C library for topological study of the electronic charge density

Area of Science:

• Computational Chemistry
• Materials Science
• Quantum Chemistry

Background:

• Topological analysis of electronic charge density provides insights into chemical bonding and atomic charges.
• Accurate calculation of electron density and its derivatives up to second order is crucial for these studies.

Purpose of the Study:

• To describe a novel grid-based computational library for topological studies of electronic charge density.
• To enable efficient calculation of electron density derivatives and related properties in 3D space.

Main Methods:

• Implementation of a multidimensional Lagrange interpolation on a regular grid.
• Derivation of gradient, Hessian matrix, and Laplacian formulas from interpolated polynomials.
• Inclusion of Newton-Raphson and Cash-Karp Runge-Kutta methods for critical point and gradient path analysis.
• Development of linear transformations for distorted grids and functions to handle various file formats (grd, CUBE, CHGCAR).

Main Results:

• A versatile 3D grid-based library for calculating electronic density and its derivatives.
• Accurate computation of molecular and crystal electronic properties, including charge density and electrostatic potential.
• Capability to analyze distorted grids and diverse data file formats.

Conclusions:

• The developed library offers an efficient and adaptable tool for topological studies of electronic charge density.
• It facilitates the determination of bond types and atomic charges in molecules and crystals.
• The library can be extended for topological analysis on any regular 3D grid.