### Abstract

We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid and apply it to the Bader charge partitioning for the electron charge density. Starting with the evolution of trajectories in space following the gradient of charge density, we derive an expression for the fraction of space neighboring each grid point that flows to its neighbors. This serves as the basis to compute the fraction of each grid volume that belongs to a basin (Bader volume) and as a weight for the discrete integration of functions over the Bader volume. Compared with other grid-based algorithms, our approach is robust, more computationally efficient with linear computational effort, accurate, and has quadratic convergence. Moreover, it is straightforward to extend to nonuniform grids, such as from a mesh-refinement approach, and can be used to both identify basins of attraction of fixed points and integrate functions over the basins.

Original language | English (US) |
---|---|

Article number | 064111 |

Journal | Journal of Chemical Physics |

Volume | 134 |

Issue number | 6 |

DOIs | |

State | Published - Feb 14 2011 |

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### ASJC Scopus subject areas

- Physics and Astronomy(all)
- Physical and Theoretical Chemistry

### Cite this

*Journal of Chemical Physics*,

*134*(6), [064111]. https://doi.org/10.1063/1.3553716

**Accurate and efficient algorithm for Bader charge integration.** / Yu, Min; Trinkle, Dallas R.

Research output: Contribution to journal › Article

*Journal of Chemical Physics*, vol. 134, no. 6, 064111. https://doi.org/10.1063/1.3553716

}

TY - JOUR

T1 - Accurate and efficient algorithm for Bader charge integration

AU - Yu, Min

AU - Trinkle, Dallas R.

PY - 2011/2/14

Y1 - 2011/2/14

N2 - We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid and apply it to the Bader charge partitioning for the electron charge density. Starting with the evolution of trajectories in space following the gradient of charge density, we derive an expression for the fraction of space neighboring each grid point that flows to its neighbors. This serves as the basis to compute the fraction of each grid volume that belongs to a basin (Bader volume) and as a weight for the discrete integration of functions over the Bader volume. Compared with other grid-based algorithms, our approach is robust, more computationally efficient with linear computational effort, accurate, and has quadratic convergence. Moreover, it is straightforward to extend to nonuniform grids, such as from a mesh-refinement approach, and can be used to both identify basins of attraction of fixed points and integrate functions over the basins.

AB - We propose an efficient, accurate method to integrate the basins of attraction of a smooth function defined on a general discrete grid and apply it to the Bader charge partitioning for the electron charge density. Starting with the evolution of trajectories in space following the gradient of charge density, we derive an expression for the fraction of space neighboring each grid point that flows to its neighbors. This serves as the basis to compute the fraction of each grid volume that belongs to a basin (Bader volume) and as a weight for the discrete integration of functions over the Bader volume. Compared with other grid-based algorithms, our approach is robust, more computationally efficient with linear computational effort, accurate, and has quadratic convergence. Moreover, it is straightforward to extend to nonuniform grids, such as from a mesh-refinement approach, and can be used to both identify basins of attraction of fixed points and integrate functions over the basins.

UR - http://www.scopus.com/inward/record.url?scp=79951777316&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=79951777316&partnerID=8YFLogxK

U2 - 10.1063/1.3553716

DO - 10.1063/1.3553716

M3 - Article

C2 - 21322665

AN - SCOPUS:79951777316

VL - 134

JO - Journal of Chemical Physics

JF - Journal of Chemical Physics

SN - 0021-9606

IS - 6

M1 - 064111

ER -