Exploring the Gradient Paths and Zero Flux Surfaces of Molecular Electrostatic Potential

Area of Science:

• Quantum Chemistry
• Theoretical Chemistry
• Computational Chemistry

Background:

• The gradient vector field of molecular electrostatic potential (∇V(r)) is an underutilized concept in molecular quantum mechanics.
• Existing atomic partitioning methods primarily rely on electron density, limiting certain topological insights.
• Understanding molecular structure and reactivity requires robust methods for defining atomic domains.

Purpose of the Study:

• To explore the conceptual and practical aspects of the ∇V(r) vector field in molecular quantum mechanics.
• To develop a novel three-dimensional atomic partitioning scheme based on zero flux surfaces (ZFSs) of ∇V(r).
• To investigate the phenomenon of closed ZFSs and their implications for atomic definition and molecular properties.

Main Methods:

• Calculation and analysis of the gradient vector field of molecular electrostatic potential (∇V(r)).
• Identification and characterization of zero flux surfaces (ZFSs) derived from ∇V(r).
• Application of the ZFS-based partitioning to various molecular systems (N2, CO, H2O, H2CO, OF(•), :CH2, NH3BF3).

Main Results:

• A novel three-dimensional atomic partitioning of molecular space based on ZFSs of ∇V(r) was successfully achieved.
• Demonstrated that ZFSs can completely enclose atoms, a phenomenon not observed in density-based partitioning, particularly for electronegative centers.
• Identified the explicit reasons and derived necessary and sufficient conditions for the existence of closed ZFSs.
• Illustrated anisotropy in MESP gradient paths for systems like CO, (•)OH, H2O, and H2CO.

Conclusions:

• The ∇V(r) vector field provides a unique and powerful framework for defining atoms in molecules, distinct from electron density-based approaches.
• The potential-based atomic picture offers new insights into molecular structure, electronegativity, and atomic interactions.
• The observed anisotropy in MESP gradient paths suggests potential for understanding molecular reactivity patterns.