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Related Concept Videos

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Continuous Charge Distributions

Imagine a bucket of water. It contains many molecules, of the order of 1026 molecules. Thus, although it contains discrete elements (molecules) at the microscopic level, macroscopically, it can be considered continuous. Small volume elements of water, infinitesimal compared to the bulk of the bucket's volume, still contain many molecules. Under this framework, quantized matter is approximated as continuous for practical purposes.
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Accurate and efficient algorithm for Bader charge integration.

Min Yu1, Dallas R Trinkle

  • 1Department of Physics, University of Illinois at Urbana-Champaign, Urbana, Illinois 61801, USA.

The Journal of Chemical Physics
|February 17, 2011
PubMed
Summary
This summary is machine-generated.

We developed a fast and accurate method to calculate Bader volumes from electron charge density grids. This approach efficiently integrates functions over these volumes, improving computational chemistry workflows.

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Area of Science:

  • Computational chemistry
  • Quantum chemistry
  • Materials science

Background:

  • Accurate integration over complex molecular volumes is crucial for chemical analysis.
  • Existing grid-based methods for Bader charge partitioning can be computationally intensive and lack robustness.

Purpose of the Study:

  • To present an efficient and accurate method for integrating functions over basins of attraction on discrete grids.
  • To apply this method to Bader charge partitioning of electron charge density.

Main Methods:

  • Deriving an expression for the fraction of space flowing between neighboring grid points based on charge density gradients.
  • Developing a discrete integration scheme using these fractions as weights for Bader volumes.
  • Demonstrating applicability to both uniform and nonuniform grids.

Main Results:

  • The proposed method achieves linear computational effort and quadratic convergence.
  • It offers robustness and improved computational efficiency compared to existing grid-based algorithms.
  • The method successfully integrates functions over Bader volumes derived from electron charge density.

Conclusions:

  • The new method provides an efficient, accurate, and robust way to compute Bader volumes and perform integrations.
  • It is readily extendable to nonuniform grids, enhancing its applicability in computational chemistry.
  • This technique offers a significant advancement for analyzing electron charge density and molecular properties.