Bond orbitals from chemical valence theory

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Chemical Bonding Theory

Background:

• Chemical valence and bond multiplicity are fundamental concepts in chemistry.
• Existing methods for analyzing chemical bonds can be complex and lack a unified framework.
• Understanding electron distribution and orbital interactions is crucial for predicting molecular properties.

Purpose of the Study:

• To introduce and define two new sets of orbitals: Localized Orbitals from the Bond-Multiplicity Operator (LOBO) and Natural Orbitals for Chemical Valence (NOCV).
• To establish a common theoretical framework connecting these orbitals to the Nalewajski-Mrozek valence and bond-multiplicity indices.
• To demonstrate the utility of NOCV for analyzing bonding in transition metal complexes, particularly for distinguishing ligand-to-metal donation and metal-to-ligand back-donation.

Main Methods:

• Derivation of LOBO as eigenvectors of the bond-multiplicity operator.
• Definition of NOCV as eigenvectors of the overall chemical valence operator.
• Application of these orbital sets within the framework of chemical valence theory.

Main Results:

• LOBO are directly linked to bond indices through the expectation value of the bond-multiplicity operator.
• NOCV provide a means to analyze electron density deformation in transition metal complexes.
• The proposed framework unifies the discussion of localized orbitals and bond multiplicity.

Conclusions:

• The LOBO and NOCV orbital sets offer a powerful and unified approach to studying chemical bonding.
• NOCV are particularly valuable for detailed analysis of bonding interactions in transition metal systems.
• This work advances the theoretical understanding of chemical valence and electron distribution.