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An algorithm to delineate and integrate topological basins in a three-dimensional quantum mechanical density

Nathaniel O J Malcolm1, Paul L A Popelier

  • 1Department of Chemistry, U.M.I.S.T., Manchester M60 1QD, UK.

Journal of Computational Chemistry
|June 24, 2003
PubMed
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A new octal tree algorithm precisely maps topological basins in 3D scalar fields, advancing Quantum Chemical Topology. This method accurately calculates basin populations and volumes for complex molecular structures.

Area of Science:

  • Quantum Chemical Topology
  • Computational Chemistry
  • Molecular Modeling

Background:

  • Quantum Chemical Topology (QCT) analyzes molecular properties using 3D scalar fields.
  • Existing algorithms primarily focus on electron density, limiting broader QCT applications.
  • A need exists for robust methods to delineate topological basins in diverse scalar fields.

Purpose of the Study:

  • To introduce a novel algorithm for delineating topological basins in 3D scalar fields beyond electron density.
  • To adapt the computer graphics octal tree search algorithm for QCT applications.
  • To enable the computation of basin properties for scalar fields like the negative Laplacian of electron density.

Main Methods:

  • Implementation of an octal tree search algorithm adapted from computer graphics.

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  • Application of the algorithm to the L(r) function (negative Laplacian of electron density).
  • Testing the algorithm on a simple molecule, water, to demonstrate its robustness and generality.

    • Main Results:

    • The octal tree algorithm successfully delineates complex topological basins in the L(r) scalar field.
    • The method proves robust, compact, and general for boundary detection.
    • For the first time, populations and volumes of core, bonding, and nonbonding (lone pair) basins derived from L(r) topology are computed.

    Conclusions:

    • The octal tree algorithm provides a powerful new tool for Quantum Chemical Topology.
    • This advancement facilitates a deeper understanding of molecular electronic structure through scalar field analysis.
    • The ability to quantify basin properties in L(r) opens new avenues for chemical research.