A grid-based Bader analysis algorithm without lattice bias

A grid-based Bader analysis algorithm without lattice bias

30 January 2009 | W Tang, E Sanville and G Henkelman
A grid-based Bader analysis algorithm without lattice bias is presented. The algorithm efficiently partitions a charge density grid into Bader volumes, which are regions of space containing a single charge density maximum. The method follows steepest ascent paths along the charge density gradient from grid point to grid point until a maximum is reached. It assigns grid points to charge density maxima and terminates subsequent paths when they reach previously assigned points. This grid-based approach ensures efficiency and linear scaling with the number of grid points. The algorithm eliminates lattice bias, which previously caused Bader surfaces to align with grid directions. A modified version of the algorithm, the near-grid method, removes lattice bias by allowing trajectories to follow off-lattice paths, while still maintaining the efficiency and linear scaling of the original method. The near-grid method calculates correction vectors to adjust trajectories and ensures accurate Bader volumes. The algorithm is robust and suitable for large systems, including plane-wave-based density functional theory calculations. The method was tested on various systems, including a water molecule and a NaCl crystal, showing improved accuracy and convergence compared to the on-grid method. The computational effort scales linearly with the number of grid points, making it efficient for large systems. The algorithm is suitable for large DFT calculations and can be used for plane-wave-based calculations of condensed phase systems.A grid-based Bader analysis algorithm without lattice bias is presented. The algorithm efficiently partitions a charge density grid into Bader volumes, which are regions of space containing a single charge density maximum. The method follows steepest ascent paths along the charge density gradient from grid point to grid point until a maximum is reached. It assigns grid points to charge density maxima and terminates subsequent paths when they reach previously assigned points. This grid-based approach ensures efficiency and linear scaling with the number of grid points. The algorithm eliminates lattice bias, which previously caused Bader surfaces to align with grid directions. A modified version of the algorithm, the near-grid method, removes lattice bias by allowing trajectories to follow off-lattice paths, while still maintaining the efficiency and linear scaling of the original method. The near-grid method calculates correction vectors to adjust trajectories and ensures accurate Bader volumes. The algorithm is robust and suitable for large systems, including plane-wave-based density functional theory calculations. The method was tested on various systems, including a water molecule and a NaCl crystal, showing improved accuracy and convergence compared to the on-grid method. The computational effort scales linearly with the number of grid points, making it efficient for large systems. The algorithm is suitable for large DFT calculations and can be used for plane-wave-based calculations of condensed phase systems.
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Understanding A grid-based Bader analysis algorithm without lattice bias