A fast and robust algorithm for Bader decomposition of charge density

An algorithm is presented for carrying out decomposition of electronic charge density into atomic contributions. As suggested by Bader [R. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, New York, 1990], space is divided up into atomic regions where the dividing surfaces are at...

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Bibliographic Details
Published in:Computational materials science Vol. 36; no. 3; pp. 354 - 360
Main Authors: Henkelman, Graeme, Arnaldsson, Andri, Jónsson, Hannes
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 01.06.2006
Elsevier Science
Subjects:
Atomic and molecular physics
Atomic charges
Atoms in molecules
Bader analysis
Boron clusters
Calculations and mathematical techniques in atomic and molecular physics (excluding electron correlation calculations)
Condensed matter: electronic structure, electrical, magnetic, and optical properties
Electron density analysis
Electron states
Electronic structure of atoms, molecules and their ions: theory
Exact sciences and technology
Linear scaling algorithm
Methods of electronic structure calculations
Physics
31.15.−p
Boron clusters
72.80.cw
Atomic charges
Linear scaling algorithm
71.55.Cw
Atoms in molecules
Electron density analysis
61.72.Tt
Bader analysis
Water
Impurity cluster
Electron charge distribution
31.15.-p
Sodium chlorides
Charge density
Substitutional impurities
Scaling laws
Electron density
Quantum theory
Atomic clusters
ISSN:0927-0256, 1879-0801
Online Access:Get full text
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Summary:An algorithm is presented for carrying out decomposition of electronic charge density into atomic contributions. As suggested by Bader [R. Bader, Atoms in Molecules: A Quantum Theory, Oxford University Press, New York, 1990], space is divided up into atomic regions where the dividing surfaces are at a minimum in the charge density, i.e. the gradient of the charge density is zero along the surface normal. Instead of explicitly finding and representing the dividing surfaces, which is a challenging task, our algorithm assigns each point on a regular ( x, y, z) grid to one of the regions by following a steepest ascent path on the grid. The computational work required to analyze a given charge density grid is approximately 50 arithmetic operations per grid point. The work scales linearly with the number of grid points and is essentially independent of the number of atoms in the system. The algorithm is robust and insensitive to the topology of molecular bonding. In addition to two test problems involving a water molecule and NaCl crystal, the algorithm has been used to estimate the electrical activity of a cluster of boron atoms in a silicon crystal. The highly stable three-atom boron cluster, B 3I is found to have a charge of −1.5 e, which suggests approximately 50% reduction in electrical activity as compared with three substitutional boron atoms.
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ISSN:0927-0256
1879-0801
DOI:10.1016/j.commatsci.2005.04.010