elements are sparse, (2) B-splines possess a superior treatment of derivatives, (3) B-splines are not associated with atomic positions when the geometry structure is optimized, making the geometry optimization easy to implement. With this mixed basis set we can directly calculate the total energy of the system instead of using the conventional supercell model with a slab sandwiched between vacuum regions. A generalized Lanczos-Krylov iterative method is implemented for the diagonalization of the Hamiltonian matrix. To demonstrate the present approach, we apply it to study the C(001)-(2x1) surface with the norm-conserving pseudopotential, the n-type delta-doped graphene, and graphene nanoribbon with Vanderbilts ultra-soft pseudopotentials. All the resulting electronic structures were found to be in good agreement with those obtained by the VSAP code, but with a reduced number of basis.