Visualization and integration of quantum topological atoms by spatial discretization into finite elements

Area of Science:

• Quantum chemistry
• Computational physics
• Materials science

Background:

• Accurate integration of electron density is crucial for understanding chemical bonding and atomic properties.
• Existing methods face challenges with complex atomic structures and tracing the electron density gradient field.

Purpose of the Study:

• To present a novel, streamlined algorithm for integrating property densities over the volume of a quantum topological atom.
• To address challenges in meshing algorithms and quadrature for accurate atomic property calculations.

Main Methods:

• A finite element meshing algorithm grows atoms outward from a nucleus-centered sphere.
• Specialized treatment for bond and ring critical points is incorporated.
• Detailed quadrature methods are applied over finite elements to integrate property densities.

Main Results:

• The algorithm successfully integrates property densities, achieving excellent integration errors (L(Omega)).
• It handles atoms with complex features like narrow tails and sharp corners effectively.
• The method generates novel visualizations, potentially forming a Graphical User Interface.

Conclusions:

• The developed algorithm provides a robust and accurate method for analyzing quantum topological atoms.
• It offers improved integration accuracy and visualization capabilities for computational chemistry.
• This approach facilitates a deeper understanding of electron density distribution and atomic properties.