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Exploring Intrinsic Bond Properties with the Fukui Matrix from Conceptual Density Matrix Functional Theory.

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We introduce conceptual density matrix functional theory (CDMFT) to study intrinsic bond reactivity. The Fukui matrix, a derivative of the density matrix, quantifies bond strength changes and predicts reaction outcomes.

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Area of Science:

  • Quantum Chemistry
  • Theoretical Chemistry
  • Computational Chemistry

Background:

  • Conceptual Density Functional Theory (CDFT) traditionally uses external potentials.
  • Investigating intrinsic bond properties like reactivity requires new theoretical frameworks.

Purpose of the Study:

  • Extend CDFT to Conceptual Density Matrix Functional Theory (CDMFT).
  • Develop a method to quantify intrinsic bond reactivity.
  • Introduce the Fukui matrix as a descriptor for bond order changes.

Main Methods:

  • Replaced the external potential v(r) with the one-electron integral h_rs in the energy functional.
  • Derived the Fukui matrix (derivative of density matrix P with respect to electron number N).
  • Utilized Mayer bond order and atoms-in-molecules partitioning for validation.

Main Results:

  • The Fukui matrix quantifies bond strength changes upon electron addition/removal via the bond order derivative.
  • The bond order derivative shows good agreement with finite difference calculations.
  • The bond order derivative successfully predicts regioselectivity in electrophilic addition and bond cleavage in mass spectrometry.

Conclusions:

  • CDMFT offers a novel approach to studying intrinsic bond properties.
  • The Fukui matrix and bond order derivative are effective descriptors of bond reactivity.
  • This method accurately predicts chemical reaction mechanisms and fragmentation patterns.