A grid-based Bader analysis algorithm without lattice bias

TLDR

The authors present a linear‑time, robust algorithm that partitions a charge‑density grid into Bader volumes by accurately representing off‑lattice ascent paths. The method follows steepest‑ascent paths along the charge‑density gradient, assigning each grid point to a maximum and terminating paths when they reach already‑assigned points. The approach preserves linear scaling, eliminates grid‑direction bias in Bader surfaces, and enables efficient analysis of large plane‑wave DFT grids.

Abstract

A computational method for partitioning a charge density grid into Bader volumes is presented which is efficient, robust, and scales linearly with the number of grid points. The partitioning algorithm follows the steepest ascent paths along the charge density gradient from grid point to grid point until a charge density maximum is reached. In this paper, we describe how accurate off-lattice ascent paths can be represented with respect to the grid points. This improvement maintains the efficient linear scaling of an earlier version of the algorithm, and eliminates a tendency for the Bader surfaces to be aligned along the grid directions. As the algorithm assigns grid points to charge density maxima, subsequent paths are terminated when they reach previously assigned grid points. It is this grid-based approach which gives the algorithm its efficiency, and allows for the analysis of the large grids generated from plane-wave-based density functional theory calculations.