A practicable real-space measure and visualization of static electron-correlation effects.

Area of Science:

• Quantum Chemistry
• Computational Chemistry
• Electronic Structure Theory

Background:

• Accurate quantum chemistry (QC) calculations necessitate the inclusion of static and dynamic electron correlation (SEC).
• Quantifying SEC is challenging, making qualitative assessments crucial for evaluating approximate QC methods.
• Current SEC diagnostics lack spatial localization of correlation effects within molecules.

Purpose of the Study:

• To develop a novel analysis tool for visualizing and quantifying static and dynamic electron correlation (SEC) effects in molecules.
• To provide insights into the spatial distribution of SEC effects, which is missing in existing scalar diagnostics.
• To enable a better understanding of the applicability of approximate quantum chemistry methods.

Main Methods:

• Introduction of a fractional occupation number weighted electron density (ρ(FOD)) analysis tool.
• Utilizing finite-temperature density functional theory (DFT) calculations (e.g., TPSS at 5000 K) to generate the scalar field.
• 3D plotting of the ρ(FOD) for a pre-defined contour surface value to visualize contributions from strongly correlated electrons.

Main Results:

• The developed tool effectively visualizes the spatial localization of SEC effects in diverse chemical systems.
• Illustrative plots demonstrate the method's applicability to small molecules, large conjugated systems, and molecules with polyradicaloid character.
• Spatial integration of the ρ(FOD) provides a single numerical value for global SEC quantification.

Conclusions:

• The ρ(FOD) plotting method offers a powerful new approach for understanding and quantifying SEC in quantum chemistry.
• This tool enhances the qualitative assessment of approximate QC methods by revealing where and how SEC manifests.
• The ability to spatially localize SEC effects is critical for advancing the accuracy and reliability of computational chemistry predictions.