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Learning to draw Fischer projections of molecules and understanding their relevance plays a crucial role in the visual depiction of organic molecules. A Fischer projection is a two-dimensional projection on a planar surface to simplify the three-dimensional wedge–dash representation of molecules. This is especially helpful in the case of molecules with multiple chiral centers that can be difficult to draw. Here, all the bonds of interest are represented as horizontal or vertical lines.
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The mathematical expression known as the wave function, ψ, contains information about each orbital and the wavelike properties of electrons in an isolated atom. When atoms are bound together in a molecule, the wave functions combine to produce new mathematical descriptions that have different shapes. This process of combining the wave functions for atomic orbitals is called hybridization and is mathematically accomplished by the linear combination of atomic orbitals. The new orbitals that...
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Determination of Aggregate Surface Morphology at the Interfacial Transition Zone ITZ
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How pervasive is the Hirshfeld partitioning?

Farnaz Heidar-Zadeh1, Paul W Ayers1

  • 1Department of Chemistry and Chemical Biology, McMaster University, Hamilton, Ontario L8S 4M1, Canada.

The Journal of Chemical Physics
|February 2, 2015
PubMed
Summary

The Hirshfeld partitioning method for molecular density is uniquely identified by using f-divergences. This approach precisely separates atomic contributions within a molecule, ensuring accuracy in chemical property calculations.

Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Theoretical Chemistry

Background:

  • Molecular density partitioning is crucial for understanding chemical properties.
  • The Hirshfeld partitioning method is a widely used technique for this purpose.
  • Existing methods lack a rigorous mathematical foundation for uniqueness.

Purpose of the Study:

  • To identify the mathematical conditions that uniquely define the Hirshfeld partitioning.
  • To explore alternative divergence measures for molecular density partitioning.
  • To provide a theoretical basis for the Hirshfeld method's success.

Main Methods:

  • Minimizing the divergence between atom-in-molecule and pro-atomic densities.
  • Applying a constraint that the sum of atomic densities equals the molecular density.

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  • Analyzing properties of local divergence measures between probability distributions.

    • Main Results:

    • The Hirshfeld partitioning is uniquely recovered under specific conditions on the divergence measure.
    • Only f-divergences, among local divergence measures, yield the Hirshfeld partitioning.
    • This work establishes the mathematical necessity and sufficiency for Hirshfeld partitioning.

    Conclusions:

    • The Hirshfeld partitioning method is mathematically unique among local divergence measures when using f-divergences.
    • This finding provides a rigorous justification for the widespread use of the Hirshfeld method.
    • The study deepens the understanding of molecular density partitioning in computational chemistry.