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The Separability Problem in Molecular Quantum Systems: Information-Theoretic Framework for Atoms in Molecules.

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Summary

This study validates common Atoms-In-Molecules (AIM) schemes using Information Theory. It provides information-theoretical justifications for partitioning molecules in computational chemistry.

Keywords:
Atoms in MoleculesFisher entropyInformation TheoryQTAIMQuantum InformationRelative entropyStockholder partition

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Area of Science:

  • Quantum Chemistry
  • Computational Chemistry
  • Information Theory

Background:

  • Molecules are quantum entities but often treated classically.
  • Experimental methods like X-Ray crystallography yield rigid molecular structures.
  • Atoms-In-Molecules (AIM) schemes partition molecules into constituent parts.

Purpose of the Study:

  • To establish the validity of AIM schemes within Information Theory.
  • To provide information-theoretical justifications for prevalent AIM methods.
  • To explore mathematical implications of molecular partitioning.

Main Methods:

  • Applied generalized principle of minimum relative entropy (Sharma-Mittal functional).
  • Utilized Fisher information within the Principle of Extreme Physical Information for topological partitioning.
  • Employed Löwdin symmetric transformations for quantum approach to atomic Hilbert spaces.

Main Results:

  • Uncovered information-theoretical justifications for Hirshfeld, Bader's, and quantum AIM schemes.
  • Demonstrated Fisher information of Bader's atoms aligns with the Principle of Extreme Physical Information.
  • Presented information-theoretic basis for Löwdin transformations in forming atomic Hilbert spaces.

Conclusions:

  • The study validates key Atoms-In-Molecules (AIM) partitioning schemes through Information Theory.
  • Provides a rigorous theoretical foundation for molecular partitioning in computational chemistry.
  • Highlights the utility of information-theoretical concepts in understanding molecular structure.