Application of Van Der Waals Density Functionals to Two Dimensional Systems Based on a Mixed Basis Approach

TL;DR

This paper introduces a mixed basis approach combining B-splines and plane waves to efficiently incorporate van der Waals interactions in two-dimensional systems, demonstrated on bilayer graphene.

Contribution

The paper develops a computationally efficient mixed basis method for vdW density functional calculations in 2D systems, reducing basis size for large-scale simulations.

Findings

Consistent binding energy results for bilayer graphene

Charge density nearly additive for weak vdW interactions

Potential for efficient modeling of large Moire-patterned systems

Abstract

A van der Waals (vdW) density functional was implemented in the mixed basis approach previously developed for studying two dimensional systems, in which the vdW interaction plays an important role. The basis functions here are taken to be the localized B-splines for the finite non-periodic dimension and plane waves for the two periodic directions. This approach will significantly reduce the size of the basis set, especially for large systems, and therefore is computationally efficient for the diagonalization of the Kohn-Sham Hamiltonian. We applied the present algorithm to calculate the binding energy for the two-layer graphene case and the results are consistent with data reported earlier. We also found that, due to the relatively weak vdW interaction, the charge density obtained self-consistently for the whole bi-layer graphene system is not significantly different from the simple addition of those for the two individual one-layer system, except when the interlayer separation is close enough that the strong electron-repulsion dominates. This finding suggests an efficient way to calculate the vdW interaction for large complex systems involving the Moire pattern configurations.