The Connectivity Matrix: A Toolbox for Monitoring Bonded Atoms and Bonds.

Area of Science:

• * Computational Chemistry
• * Quantum Chemistry
• * Theoretical Chemistry

Background:

• * The reaction fragility (RF) spectra technique monitors electron density evolution during chemical reactions.
• * Understanding potential energy contributions and atomic roles is crucial for elucidating reaction mechanisms.

Purpose of the Study:

• * To introduce a novel formulation for the diagonal elements of the connectivity matrix.
• * To demonstrate the direct link between these matrix elements and the electron density function.
• * To achieve the separation of potential energy into atomic and/or bond contributions.

Main Methods:

• * Developed a novel formulation for the diagonal matrix elements of the connectivity matrix.
• * Combined the connectivity matrix concept with atomization energy.
• * Analyzed energy derivative diagrams for atoms and bonds along reaction paths.
• * Diagonalized the connectivity matrix to obtain eigenvectors.

Main Results:

• * Demonstrated a direct link between the connectivity matrix diagonal elements and the electron density function ρ(r).
• * Successfully separated potential energy into atomic and/or bond contributions.
• * Generated energy derivative diagrams offering new insights into reaction mechanisms.
• * Eigenvectors from matrix diagonalization revealed the role of individual atoms in structural changes.

Conclusions:

• * The enhanced connectivity matrix formulation provides a robust method for analyzing electron density evolution.
• * The approach offers valuable insights into reaction mechanisms by dissecting potential energy contributions.
• * Eigenvector analysis effectively highlights the influence of specific atoms on reaction pathways.